diff --git a/.gitignore b/.gitignore index 2ce6417..5b03dce 100644 --- a/.gitignore +++ b/.gitignore @@ -10,5 +10,9 @@ build .spyder* examples/.ipynb_checkpoints +validation/.ipynb_checkpoints examples/examples-notebook/.ipynb_checkpoints/ +.ipynb_checkpoints + + diff --git a/src/pyfme/aero/E205.txt b/src/pyfme/aero/E205.txt new file mode 100644 index 0000000..0651fbe --- /dev/null +++ b/src/pyfme/aero/E205.txt @@ -0,0 +1,54 @@ +1.00000 0.00000 +0.99974 0.00085 +0.99392 0.00159 +0.98578 0.00307 +0.97290 0.00499 +0.94617 0.00876 +0.91866 0.01274 +0.88020 0.01864 +0.83393 0.02611 +0.79263 0.03228 +0.73829 0.04008 +0.68535 0.04742 +0.63333 0.05440 +0.58021 0.06127 +0.53232 0.06738 +0.48264 0.07291 +0.44197 0.07676 +0.38814 0.08039 +0.32774 0.08186 +0.26612 0.08023 +0.21066 0.07548 +0.14521 0.06478 +0.09684 0.05300 +0.06230 0.04164 +0.04043 0.03241 +0.02021 0.02210 +0.01003 0.01499 +0.00152 0.00614 +0.00000 0.00000 +0.00089 -.00334 +0.00310 -.00596 +0.00816 -.00968 +0.01807 -.01343 +0.03718 -.01680 +0.07273 -.02114 +0.13766 -.02413 +0.20297 -.02449 +0.26877 -.02305 +0.34581 -.02057 +0.42989 -.01762 +0.49449 -.01526 +0.56883 -.01258 +0.63816 -.01012 +0.69937 -.00831 +0.75692 -.00681 +0.82133 -.00505 +0.87969 -.00361 +0.92076 -.00233 +0.96116 -.00099 +0.98546 -.00048 +0.98991 -.00068 +0.99485 -.00044 +0.99873 -.00063 +1.00000 0.00000 \ No newline at end of file diff --git a/src/pyfme/aero/__init__.py b/src/pyfme/aero/__init__.py new file mode 100644 index 0000000..b38c44f --- /dev/null +++ b/src/pyfme/aero/__init__.py @@ -0,0 +1 @@ +from .avl import avl_run \ No newline at end of file diff --git a/src/pyfme/aero/avl.py b/src/pyfme/aero/avl.py new file mode 100644 index 0000000..d02dbe4 --- /dev/null +++ b/src/pyfme/aero/avl.py @@ -0,0 +1,205 @@ +import numpy as np +nl = np.linalg +import os +import subprocess +import sys +import pandas as pd + +FORCES = ['CL', 'CD', 'CY', 'Cl', 'Cm', 'Cn'] +STAB = [F+d for F in ['CL', 'CY', 'Cl', 'Cm', 'Cn'] for d in ['a', 'b', 'p', 'q', 'r']] +CONT = [F+d for F in ['CL', 'CY', 'Cl', 'Cm', 'Cn'] for d in ['d1', 'd2', 'd3']] +# Note: missing drag + +class avl_run(): + def __init__(self, geom_file, num_control_surfaces, run_file="runs", path_to_avl='.'): + self.geom_file = geom_file + self.run_file = run_file + self.avl = path_to_avl + self.num_ctrl = num_control_surfaces + + def run(self, state, controls): + """ + State is a stack of [alpha, beta, phat, qhat, rhat] horizontal vectors + Controls is a [elevator, aileron, rudder] + """ + if controls.ndim > 1: + assert controls.shape[0] == state.shape[0] + + else: + state = np.expand_dims(state, 0) + controls = np.expand_dims(controls, 0) + N = controls.shape[0] + + # Modify run file + f = open(self.run_file, 'w') + for i in range(N): + print(state[i]) + alpha, beta, phat, qhat, rhat = state[i] + elevator, aileron, rudder = controls[i] + f.write(f""" + +--------------------------------------------- +Run case {i+1}: -unnamed- + +alpha -> alpha = {alpha} +beta -> beta = {beta} +pb/2V -> pb/2V = {phat} +qc/2V -> qc/2V = {qhat} +rb/2V -> rb/2V = {rhat} +elevator -> elevator = {elevator} +aileron -> aileron = {aileron} +rudder -> rudder = {rudder} + +alpha = {alpha} deg +beta = {beta} deg +pb/2V = {phat} +qc/2V = {qhat} +rb/2V = {rhat} +CL = 0.310719 +CDo = 0.00000 +bank = 0.00000 deg +elevation = 0.00000 deg +heading = 0.00000 deg +Mach = 0.00000 +velocity = 5.00000 Lunit/Tunit +density = 1.12500 Munit/Lunit^3 +grav.acc. = 9.81000 Lunit/Tunit^2 +turn_rad. = 0.00000 Lunit +load_fac. = 1.00000 +X_cg = 0.300000 Lunit +Y_cg = 0.00000 Lunit +Z_cg = 0.00000 Lunit +mass = 5.00000 Munit +Ixx = 1.00000 Munit-Lunit^2 +Iyy = 0.02000 Munit-Lunit^2 +Izz = 1.00000 Munit-Lunit^2 +Ixy = 0.00000 Munit-Lunit^2 +Iyz = 0.00000 Munit-Lunit^2 +Izx = 0.00000 Munit-Lunit^2 +visc CL_a = 0.00000 +visc CL_u = 0.00000 +visc CM_a = 0.00000 +visc CM_u = 0.00000 +""") + f.close() + + # Create bash script + f = open('cmd_file.run', 'w') + # f.write(f"LOAD {self.geom_file}\n") # load geom file + f.write(f'PLOP\ng\n\n') # disable graphics + f.write(f"CASE {self.run_file}\nOPER\n") + for i in range(N): + results_file = f"rslt_{i}.stab" + f.write(f"{i+1}\nx\nst\n{results_file}\n") + f.write("\n\nQUIT") + f.close() + + # Run bash + with open('cmd_file.run', 'r') as commands: + avl_run = subprocess.Popen([f"{self.avl}\\avl.exe", self.geom_file], + stderr=sys.stderr, + stdout=open(os.devnull, 'w'), + stdin=subprocess.PIPE) + for line in commands: + avl_run.stdin.write(line.encode('utf-8')) + avl_run.communicate() + avl_run.wait() + + # sort out results + data = pd.DataFrame({k: 0.0 for k in FORCES + STAB + CONT}, index=np.arange(N)) + data['de'] = controls[:, 0] + data['da'] = controls[:, 1] + data['dr'] = controls[:, 2] + data['alpha'] = state[:, 0] + data['beta'] = state[:, 1] + data['p'] = state[:, 2] + data['q'] = state[:, 3] + data['r'] = state[:, 4] + + for i in range(N): + with open(f"rslt_{i}.stab", 'r') as f: + lines = f.readlines() + data.Cl[i] = float(lines[19][33:41].strip()) + data.Cm[i] = float(lines[20][33:41].strip()) + data.Cn[i] = float(lines[21][33:41].strip()) + + data.CL[i] = float(lines[23][10:20].strip()) + data.CD[i] = float(lines[24][10:20].strip()) + data.CY[i] = float(lines[20][10:20].strip()) + + num_ctrl = self.num_ctrl # number of control surfaces + data.CLa[i] = float(lines[36 + num_ctrl][24:34].strip()) # CL_a + data.CYa[i] = float(lines[37 + num_ctrl][24:34].strip()) # CY_a + data.Cla[i] = float(lines[38 + num_ctrl][24:34].strip()) # Cl_a + data.Cma[i] = float(lines[39 + num_ctrl][24:34].strip()) # Cm_a + data.Cna[i] = float(lines[40 + num_ctrl][24:34].strip()) # Cn_a + data.CLb[i] = float(lines[36 + num_ctrl][43:54].strip()) # CL_b + data.CYb[i] = float(lines[37 + num_ctrl][43:54].strip()) # CY_b + data.Clb[i] = float(lines[38 + num_ctrl][43:54].strip()) # Cl_b + data.Cmb[i] = float(lines[39 + num_ctrl][43:54].strip()) # Cm_b + data.Cnb[i] = float(lines[40 + num_ctrl][43:54].strip()) # Cn_b + + data.CLp[i] = float(lines[44 + num_ctrl][24:34].strip()) + data.CLq[i] = float(lines[44 + num_ctrl][43:54].strip()) + data.CLr[i] = float(lines[44 + num_ctrl][65:74].strip()) + data.CYp[i] = float(lines[45 + num_ctrl][24:34].strip()) + data.CYq[i] = float(lines[45 + num_ctrl][43:54].strip()) + data.CYr[i] = float(lines[45 + num_ctrl][65:74].strip()) + data.Clp[i] = float(lines[46 + num_ctrl][24:34].strip()) + data.Clq[i] = float(lines[46 + num_ctrl][43:54].strip()) + data.Clr[i] = float(lines[44 + num_ctrl][65:74].strip()) + data.Cmp[i] = float(lines[47 + num_ctrl][24:34].strip()) + data.Cmq[i] = float(lines[47 + num_ctrl][43:54].strip()) + data.Cmr[i] = float(lines[44 + num_ctrl][65:74].strip()) + data.Cnp[i] = float(lines[48 + num_ctrl][24:34].strip()) + data.Cnq[i] = float(lines[48 + num_ctrl][43:54].strip()) + data.Cnr[i] = float(lines[48 + num_ctrl][65:74].strip()) + + INI = [24,43,65] + FIN = [34,54,74] + for n_ctrl in range(num_ctrl): + data['CLd'+str(n_ctrl + 1)][i] = float(lines[52 + num_ctrl] + [INI[n_ctrl]:FIN[n_ctrl]].strip()) # CL_a + data['CYd'+str(n_ctrl + 1)][i] = float(lines[53 + num_ctrl] + [INI[n_ctrl]:FIN[n_ctrl]].strip()) # CY_a + data['Cld'+str(n_ctrl + 1)][i] = float(lines[54 + num_ctrl] + [INI[n_ctrl]:FIN[n_ctrl]].strip()) # Cl_a + data['Cmd'+str(n_ctrl + 1)][i] = float(lines[55 + num_ctrl] + [INI[n_ctrl]:FIN[n_ctrl]].strip()) # Cm_a + data['Cnd'+str(n_ctrl + 1)][i] = float(lines[56 + num_ctrl] + [INI[n_ctrl]:FIN[n_ctrl]].strip()) # Cn_a + + os.remove(f"rslt_{i}.stab") + os.remove(self.run_file) + os.remove('cmd_file.run') + return(data) + +##### TODO : try to see if I can leave an AVL session open + +# def count_control_surfaces(geomfile): +# with open(geomfile,'r') as f: +# for line in f: +# + + +if __name__ == "__main__": + states = [] + controls = [] + for al in np.linspace(-10,20,30): + # for de in np.linspace(-26,28,10): + # controls.append(np.array([de,0,0])) + # states.append(np.array([al,0,0,0,0])) + # for da in np.linspace(-15, 10): + # controls.append(np.array([0,da,0])) + # states.append(np.array([al,0,0,0,0])) + # for dr in np.linspace(-5,5,10): + # controls.append(np.array([0,0,dr])) + states.append(np.array([al,0,0,0,0])) + controls.append(np.array([0,0,0])) + states = np.array(states) + controls = np.array(controls) + # states = np.array([np.arange(5)/100, np.arange(5)/600]) + # controls = np.array([np.arange(3)/3, np.arange(3)/4]) + a = avl_run(num_control_surfaces=3, geom_file='hypo', run_file='runs') + data = a.run(states, controls) + data.to_pickle('MeterSpanUAV.pkl') \ No newline at end of file diff --git a/src/pyfme/aero/hypo.avl b/src/pyfme/aero/hypo.avl new file mode 100644 index 0000000..4e4a9a9 --- /dev/null +++ b/src/pyfme/aero/hypo.avl @@ -0,0 +1,132 @@ +Hypothetical Airplane +#Mach + 0.0 +#IYsym IZsym Zsym + 0 0 0.0 +#Sref Cref Bref +0.135 0.15 0.9 +#Xref Yref Zref +0.35 0.0 0.0 +# +# +#==================================================================== +SURFACE +Wing +#Nchordwise Cspace Nspanwise Sspace +10 0.0 20 0.0 +# +YDUPLICATE +0.0 +# +ANGLE +0.0 +# +TRANSLATE +0.3 0.0 0.01 +# + +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.00 0. 0. 0.1875 2.0 0 0 + +AFILE +E205.txt + +CLAF +0.927097 + +CDCL +-.25 .02 .877 .0116 1.099 .028 + +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.01875 .45 0. 0.1125 0.0 0 0 + +AFILE +E205.txt + +CLAF +0.927097 + +CDCL +-.25 .02 .877 .0116 1.099 .028 +#==================================================================== +SURFACE +H-stab +#Nchordwise Cspace Nspanwise Sspace +5 0.0 10 0.0 +# +YDUPLICATE +0.0 +# +TRANSLATE +0.9 0.0 0.01 +# + +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.0 0.0 0.0 0.0913 0. 0 0 + +CLAF +0.938569 + +CDCL +-.56 .0202 .528 .0129 .792 .0575 + +#Cname Cgain Xhinge HingeVec SgnDup +CONTROL +elevator 1.0 0.001 0.0 1.0 0.0 1.0 +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.004564 0.2025 0.0 0.073 0. 0 0 + +CLAF +0.938569 + +CDCL +-.56 .0202 .528 .0129 .792 .0575 + +#Cname Cgain Xhinge HingeVec SgnDup +CONTROL +elevator 1.0 0.001 0.0 1.0 0.0 1.0 +# +#==================================================================== +SURFACE +V-stab +#Nchordwise Cspace Nspanwise Sspace +6 1.0 5 1.0 +TRANSLATE +0.7885 0.0 0.01 +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.0 0. 0.0 0.1141 0. 0 0 + +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.03227 0.0 .205 0.0912 0. 0 0 + +#------------------------------------------------------------- +#==================================================================== +SURFACE +Fuselage +#Nchordwise Cspace Nspanwise Sspace +2 1.0 2 1.0 +TRANSLATE +0. 0.0 0.0 +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.0 0. -0.01 1 0. 0 0 + +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.0 0.0 0.01 1 0 0 0 + +#------------------------------------------------------------- diff --git a/src/pyfme/aircrafts/E205.txt b/src/pyfme/aircrafts/E205.txt new file mode 100644 index 0000000..0651fbe --- /dev/null +++ b/src/pyfme/aircrafts/E205.txt @@ -0,0 +1,54 @@ +1.00000 0.00000 +0.99974 0.00085 +0.99392 0.00159 +0.98578 0.00307 +0.97290 0.00499 +0.94617 0.00876 +0.91866 0.01274 +0.88020 0.01864 +0.83393 0.02611 +0.79263 0.03228 +0.73829 0.04008 +0.68535 0.04742 +0.63333 0.05440 +0.58021 0.06127 +0.53232 0.06738 +0.48264 0.07291 +0.44197 0.07676 +0.38814 0.08039 +0.32774 0.08186 +0.26612 0.08023 +0.21066 0.07548 +0.14521 0.06478 +0.09684 0.05300 +0.06230 0.04164 +0.04043 0.03241 +0.02021 0.02210 +0.01003 0.01499 +0.00152 0.00614 +0.00000 0.00000 +0.00089 -.00334 +0.00310 -.00596 +0.00816 -.00968 +0.01807 -.01343 +0.03718 -.01680 +0.07273 -.02114 +0.13766 -.02413 +0.20297 -.02449 +0.26877 -.02305 +0.34581 -.02057 +0.42989 -.01762 +0.49449 -.01526 +0.56883 -.01258 +0.63816 -.01012 +0.69937 -.00831 +0.75692 -.00681 +0.82133 -.00505 +0.87969 -.00361 +0.92076 -.00233 +0.96116 -.00099 +0.98546 -.00048 +0.98991 -.00068 +0.99485 -.00044 +0.99873 -.00063 +1.00000 0.00000 \ No newline at end of file diff --git a/src/pyfme/aircrafts/MeterSpanUAV.pkl b/src/pyfme/aircrafts/MeterSpanUAV.pkl new file mode 100644 index 0000000..2e14a50 Binary files /dev/null and b/src/pyfme/aircrafts/MeterSpanUAV.pkl differ diff --git a/src/pyfme/aircrafts/__init__.py b/src/pyfme/aircrafts/__init__.py index b6b8531..53979fa 100644 --- a/src/pyfme/aircrafts/__init__.py +++ b/src/pyfme/aircrafts/__init__.py @@ -1,2 +1,5 @@ from .cessna_310 import Cessna310 -from .cessna_172 import Cessna172 +from .cessna_172 import Cessna172, SimplifiedCessna172 +from .boeing_linear import LinearB747 +from .uav import MeterSpanUAV + diff --git a/src/pyfme/aircrafts/aircraft.py b/src/pyfme/aircrafts/aircraft.py index 1f10875..c961c58 100644 --- a/src/pyfme/aircrafts/aircraft.py +++ b/src/pyfme/aircrafts/aircraft.py @@ -130,8 +130,63 @@ def _calculate_aerodynamics_2(self, TAS, alpha, beta, environment): self.Mach = self.TAS / environment.a self.q_inf = 0.5 * environment.rho * self.TAS ** 2 + @abstractmethod def calculate_forces_and_moments(self, state, environment, controls): self._set_current_controls(controls) self._calculate_aerodynamics(state, environment) + + + def calculate_derivatives(self, state, environment, controls, eps=1e-3): + """ + Calculate dimensional derivatives of the forces at the vicinity of the state. + The output consists in 2 dictionaries, one for force one for moment + key: type of variables derivatives are taken for + val : 3x3 np array with X,Y,Z and L,M,N as columns, and the variable we differentiate against in lines + (u,v,w ; phi,theta,psi ; p,q,r ; x,y,z) + """ + names = {'velocity': ['u', 'v', 'w'], + 'angular_vel': ['p', 'q', 'r'], + 'acceleration': ['w_dot']} + Fnames = ['X', 'Y', 'Z'] + Mnames = ['L', 'M', 'N'] + + # F, M = self.calculate_forces_and_moments(state, environment, controls) + + # Rotation for stability derivatives in stability axis + V = np.sqrt(state.velocity.u**2 + state.velocity.v**2 + state.velocity.w**2) + alpha = np.arctan2(state.velocity.w, state.velocity.u) + beta = np.arcsin(state.velocity.v / V) + + + derivatives = {} + for keyword in names.keys(): + for i in range(len(names[keyword])): + eps_v0 = np.zeros(3) + + # plus perturb + eps_v0[i] = eps/2 + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + forces_p, moments_p = self.calculate_forces_and_moments(state, environment, controls) + forces_p = body2wind(forces_p, alpha, beta) + moments_p = body2wind(moments_p, alpha, beta) + state.cancel_perturbation() + + # minus perturb + eps_v0[i] = - eps/2 + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + forces_m, moments_m = self.calculate_forces_and_moments(state, environment, controls) + forces_m = body2wind(forces_m, alpha, beta) + moments_m = body2wind(moments_m, alpha, beta) + state.cancel_perturbation() + + k = names[keyword][i] + for j in range(3): + # print(Fnames[j] + k, forces[j]) + derivatives[Fnames[j] + k] = (forces_p[j] - forces_m[j]) / eps + derivatives[Mnames[j] + k] = (moments_p[j] - moments_m[j]) / eps + + return derivatives diff --git a/src/pyfme/aircrafts/boeing_linear.py b/src/pyfme/aircrafts/boeing_linear.py new file mode 100644 index 0000000..402f54f --- /dev/null +++ b/src/pyfme/aircrafts/boeing_linear.py @@ -0,0 +1,87 @@ +# -*- coding: utf-8 -*- +""" +Python Flight Mechanics Engine (PyFME). +Copyright (c) AeroPython Development Team. +Distributed under the terms of the MIT License. +---------- +Cessna 172 +---------- + +References +---------- +[1] ETKIN, Dynamics of Flight, Stability and Control +---------- +""" + + +import numpy as np +import pdb + +from pyfme.aircrafts.aircraft import Aircraft +from pyfme.models.state import AircraftState, EarthPosition, EulerAttitude, BodyVelocity +from pyfme.environment.atmosphere import ISA1976 +from pyfme.environment.wind import NoWind +from pyfme.environment.gravity import VerticalConstant +from pyfme.environment.environment import Environment + +class LinearB747(Aircraft): + """ + Purely linear model of a Boeing 747 around a particular equilibrium condition + """ + + def __init__(self): + + # Mass & Inertia + self.mass = 2.83176e6/9.81 # kg + self.inertia = np.diag([.247e8, .449e8, .673e8]) # kg·m² + self.inertia[0, 2] = -.212e7 + self.inertia[2, 0] = -.212e7 + + # Geometry + self.Sw = 511 # m2 + self.chord = 8.324 # m + self.span = 59.64 # m + + # Aerodynamic Data# Values used for testing + self.stability_derivatives = { + 'Xu': -1.982e3, + 'Xw': 4.025e3, + 'Xq': 0, + 'Xw_dot': 0, + 'Zu': -2.595e4, + 'Zw': -9.030e4, + 'Zq': -4.524e5, + 'Zw_dot': 1.909e3, + 'Mu': 1.593e4, + 'Mw': -1.563e5, + 'Mq': -1.521e7, + 'Mw_dot': -1.702e4, + 'Yv': -1.610e4, + 'Yp': 0, + 'Yr': 0, + 'Lv': -3.062e5, + 'Lp': -1.076e7, + 'Lr': 9.925e6, + 'Nv': 2.131e5, + 'Np': -1.330e6, + 'Nr': -8.934e6 + } + + def calculate_derivatives(self, state, environment, controls=None, eps=0): + return self.stability_derivatives + + def trimmed_conditions(self): + # state + att = EulerAttitude(0, 0, 0) # from Etkin + vel = BodyVelocity(235.9, 0, 0, att) # from Etkin + pos = EarthPosition(0, 0, -1000) # arbitrary + state = AircraftState(pos, att, vel) + + # environment + atmosphere = ISA1976() + gravity = VerticalConstant() + wind = NoWind() + environment = Environment(atmosphere, gravity, wind) + environment._rho = 0.3045 + + return state, environment \ No newline at end of file diff --git a/src/pyfme/aircrafts/cessna_172.py b/src/pyfme/aircrafts/cessna_172.py index 8414c41..b03d29f 100644 --- a/src/pyfme/aircrafts/cessna_172.py +++ b/src/pyfme/aircrafts/cessna_172.py @@ -74,11 +74,14 @@ deflection and the angle of attack via [2] """ import numpy as np +import pdb from scipy.interpolate import RectBivariateSpline +from scipy.stats import linregress from pyfme.aircrafts.aircraft import Aircraft from pyfme.models.constants import slugft2_2_kgm2, lbs2kg -from pyfme.utils.coordinates import wind2body +from pyfme.utils.coordinates import wind2body, body2wind +from copy import deepcopy as cp class Cessna172(Aircraft): @@ -92,6 +95,13 @@ def __init__(self): # Mass & Inertia self.mass = 2300 * lbs2kg # kg self.inertia = np.diag([948, 1346, 1967]) * slugft2_2_kgm2 # kg·m² + self.inertia[0, 2] = - 10000*slugft2_2_kgm2 + self.inertia[2, 0] = - 10000*slugft2_2_kgm2 + self.inertia[1, 0] = - 20000*slugft2_2_kgm2 + self.inertia[0, 1] = - 20000*slugft2_2_kgm2 + self.inertia[1, 2] = - 10000*slugft2_2_kgm2 + self.inertia[2, 1] = - 10000*slugft2_2_kgm2 + self.inertia_inverse = np.linalg.inv(self.inertia) # Geometry self.Sw = 16.2 # m2 @@ -142,7 +152,7 @@ def __init__(self): self.CN_r_data = np.array([-0.028, -0.027, -0.027, -0.0275, -0.0293, -0.0325, -0.037, -0.043, -0.05484, -0.058, -0.0592, -0.06015]) self.CN_delta_rud_data = (-1)*np.array([-0.211, -0.215, -0.218, -0.22, -0.224, -0.226, -0.228, -0.229, -0.23, -0.23, -0.23, -0.23]) self.CN_delta_aile_data = np.array([[-0.004321, -0.002238, -0.0002783, 0.001645, 0.003699, 0.005861, 0.008099, 0.01038, 0.01397, 0.01483, 0.01512, 0.01539], - [-0.003318, -0.001718, -0.0002137, 0.001263, 0.00284, 0.0045, 0.006218, 0.00797, 0.01072, 0.01138, 0.01161, 0.01181], + [-0.003318, -0.001718, -0.0002137, 0.001263, 0.00284, 0.0045, 0.006218, 0.00797, 0.01072, 0.01138, 0.01161, 0.01181], [-0.002016, -0.001044, -0.000123, 0.0007675, 0.00173, 0.002735, 0.0038, 0.004844, 0.00652, 0.00692, 0.00706, 0.0072], [-0.00101, -0.000522, -0.0000649, 0.000384, 0.000863, 0.00137, 0.0019, 0.00242, 0.00326, 0.00346, 0.00353, 0.0036], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], @@ -353,4 +363,198 @@ def calculate_forces_and_moments(self, state, environment, controls): self.total_forces = Ft + Fg + Fa self.total_moments = np.array([l, m, n]) + self.Fa_wind = Fa_wind + + # return state.velocity._vel_body, state.angular_vel._vel_ang_body return self.total_forces, self.total_moments + + + def calculate_derivatives(self, state, environment, controls, eps=1e-3): + """ + Calculate dimensional derivatives of the forces at the vicinity of the state. + The output consists in 2 dictionaries, one for force one for moment + key: type of variables derivatives are taken for + val : 3x3 np array with X,Y,Z and L,M,N as columns, and the variable we differentiate against in lines + (u,v,w ; phi,theta,psi ; p,q,r ; x,y,z) + """ + names = {'velocity': ['u', 'v', 'w'], + 'angular_vel': ['p', 'q', 'r'], + 'acceleration': ['w_dot']} + Fnames = ['X', 'Y', 'Z'] + Mnames = ['L', 'M', 'N'] + + # F, M = self.calculate_forces_and_moments(state, environment, controls) + + # Rotation for stability derivatives in stability axis + V = np.sqrt(state.velocity.u**2 + state.velocity.v**2 + state.velocity.w**2) + alpha = np.arctan2(state.velocity.w, state.velocity.u) + beta = np.arcsin(state.velocity.v / V) + + + derivatives = {} + for keyword in names.keys(): + for i in range(len(names[keyword])): + eps_v0 = np.zeros(3) + + # plus perturb + eps_v0[i] = eps/2 + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + forces_p, moments_p = self.calculate_forces_and_moments(state, environment, controls) + forces_p = body2wind(forces_p, alpha, beta) + moments_p = body2wind(moments_p, alpha, beta) + state.cancel_perturbation() + + # minus perturb + eps_v0[i] = - eps/2 + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + forces_m, moments_m = self.calculate_forces_and_moments(state, environment, controls) + forces_m = body2wind(forces_m, alpha, beta) + moments_m = body2wind(moments_m, alpha, beta) + state.cancel_perturbation() + + k = names[keyword][i] + for j in range(3): + # print(Fnames[j] + k, forces[j]) + derivatives[Fnames[j] + k] = (forces_p[j] - forces_m[j]) / eps + derivatives[Mnames[j] + k] = (moments_p[j] - moments_m[j]) / eps + + return derivatives + + +class SimplifiedCessna172(Cessna172): + def __init__(self): + super().__init__() + self.CL_0 = 0.148 + self.CM_0 = 0.0075 + self.CL_alpha = 5.440E+00 + self.CL_q = np.mean(self.CL_q_data) + self.CL_delta_elev = np.sum(self.delta_elev_data*self.CL_delta_elev_data)/np.sum(self.delta_elev_data**2) + + self.CM_alpha2, self.CM_alpha, self.CM_0 = np.polyfit(self.alpha_data, self.CM_data, 2) + self.CM_q = 2*np.mean(self.CM_q_data) + self.CM_delta_elev = np.sum(self.delta_elev_data*self.CM_delta_elev_data)/np.sum(self.delta_elev_data**2) + + + # pre-stall drag model + ICL_max = self.CL_data.argmax() + cl = self.CL_data[:ICL_max-2] + cd = self.CD_data[:ICL_max-2] + al = self.alpha_data[: ICL_max] + self.CD_K1, self.CD_0, r_value, p_value, std_err = linregress(cl ** 2, cd) + self.CL_MAX = self.CL_data[ICL_max] + + self.CY_beta = np.mean(self.CY_beta_data) + self.CY_p = np.mean(self.CY_p_data) + self.CY_r = np.mean(self.CY_r_data) + self.CY_delta_rud = np.mean(self.CY_delta_rud_data) + + # XXX: Tunned Cl_delta_rud + self.Cl_beta = 0.1*np.mean(self.Cl_beta_data) + self.Cl_p = np.mean(self.Cl_p_data) + self.Cl_r_cl = np.sum(self.CL_data*self.Cl_r_data)/np.sum(self.CL_data**2) + self.Cl_delta_rud = .075*np.mean(self.Cl_delta_rud_data) + self.Cl_delta_aile = np.sum(self.delta_aile_data*self.Cl_delta_aile_data)/np.sum(self.delta_aile_data**2) + + # XXX: Tunned CN_delta_rud + self.CN_beta = np.mean(self.CN_beta_data) + self.CN_p_al = np.sum(self.alpha_data*self.CN_p_data)/np.sum(self.alpha_data**2) + self.CN_r_cl, self.CN_r_0, _, _,_ = linregress(self.CL_data**2,self.CN_r_data) + self.CN_delta_rud = 0.075*np.mean(self.CN_delta_rud_data) + x = np.reshape(self.CL_data, (1, 12)) * np.reshape(self.delta_aile_data, (9, 1)) + self.CN_delta_aile_cl = np.sum(self.CN_delta_aile_data*x) / np.sum(x**2) + + # simplistic thrust model + self.RPM_delta_t = 1800 + self.RPM_idle = 1000 + self.Ct_J2, self.Ct_J, self.Ct_0 = np.polyfit(self.J_data, self.Ct_data, 2) + + def _calculate_aero_lon_forces_moments_coeffs(self, state): + """ + Simplified dynamics for the Cessna 172: strictly linear dynamics. + Stability derivatives are considered constant, the value for small angles is kept. + + Parameters + ---------- + state + + Returns + ------- + + """ + + delta_elev = np.rad2deg(self.controls['delta_elevator']) # deg + alpha_DEG = np.rad2deg(self.alpha) # deg + alpha_RAD = self.alpha # rad + c = self.chord # m + V = self.TAS # m/s + p, q, r = (state.angular_vel.p, state.angular_vel.q, + state.angular_vel.r) # rad/s + + self.CL = ( + self.CL_0 + + self.CL_alpha*alpha_RAD + + self.CL_delta_elev*delta_elev + + self.CL_q * q * c/(2*V) + ) + # STALL + self.CL = self.CL if abs(self.CL) < self.CL_MAX else np.sign(self.CL)*self.CL_MAX + + self.CD = self.CD_0 + self.CD_K1*self.CL**2 + + self.CM = ( + self.CM_0 + + (self.CM_alpha2*alpha_DEG + self.CM_alpha)*alpha_DEG + + self.CM_delta_elev * delta_elev + + self.CM_q * q * c/(2*V) + ) + + def _calculate_aero_lat_forces_moments_coeffs(self, state): + delta_aile = np.rad2deg(self.controls['delta_aileron']) # deg + delta_rud_RAD = self.controls['delta_rudder'] # rad + alpha_DEG = np.rad2deg(self.alpha) # deg + b = self.span + V = self.TAS + p, q, r = state.angular_vel.p, state.angular_vel.q, state.angular_vel.r + + self.CY = ( + self.CY_beta * self.beta + + self.CY_delta_rud * delta_rud_RAD + + b/(2 * V) * (self.CY_p * p + self.CY_r * r) + ) + + self.Cl = ( + self.Cl_beta * self.beta + + self.Cl_delta_aile * delta_aile + + self.Cl_delta_rud * delta_rud_RAD + + b/(2 * V) * (self.Cl_p * p + self.Cl_r_cl * self.CL * r) + ) + + self.CN = ( + self.CN_beta * self.beta + + (self.CN_delta_aile_cl*self.CL*delta_aile) + + self.CN_delta_rud * delta_rud_RAD + + b/(2 * V) * (self.CN_p_al*alpha_DEG * p + (self.CN_r_cl*self.CL**2 + self.CN_r_0) * r) + ) + + def _calculate_thrust_forces_moments(self, environment): + delta_t = self.controls['delta_t'] + rho = environment.rho + V = self.TAS + prop_rad = self.propeller_radius + + # throttle controls the revolutions of the propeller linearly. + RPM = self.RPM_delta_t*delta_t + self.RPM_idle # rpm + omega_RAD = (RPM * 2 * np.pi) / 60.0 # rad/s + + # We calculate the relation between the thrust coefficient Ct and the + # advance ratio J using the program JavaProp + J = (np.pi * V) / (omega_RAD * prop_rad) # non-dimensional + Ct = self.Ct_J2*J + self.Ct_J*J + self.Ct_0 # non-dimensional + + T = (2/np.pi)**2 * rho * (omega_RAD * prop_rad)**2 * Ct # N + + # We will consider that the engine is aligned along the OX (body) axis + Ft = np.array([T, 0, 0]) + return Ft \ No newline at end of file diff --git a/src/pyfme/aircrafts/uav.py b/src/pyfme/aircrafts/uav.py new file mode 100644 index 0000000..7bdc087 --- /dev/null +++ b/src/pyfme/aircrafts/uav.py @@ -0,0 +1,201 @@ +# -*- coding: utf-8 -*- +""" +Python Flight Mechanics Engine (PyFME). +Copyright (c) AeroPython Development Team. +Distributed under the terms of the MIT License. +---------- +Hypothetical Fixed Wing UAV - AVL is ran to get forces and moments +---------- +""" + +import numpy as np +nl = np.linalg +import pdb +from scipy.interpolate import RectBivariateSpline +from scipy.stats import linregress + +from pyfme.aircrafts.aircraft import Aircraft +from pyfme.models.constants import slugft2_2_kgm2, lbs2kg +from pyfme.utils.coordinates import wind2body, body2wind +from copy import deepcopy as cp +from pyfme.aero.avl import avl_run +import pandas as pd +import matplotlib.pyplot as plt + + +class MeterSpanUAV(Aircraft): + """ + """ + + def __init__(self, avl_file): + + # AVL stuff + # self.avl = avl_run(avl_geometry_file, ) + self.data = pd.read_pickle(avl_file) + self._build_aero_model() + + # Mass & inertia + self.mass = .50 + self.inertia = np.diag((.01, 0.02, 0.01)) + self.cg = [.3, 0, 0] + + # Reference values + self.Sw = .9**2/6 # m2 + self.span = .9 # m + self.chord = self.Sw/ self.span # m + self.propeller_radius = 0 # m + + # CONTROLS + self.controls = {'delta_elevator': 0, + 'delta_aileron': 0, + 'delta_rudder': 0, + 'delta_t': 0} + + self.control_limits = {'delta_elevator': (np.deg2rad(-26), + np.deg2rad(28)), # rad + 'delta_aileron': (np.deg2rad(-15), + np.deg2rad(20)), # rad + 'delta_rudder': (np.deg2rad(-16), + np.deg2rad(16)), # rad + 'delta_t': (0, 1)} # non-dimensional + + # Aerodynamic Coefficients + self.CL, self.CD, self.Cm = 0, 0, 0 + self.CY, self.Cl, self.Cn = 0, 0, 0 + + # Thrust Coefficient + self.Ct = 0 + + self.total_forces = np.zeros(3) + self.total_moments = np.zeros(3) + + # Velocities + self.TAS = 0 # True Air Speed. + self.CAS = 0 # Calibrated Air Speed. + self.EAS = 0 # Equivalent Air Speed. + self.Mach = 0 # Mach number + self.q_inf = 0 # Dynamic pressure at infinity (Pa) + + # Angles + self.alpha = 0 # rad + self.beta = 0 # rad + self.alpha_dot = 0 # rad/s + + def _build_aero_model(self): + self.CL_0 = 0.148 + self.CM_0 = 0.0075 + self.CL_alpha = 5.440E+00 + self.CL_q = np.mean(self.data.CLq) + self.CL_delta_elev = np.sum(self.data.de*self.data.CLd1)/np.sum(self.data.de**2) + + self.CM_alpha2, self.CM_alpha, self.CM_0 = np.polyfit(self.data.alpha, self.data.Cm, 2) + self.CM_q = 2*np.mean(self.data.Cmq) + self.CM_delta_elev = np.sum(self.data.de*self.data.Cmd1)/np.sum(self.data.de**2) + + # pre-stall drag model + ICL_max = self.data.CL.idxmax() + cl = self.data.CL[:ICL_max-2] + cd = self.data.CD[:ICL_max-2] + al = self.data.alpha[: ICL_max] + self.CD_K1, self.CD_0, r_value, p_value, std_err = linregress(cl ** 2, cd) + self.CL_MAX = self.data.CL[ICL_max] + + self.CY_beta = np.mean(self.data.CYb) + self.CY_p = np.mean(self.data.CYp) + self.CY_r = np.mean(self.data.CYr) + self.CY_delta_rud = np.mean(self.data.dr) + + self.Cl_beta = np.mean(self.data.Clb) + self.Cl_p = np.mean(self.data.Clp) + self.Cl_r_cl = np.sum(self.data.CL*self.data.Clr)/np.sum(self.data.CL**2) + self.Cl_delta_rud = np.mean(self.data.Cld2) + self.Cl_delta_aile = np.sum(self.data.da*self.data.Cld2)/np.sum(self.data.da**2) + + self.CN_beta = np.mean(self.data.Cnb) + self.CN_p_al = np.sum(self.data.alpha*self.data.Cnp)/np.sum(self.data.alpha**2) + self.CN_r_cl, self.CN_r_0, _, _,_ = linregress(self.data.CL**2,self.data.Cnr) + self.CN_delta_rud = np.mean(self.data.Cnd3) + # x = np.reshape(self.data.CL, (1, 12)) * np.reshape(self.data.da, (9, 1)) + # self.CN_delta_aile_cl = np.sum(self.data.Cnd2*x) / np.sum(x**2) + + @property + def delta_elevator(self): + return self.controls['delta_elevator'] + + @property + def delta_rudder(self): + return self.controls['delta_rudder'] + + @property + def delta_aileron(self): + return self.controls['delta_aileron'] + + @property + def delta_t(self): + return self.controls['delta_t'] + + def calculate_aero_coeffs(self, state, controls): + # Compute features + V = nl.norm(state.velocity.vel_body) + p = state.angular_vel.p * self.span / (2*V) + q = state.angular_vel.q * self.chord / (2*V) + r = state.angular_vel.r * self.span / (2*V) + alpha = np.arctan2(state.velocity.w, state.velocity.u) + beta = np.arcsin(state.velocity.v, V) + + # Run AVL + avl_state = np.array([alpha, beta, p, q, r]) + avl_controls = np.array([self.delta_elevator, self.delta_aileron, self.delta_rudder]) + data = self.avl.run(avl_state, avl_controls) + + # set values for non-dimensional coefficients. + for attr in data.columns: + setattr(self, attr, data[attr][0]) + + def _calculate_aero_forces_moments(self, state): + q = self.q_inf + Sw = self.Sw + c = self.chord + b = self.span + + self.calculate_aero_coeffs(state) + + L = q * Sw * self.CL + D = q * Sw * self.CD + Y = q * Sw * self.CY + l = q * Sw * b * self.Cl + m = q * Sw * c * self.Cm + n = q * Sw * b * self.Cn + + return L, D, Y, l, m, n + + def _calculate_thrust_forces_moments(self, environment): + return np.array([1, 0, 0]), np.array([0, 0, 0]) + + def calculate_forces_and_moments(self, state, environment, controls): + # Update controls and aerodynamics + super().calculate_forces_and_moments(state, environment, controls) + + Ft, Mt = self._calculate_thrust_forces_moments(environment) + L, D, Y, l, m, n = self._calculate_aero_forces_moments(state) + Fg = environment.gravity_vector * self.mass + + Fa_wind = np.array([-D, Y, -L]) + Fa_body = wind2body(Fa_wind, self.alpha, self.beta) + Fa = Fa_body + + self.total_forces = Ft + Fg + Fa + self.total_moments = np.array([l, m, n]) + + self.Fa_wind = Fa_wind + + # return state.velocity._vel_body, state.angular_vel._vel_ang_body + return self.total_forces, self.total_moments + + + +if __name__=='__main__': + a = MeterSpanUAV('MeterSpanUAV.pkl') + plt.plot(a.data.CL, a.data.alpha) + plt.show() + diff --git a/src/pyfme/environment/atmosphere.py b/src/pyfme/environment/atmosphere.py index c09c6fb..1596ef4 100644 --- a/src/pyfme/environment/atmosphere.py +++ b/src/pyfme/environment/atmosphere.py @@ -258,3 +258,9 @@ def __call__(self, h): a = sqrt(gamma * R_a * T) return T, p, rho, a + + +class SeaLevel(ISA1976): + def __call__(self, h): + return super().__call__(h=0.01) + diff --git a/src/pyfme/models/euler_flat_earth.py b/src/pyfme/models/euler_flat_earth.py index f0d1623..bcce3c4 100644 --- a/src/pyfme/models/euler_flat_earth.py +++ b/src/pyfme/models/euler_flat_earth.py @@ -15,13 +15,18 @@ import numpy as np from numpy import sin, cos - +from copy import deepcopy as dcp +import pdb from pyfme.models.dynamic_system import AircraftDynamicSystem from pyfme.models.state import ( AircraftState, EarthPosition, EulerAttitude, BodyVelocity, BodyAngularVelocity, BodyAcceleration, BodyAngularAcceleration ) +from pyfme.utils.coordinates import body2wind, wind2body +import math +from numba import jit +_FLOAT_EPS_4 = np.finfo(float).eps * 4.0 class EulerFlatEarth(AircraftDynamicSystem): """Euler Flat Earth Dynamic System. @@ -31,37 +36,47 @@ class EulerFlatEarth(AircraftDynamicSystem): performed on Earth axis. """ - def fun(self, t, x): + def fun(self, t, x=None): + + if x is not None: + # update full state if necessary + self._update_full_system_state_from_state(x, self.state_vector_dot) - self._update_full_system_state_from_state(x, self.state_vector_dot) updated_simulation = self.update_simulation(t, self.full_state) mass = updated_simulation.aircraft.mass inertia = updated_simulation.aircraft.inertia + inertia_inverse = updated_simulation.aircraft.inertia_inverse forces = updated_simulation.aircraft.total_forces moments = updated_simulation.aircraft.total_moments - rv = _system_equations(t, x, mass, inertia, forces, moments) + rv = _system_equations(t, x, mass, inertia, inertia_inverse, forces, moments) return rv - def steady_state_trim_fun(self, full_state, environment, aircraft, + def right_hand_side(self, full_state, environment, aircraft, controls): - - environment.update(full_state) + try: + environment.update(full_state) + except: + pdb.set_trace() aircraft.calculate_forces_and_moments(full_state, environment, controls) mass = aircraft.mass inertia = aircraft.inertia + inertia_inverse = aircraft.inertia_inverse forces = aircraft.total_forces moments = aircraft.total_moments t0 = 0 x0 = self._get_state_vector_from_full_state(full_state) - rv = _system_equations(t0, x0, mass, inertia, forces, moments) - return rv[:6] + return _system_equations(t0, x0, mass, inertia, inertia_inverse, forces, moments) + + def steady_state_trim_fun(self, full_state, environment, aircraft, + controls): + return self.right_hand_side(full_state, environment, aircraft, controls)[:6] def _update_full_system_state_from_state(self, state, state_dot): @@ -82,8 +97,8 @@ def _adapt_full_state_to_dynamic_system(self, full_state): full_state.position.lat, full_state.position.lon) - att = EulerAttitude(full_state.attitude.theta, - full_state.attitude.phi, + att = EulerAttitude(full_state.attitude.phi, + full_state.attitude.theta, full_state.attitude.psi) vel = BodyVelocity(full_state.velocity.u, @@ -129,9 +144,241 @@ def _get_state_vector_from_full_state(self, full_state): ) return x0 + def linearized_model(self, state, aircraft, environment, controls=None, method="direct", eps=1e-3): + """ + Outputs matrices A_long and A_lat that are the lateral and longitudinal state matrices for the linearized system. + As done in Etkin [2], these matrices are useful in stability axis. + method can be: + - "direct", in which case we compute the derivative of the accelerations : X_dot = f(X,U), so + Aij = dfi/dxj(X,U) + - "from forces", in which case we compute the dimensional force derivatives and use formulas in Etkin + (/!\ contains assumptions on the point at which we linearize + """ + + if method=="from_forces": + # get derivatives + d = aircraft.calculate_derivatives(state, environment, controls,eps) + + # recover state variables + u, v, w = state.velocity.vel_body + alpha = np.arctan2(w,u) + beta = np.arcsin(v/np.sqrt(u**2 + v**2 + w**2)) + theta = np.copy(state.attitude.theta) - alpha + u, v, w = body2wind(state.velocity.vel_body, alpha, beta) + g = environment.gravity_magnitude + + # get inertias (move them to stability axis) + m = aircraft.mass + Lwb = np.array([[cos(alpha) * cos(beta),sin(beta),sin(alpha) * cos(beta)], + [- cos(alpha) * sin(beta),cos(beta),-sin(alpha) * sin(beta)], + [-sin(alpha), 0, cos(alpha)]]) + I = (Lwb.dot(aircraft.inertia)).dot(Lwb.T) + Ix = I[0,0] + Iy = I[1, 1] + Iz = I[2, 2] + Ixz = - I[0, 2] + assert abs(I[1,0]) < 1e-10 and abs(I[2,0]) < 1e-10, "This method is only valid for symmetrical aircrafts" + + Ixprime = (Ix*Iz - Ixz**2)/Iz + Izprime = (Ix*Iz - Ixz**2)/Ix + Ixzprime = Ixz/(Ix*Iz - Ixz**2) + + # Longitudinal matrix + # Todo : add alpha_dot derivatives + A1 = np.array([d['Xu'] / m, d['Xw'] / m, 0, -g*np.cos(theta)]) + A2 = np.array([d['Zu'], d['Zw'], d['Zq'] + m*u, -m*g*np.sin(theta)])/(m - d['Zw_dot']) + A3 = (np.array([d['Mu'], d['Mw'], d['Mq'], 0]) + A2*d['Mw_dot']) / Iy + A4 = np.array([0, 0, 1, 0]) + A_long = np.vstack((A1, A2, A3, A4)) + + # Lateral dynamics + A1 = np.array([d['Yv']/m, d['Yp']/m, d['Yr']/m - u, g*np.cos(theta)]) + A2 = np.array([d['Lv']/Ixprime + d['Nv']*Ixzprime, d['Lp']/Ixprime + d['Np']*Ixzprime, + d['Lr']/Ixprime + d['Nr']*Ixzprime, 0]) + A3 = np.array([d['Lv']*Ixzprime + d['Nv']/Izprime, d['Lp']*Ixzprime + d['Np']/Izprime, + d['Lr'] * Ixzprime + d['Nr'] / Izprime, 0]) + A4 = np.array([0, 1, np.tan(theta), 0]) + A_lat = np.vstack((A1, A2, A3, A4)) + + elif method=="direct": + # Rotation for stability derivatives in stability axis + V = np.sqrt(state.velocity.u ** 2 + state.velocity.v ** 2 + state.velocity.w ** 2) + alpha = np.arctan2(state.velocity.w, state.velocity.u) + beta = np.arcsin(state.velocity.v / V) + + derivatives = {} + for keyword in ['velocity', 'angular_vel', 'attitude']: + derivatives[keyword] = {} + for i in range(3): + derivatives[keyword][i] = {} + eps_v0 = np.zeros(3) + + # plus perturb + eps_v0[i] = eps / 2 + if keyword == 'attitude': + eps_vec = eps_v0 + else: + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + state_dot = self.right_hand_side(state, environment, aircraft, controls) + accel_p = body2wind(state_dot[0:3], alpha, beta) + ang_accel_p = body2wind(state_dot[3:6], alpha, beta) + angle_der_p = state_dot[6:9] + state.cancel_perturbation() + + # minus perturb + eps_v0[i] = - eps / 2 + if keyword == 'attitude': + eps_vec = eps_v0 + else: + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + state_dot = self.right_hand_side(state, environment, aircraft, controls) + accel_m = body2wind(state_dot[0:3], alpha, beta) + ang_accel_m = body2wind(state_dot[3:6], alpha, beta) + angle_der_m = state_dot[6:9] + state.cancel_perturbation() + + derivatives[keyword][i]["acceleration"] = (accel_p - accel_m)/eps + derivatives[keyword][i]["angular_accel"] = (ang_accel_p - ang_accel_m)/eps + derivatives[keyword][i]["angle_der"] = (angle_der_p - angle_der_m)/eps + + # Longitudinal + # line1 : d(delta_u_dot)/dall + A1 = np.array([derivatives['velocity'][0]["acceleration"][0], derivatives['velocity'][2]["acceleration"][0], + derivatives['angular_vel'][1]["acceleration"][0], derivatives['attitude'][0]["acceleration"][0] + ]) + # line2 : d(w_dot)/dall + A2 = np.array([derivatives['velocity'][0]["acceleration"][2], derivatives['velocity'][2]["acceleration"][2], + derivatives['angular_vel'][1]["acceleration"][2], derivatives['attitude'][0]["acceleration"][2] + ]) + # line3 : d(q_dot)/dall + A3 = np.array([derivatives['velocity'][0]["angular_accel"][1], derivatives['velocity'][2]["angular_accel"][1], + derivatives['angular_vel'][1]["angular_accel"][1], derivatives['attitude'][0]["angular_accel"][1] + ]) + # line4 : d(theta_dot)/dall + A4 = np.array([derivatives['velocity'][0]["angle_der"][0], derivatives['velocity'][2]["angle_der"][0], + derivatives['angular_vel'][1]["angle_der"][0], derivatives['attitude'][0]["angle_der"][0] + ]) + A_long = np.vstack((A1, A2, A3, A4)) + + # Lateral + # line1 d(v_dot)/dall + A1 = np.array([derivatives['velocity'][1]["acceleration"][1], derivatives['angular_vel'][0]["acceleration"][1], + derivatives['angular_vel'][2]["acceleration"][1], derivatives['attitude'][1]["acceleration"][1] + ]) + # line2 d(p_dot)/dall + A2 = np.array([derivatives['velocity'][1]["angular_accel"][0], derivatives['angular_vel'][0]["angular_accel"][0], + derivatives['angular_vel'][2]["angular_accel"][0], derivatives['attitude'][1]["angular_accel"][0] + ]) + # line3 d(r_dot)/dall + A3 = np.array( + [derivatives['velocity'][1]["angular_accel"][2], derivatives['angular_vel'][0]["angular_accel"][2], + derivatives['angular_vel'][2]["angular_accel"][2], derivatives['attitude'][1]["angular_accel"][2] + ]) + # line4 d(phi_dot)/dall + A4 = np.array( + [derivatives['velocity'][1]["angle_der"][1], derivatives['angular_vel'][0]["angle_der"][1], + derivatives['angular_vel'][2]["angle_der"][1], derivatives['attitude'][1]["angle_der"][1] + ]) + A_lat = np.vstack((A1, A2, A3, A4)) + + else: + raise NotImplementedError + + return A_long, A_lat + +def mat2euler(M, cy_thresh=None): + ''' Discover Euler angle vector from 3x3 matrix + + Uses the conventions above. + + Parameters + ---------- + M : array-like, shape (3,3) + cy_thresh : None or scalar, optional + threshold below which to give up on straightforward arctan for + estimating x rotation. If None (default), estimate from + precision of input. + + Returns + ------- + z : scalar + y : scalar + x : scalar + Rotations in radians around z, y, x axes, respectively + + Notes + ----- + If there was no numerical error, the routine could be derived using + Sympy expression for z then y then x rotation matrix, which is:: + + [ cos(y)*cos(z), -cos(y)*sin(z), sin(y)], + [cos(x)*sin(z) + cos(z)*sin(x)*sin(y), cos(x)*cos(z) - sin(x)*sin(y)*sin(z), -cos(y)*sin(x)], + [sin(x)*sin(z) - cos(x)*cos(z)*sin(y), cos(z)*sin(x) + cos(x)*sin(y)*sin(z), cos(x)*cos(y)] + + with the obvious derivations for z, y, and x + + z = atan2(-r12, r11) + y = asin(r13) + x = atan2(-r23, r33) + + Problems arise when cos(y) is close to zero, because both of:: + + z = atan2(cos(y)*sin(z), cos(y)*cos(z)) + x = atan2(cos(y)*sin(x), cos(x)*cos(y)) + + will be close to atan2(0, 0), and highly unstable. + + The ``cy`` fix for numerical instability below is from: *Graphics + Gems IV*, Paul Heckbert (editor), Academic Press, 1994, ISBN: + 0123361559. Specifically it comes from EulerAngles.c by Ken + Shoemake, and deals with the case where cos(y) is close to zero: + + See: http://www.graphicsgems.org/ + + The code appears to be licensed (from the website) as "can be used + without restrictions". + ''' + M = np.asarray(M) + if cy_thresh is None: + try: + cy_thresh = np.finfo(M.dtype).eps * 4 + except ValueError: + cy_thresh = _FLOAT_EPS_4 + r11, r12, r13, r21, r22, r23, r31, r32, r33 = M.flat + # cy: sqrt((cos(y)*cos(z))**2 + (cos(x)*cos(y))**2) + cy = math.sqrt(r33*r33 + r23*r23) + if cy > cy_thresh: # cos(y) not close to zero, standard form + z = math.atan2(-r12, r11) # atan2(cos(y)*sin(z), cos(y)*cos(z)) + y = math.atan2(r13, cy) # atan2(sin(y), cy) + x = math.atan2(-r23, r33) # atan2(cos(y)*sin(x), cos(x)*cos(y)) + else: # cos(y) (close to) zero, so x -> 0.0 (see above) + # so r21 -> sin(z), r22 -> cos(z) and + z = math.atan2(r21, r22) + y = math.atan2(r13, cy) # atan2(sin(y), cy) + x = 0.0 + return z, y, x + +def wind2body4attitude(eps_v0, alpha, beta): + """ + Fix for the fact that theta, phi, psi is the wrong axis order. To use rotation, it has to be phi, theta, psi + """ + eps_vec = np.array([eps_v0[1], eps_v0[0], eps_v0[2]]) + eps_vec = wind2body(eps_vec, alpha, beta) + return np.array([eps_vec[1], eps_vec[0], eps_vec[2]]) + +def body2wind4attitude(eps_v0, alpha, beta): + """ + Fix for the fact that theta, phi, psi is the wrong axis order. To use rotation, it has to be phi, theta, psi + """ + eps_vec = np.array([eps_v0[1], eps_v0[0], eps_v0[2]]) + eps_vec = body2wind(eps_vec, alpha, beta) + return np.array([eps_vec[1], eps_vec[0], eps_vec[2]]) -# TODO: numba jit -def _system_equations(time, state_vector, mass, inertia, forces, moments): + +@jit +def _system_equations(time, state_vector, mass, inertia, inertia_inverse, forces, moments): """Euler flat earth equations: linear momentum equations, angular momentum equations, angular kinematic equations, linear kinematic equations. @@ -182,6 +429,8 @@ def _system_equations(time, state_vector, mass, inertia, forces, moments): """ # Note definition of total_moments of inertia p.21 Gomez Tierno, et al # Mecánica de vuelo + I = inertia + invI = inertia_inverse Ix = inertia[0, 0] Iy = inertia[1, 1] Iz = inertia[2, 2] @@ -191,6 +440,7 @@ def _system_equations(time, state_vector, mass, inertia, forces, moments): L, M, N = moments u, v, w = state_vector[0:3] + omega = state_vector[3:6] p, q, r = state_vector[3:6] theta, phi, psi = state_vector[6:9] @@ -200,13 +450,14 @@ def _system_equations(time, state_vector, mass, inertia, forces, moments): dw_dt = Fz / mass + q * u - p * v # Angular momentum equations - dp_dt = (L * Iz + N * Jxz - q * r * (Iz ** 2 - Iz * Iy + Jxz ** 2) + - p * q * Jxz * (Ix + Iz - Iy)) / (Ix * Iz - Jxz ** 2) - dq_dt = (M + (Iz - Ix) * p * r - Jxz * (p ** 2 - r ** 2)) / Iy - dr_dt = (L * Jxz + N * Ix + p * q * (Ix ** 2 - Ix * Iy + Jxz ** 2) - - q * r * Jxz * (Iz + Ix - Iy)) / (Ix * Iz - Jxz ** 2) - - # Angular Kinematic equations + dp_dt, dq_dt, dr_dt = invI @ (moments - np.cross(omega, (I @ omega))) + # dp_dt = (L * Iz + N * Jxz - q * r * (Iz ** 2 - Iz * Iy + Jxz ** 2) + + # p * q * Jxz * (Ix + Iz - Iy)) / (Ix * Iz - Jxz ** 2) + # dq_dt = (M + (Iz - Ix) * p * r - Jxz * (p ** 2 - r ** 2)) / Iy + # dr_dt = (L * Jxz + N * Ix + p * q * (Ix ** 2 - Ix * Iy + Jxz ** 2) - + # q * r * Jxz * (Iz + Ix - Iy)) / (Ix * Iz - Jxz ** 2) + + # Angular Kinematic equations (min and max to prevent blow up) dtheta_dt = q * cos(phi) - r * sin(phi) dphi_dt = p + (q * sin(phi) + r * cos(phi)) * np.tan(theta) dpsi_dt = (q * sin(phi) + r * cos(phi)) / cos(theta) @@ -222,4 +473,4 @@ def _system_equations(time, state_vector, mass, inertia, forces, moments): phi) * cos(theta) return np.array([du_dt, dv_dt, dw_dt, dp_dt, dq_dt, dr_dt, dtheta_dt, - dphi_dt, dpsi_dt, dx_dt, dy_dt, dz_dt]) + dphi_dt, dpsi_dt, dx_dt, dy_dt, dz_dt]) \ No newline at end of file diff --git a/src/pyfme/models/state/acceleration.py b/src/pyfme/models/state/acceleration.py index 4488010..8b8b7cb 100644 --- a/src/pyfme/models/state/acceleration.py +++ b/src/pyfme/models/state/acceleration.py @@ -36,6 +36,7 @@ def __init__(self): self._accel_body = np.zeros(3) # m/s² # Local horizon (NED) self._accel_NED = np.zeros(3) # m/s² + self._accel_body_ref = None @abstractmethod def update(self, coords, attitude): @@ -92,6 +93,17 @@ def update(self, coords, attitude): attitude.phi, attitude.psi) + def perturbate(self, eps_vector, **kwargs): + assert self._accel_body_ref is None, "Cancel perturbation on velocity before perturbating again" + self._accel_body_ref = np.copy(self._accel_body) + self.update(self._accel_body + eps_vector, kwargs['attitude']) + + def cancel_perturbation(self, **kwargs): + if self._accel_body_ref is not None: + self.update(self._accel_body_ref, kwargs['attitude']) + self._accel_body_ref = None + + def __repr__(self): rv = (f"u_dot: {self.u_dot:.2f} m/s², v_dot: {self.v_dot:.2f} m/s², " f"w_dot: {self.u_dot:.2f} m/s²") diff --git a/src/pyfme/models/state/aircraft_state.py b/src/pyfme/models/state/aircraft_state.py index 737e685..c68077e 100644 --- a/src/pyfme/models/state/aircraft_state.py +++ b/src/pyfme/models/state/aircraft_state.py @@ -14,6 +14,8 @@ from .angular_velocity import BodyAngularVelocity from .acceleration import BodyAcceleration from .angular_acceleration import BodyAngularAcceleration +from pyfme.utils.coordinates import wind2body +from json import dump class AircraftState: @@ -35,6 +37,7 @@ def __init__(self, position, attitude, velocity, angular_vel=None, self.acceleration = acceleration self.angular_accel = angular_accel + @property def value(self): """Only for testing purposes""" @@ -53,3 +56,47 @@ def __repr__(self): f"{self.angular_accel} \n" ) return rv + + def perturbate(self, eps_vector, keyword): + """ + Perturbates the "keyword" part of the state (position, attitude, velocity, angular_vel) by eps_vec (size (3,)). + Each vector V becomes V + eps_vector, so eps is the change in each direction. + The perturbations can optionally be specified in the stability_axis. Note that it is common to linearize the + dynamics in stability axis + """ + # Get the "keyword" part of the state + attr = getattr(self, keyword) + + # Perturbate + attr.perturbate(eps_vector, attitude=self.attitude) + + def cancel_perturbation(self): + """ + Brings back to reference state. + """ + for keyword in ['position', 'attitude', 'velocity', 'angular_vel', 'acceleration']: + getattr(self, keyword).cancel_perturbation(attitude=self.attitude) + + return self + + def save_to_json(self, filename): + state = dict() + + state['x_e'] = self.position.x_earth + state['y_e'] = self.position.y_earth + state['z_e'] = self.position.z_earth + + state['phi'] = self.attitude.phi + state['theta'] = self.attitude.theta + state['psi'] = self.attitude.psi + + state['u'] = self.velocity.u + state['v'] = self.velocity.v + state['w'] = self.velocity.w + + state['p'] = self.angular_vel.p + state['q'] = self.angular_vel.q + state['r'] = self.angular_vel.r + + with open(filename, 'w') as f: + dump(state, f) \ No newline at end of file diff --git a/src/pyfme/models/state/angular_velocity.py b/src/pyfme/models/state/angular_velocity.py index 8d7d349..0b681a4 100644 --- a/src/pyfme/models/state/angular_velocity.py +++ b/src/pyfme/models/state/angular_velocity.py @@ -32,6 +32,7 @@ def __init__(self): self._vel_ang_body = np.zeros(3) # rad/s # EULER ANGLE RATES (theta_dot, phi_dot, psi_dot) self._euler_ang_rate = np.zeros(3) # rad/s + self._vel_ang_body_ref = None @abstractmethod def update(self, coords, attitude): @@ -88,6 +89,16 @@ def update(self, coords, attitude): # rates self._euler_ang_rate = np.zeros(3) # rad/s + def perturbate(self, eps_vector, **kwargs): + assert self._vel_ang_body_ref is None, "Cancel perturbation on velocity before perturbating again" + self._vel_ang_body_ref = np.copy(self._vel_ang_body) + self.update(self._vel_ang_body + eps_vector, kwargs['attitude']) + + def cancel_perturbation(self, **kwargs): + if self._vel_ang_body_ref is not None: + self.update(self._vel_ang_body_ref, kwargs['attitude']) + self._vel_ang_body_ref = None + def __repr__(self): return (f"P: {self.p:.2f} rad/s, " f"Q: {self.q:.2f} rad/s, " diff --git a/src/pyfme/models/state/attitude.py b/src/pyfme/models/state/attitude.py index 395b2c9..f8baae2 100644 --- a/src/pyfme/models/state/attitude.py +++ b/src/pyfme/models/state/attitude.py @@ -37,6 +37,7 @@ def __init__(self): self._euler_angles = np.zeros(3) # rad # Quaternions (q0, q1, q2, q3) self._quaternions = np.zeros(4) + self._euler_angles_ref = None @abstractmethod def update(self, value): @@ -96,6 +97,16 @@ def update(self, value): # TODO: transform quaternions to Euler angles self._quaternions = np.zeros(4) + def perturbate(self, eps_vector, **kwargs): + assert self._euler_angles_ref is None, "Cancel perturbation on velocity before perturbating again" + self._euler_angles_ref = np.copy(self._euler_angles) + self.update(self._euler_angles + eps_vector) + + def cancel_perturbation(self, **kwargs): + if self._euler_angles_ref is not None: + self.update(self._euler_angles_ref) + self._euler_angles_ref = None + def __repr__(self): rv = (f"theta: {self.theta:.3f} rad, phi: {self.phi:.3f} rad, " f"psi: {self.psi:.3f} rad") diff --git a/src/pyfme/models/state/position.py b/src/pyfme/models/state/position.py index e40c985..814172a 100644 --- a/src/pyfme/models/state/position.py +++ b/src/pyfme/models/state/position.py @@ -46,6 +46,7 @@ def __init__(self, geodetic, geocentric, earth): self._geocentric_coordinates = np.asarray(geocentric, dtype=float) # m # Earth coordinates (x_earth, y_earth, z_earth) self._earth_coordinates = np.asarray(earth, dtype=float) # m + self._earth_coordinates_ref = None @abstractmethod def update(self, coords): @@ -133,6 +134,16 @@ def update(self, value): # Update Earth coordinates with value self._earth_coordinates[:] = value + def perturbate(self, eps_vector, **kwargs): + assert self._earth_coordinates_ref is None, "Cancel perturbation on position before perturbating again" + self._earth_coordinates_ref = np.copy(self._earth_coordinates) + self.update(self._earth_coordinates + eps_vector) + + def cancel_perturbation(self, **kwargs): + if self._earth_coordinates_ref is not None: + self.update(self._earth_coordinates_ref) + self._earth_coordinates_ref = None + def __repr__(self): rv = (f"x_e: {self.x_earth:.2f} m, y_e: {self.y_earth:.2f} m, " f"z_e: {self.z_earth:.2f} m") diff --git a/src/pyfme/models/state/velocity.py b/src/pyfme/models/state/velocity.py index ccbcc99..719e3f0 100644 --- a/src/pyfme/models/state/velocity.py +++ b/src/pyfme/models/state/velocity.py @@ -43,6 +43,8 @@ def __init__(self): self._vel_body = np.zeros(3) # m/s # Local horizon (NED) self._vel_NED = np.zeros(3) # m/s + # Reference in case of perturbation + self._vel_body_ref = None @abstractmethod def update(self, coords, attitude): @@ -100,6 +102,16 @@ def update(self, value, attitude): attitude.phi, attitude.psi) # m/s + def perturbate(self, eps_vector, **kwargs): + assert self._vel_body_ref is None, "Cancel perturbation on velocity before perturbating again" + self._vel_body_ref = np.copy(self._vel_body) + self.update(self._vel_body + eps_vector, kwargs['attitude']) + + def cancel_perturbation(self, **kwargs): + if self._vel_body_ref is not None: + self.update(self._vel_body_ref, kwargs['attitude']) + self._vel_body_ref = None + def __repr__(self): return f"u: {self.u:.2f} m/s, v: {self.v:.2f} m/s, w: {self.w:.2f} m/s" diff --git a/src/pyfme/simulator.py b/src/pyfme/simulator.py index bb08d1e..b2ed055 100644 --- a/src/pyfme/simulator.py +++ b/src/pyfme/simulator.py @@ -14,6 +14,7 @@ import pandas as pd import tqdm +from pyfme.utils.coordinates import AlphaBetaRangeError class Simulation: @@ -91,13 +92,13 @@ class Simulation: } def __init__(self, aircraft, system, environment, controls, dt=0.01, - save_vars=None): + save_vars=None, verbose=True): """ Simulation object Parameters ---------- - aircraft : Aircraft + aircraft : Aircraft Aircraft model system : System System model @@ -117,6 +118,7 @@ def __init__(self, aircraft, system, environment, controls, dt=0.01, self.controls = controls self.dt = dt + self.verbose = verbose if not save_vars: self._save_vars = self._default_save_vars @@ -156,7 +158,8 @@ def propagate(self, time): dt = self.dt half_dt = self.dt/2 - bar = tqdm.tqdm(total=time, desc='time', initial=self.system.time) + if self.verbose: + bar = tqdm.tqdm(total=time, desc='time', initial=self.system.time) # To deal with floating point issues we cannot check equality to # final time to finish propagation @@ -168,11 +171,17 @@ def propagate(self, time): self.aircraft.calculate_forces_and_moments(self.system.full_state, self.environment, controls) - self.system.time_step(dt) + try: + self.system.time_step(dt) + except AlphaBetaRangeError: + break self._save_time_step() - bar.update(dt) - bar.close() + if self.verbose: + bar.update(dt) + + if self.verbose: + bar.close() results = pd.DataFrame(self.results) results.set_index('time', inplace=True) diff --git a/src/pyfme/utils/anemometry.py b/src/pyfme/utils/anemometry.py index fb5ca6e..6e79528 100644 --- a/src/pyfme/utils/anemometry.py +++ b/src/pyfme/utils/anemometry.py @@ -23,7 +23,7 @@ position error. """ -from math import asin, atan, sqrt +from math import asin, atan2, sqrt from pyfme.models.constants import RHO_0, P_0, SOUND_VEL_0, GAMMA_AIR @@ -78,7 +78,7 @@ def calculate_alpha_beta_TAS(u, v, w): TAS = sqrt(u ** 2 + v ** 2 + w ** 2) - alpha = atan(w / u) + alpha = atan2(w, u) beta = asin(v / TAS) return alpha, beta, TAS diff --git a/src/pyfme/utils/coordinates.py b/src/pyfme/utils/coordinates.py index 8f48750..ab2daeb 100644 --- a/src/pyfme/utils/coordinates.py +++ b/src/pyfme/utils/coordinates.py @@ -309,6 +309,14 @@ def hor2wind(hor_coords, gamma, mu, chi): return wind_coords +class AlphaBetaRangeError(Exception): + """Exception raised if alpha and beta get too big + """ + + def __init__(self, message): + self.message = message + + def check_alpha_beta_range(alpha, beta): """Check alpha, beta values are inside the defined range. This comprobation can also detect if the value of the angle is in degrees in @@ -319,9 +327,9 @@ def check_alpha_beta_range(alpha, beta): beta_min, beta_max = (-np.pi, np.pi) if not (alpha_min <= alpha <= alpha_max): - raise ValueError('Alpha value is not inside correct range') + raise AlphaBetaRangeError('Alpha value is not inside correct range') elif not (beta_min <= beta <= beta_max): - raise ValueError('Beta value is not inside correct range') + raise AlphaBetaRangeError('Beta value is not inside correct range') def body2wind(body_coords, alpha, beta): diff --git a/src/pyfme/utils/export.py b/src/pyfme/utils/export.py new file mode 100644 index 0000000..0ae04a6 --- /dev/null +++ b/src/pyfme/utils/export.py @@ -0,0 +1,18 @@ +# -*- coding: utf-8 -*- +""" +Python Flight Mechanics Engine (PyFME). +Copyright (c) AeroPython Development Team. +Distributed under the terms of the MIT License. + +Export results and state to other formats +---------------- +Creates a few functions to save simulation outputs to other formats +Other functions and methods doing the same thing: + AircraftState.save_to_json() +""" +from scipy.io import savemat + + +def results2matlab(results, filename): + ref = results.to_dict(orient='list') + savemat(filename, ref) diff --git a/validation/PyFME vs Eigenvalue analysis.ipynb b/validation/PyFME vs Eigenvalue analysis.ipynb new file mode 100644 index 0000000..0f95f61 --- /dev/null +++ b/validation/PyFME vs Eigenvalue analysis.ipynb @@ -0,0 +1,1515 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# PyFME Validation : comparing response with eigenvalue analysis" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.aircrafts import LinearB747, Cessna172, SimplifiedCessna172\n", + "from pyfme.models import EulerFlatEarth\n", + "import numpy as np\n", + "nl = np.linalg\n", + "import matplotlib.pyplot as plt\n", + "from pyfme.environment.atmosphere import ISA1976, SeaLevel\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant\n", + "from pyfme.environment import Environment\n", + "from pyfme.utils.trimmer import steady_state_trim\n", + "from pyfme.models.state.position import EarthPosition\n", + "from pyfme.simulator import Simulation\n", + "from pyfme.utils.coordinates import wind2body, body2wind\n", + "from pyfme.utils.input_generator import Constant" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We start by defining the airplane, the environment and the trim position." + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = SimplifiedCessna172()" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "atmosphere = SeaLevel()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()\n", + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}\n", + "trimmed_state, trimmed_controls = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ")\n", + "environment.update(trimmed_state)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then we linearize the model around the trim condition. It gives us two matrices for lateral and longitudinal small perturbations.\n", + "Under the hood, the code computes dimensional stability derivatives using numerical differentiation, and then uses the analytical formulas for the linearized system given in [1]." + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "A_long, A_lat = system.linearized_model(trimmed_state, aircraft, environment, trimmed_controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Longitudinal eigenvalues : \n", + "(-2.87760089356+4.12505582128j)\n", + "(-2.87760089356-4.12505582128j)\n", + "(-0.03785343075+0.257120129321j)\n", + "(-0.03785343075-0.257120129321j)\n" + ] + } + ], + "source": [ + "long_val, long_vec=nl.eig(A_long)\n", + "long_val = np.expand_dims(long_val, axis = 0)\n", + "print(f\"Longitudinal eigenvalues : \")\n", + "for l in long_val[0]:\n", + " print(l)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected we find two damped oscillatory modes in the longitudinal dynamics: phugoid and short period." + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lateral eigenvalues : \n", + "(-6.96516821579+0j)\n", + "(-0.204583217243+1.17359637036j)\n", + "(-0.204583217243-1.17359637036j)\n", + "(0.0324906079983+0j)\n" + ] + } + ], + "source": [ + "lat_val, lat_vec=nl.eig(A_lat)\n", + "lat_val = np.expand_dims(lat_val, axis = 0)\n", + "print(f\"Lateral eigenvalues : \")\n", + "for l in lat_val[0]:\n", + " print(l)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the lateral case, we get one oscillatory mode (dutch roll), a stable rolling convergence and an unstable - but very slow - spiral mode." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Eigenvalue trajectories" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compute the predicted trajectories for small perturbations." + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# helper function to go from stability to body axis\n", + "def linear_stab_2_body(long_state=np.zeros(4), lat_state=np.zeros(4), u0=0, theta0=0,alpha0=0, beta0=0):\n", + " # velocities\n", + " v = wind2body(np.array([long_state[0] + u0, lat_state[0], long_state[1]]), alpha=alpha0, beta=beta0)\n", + " # Roll rates\n", + " r = wind2body(np.array([lat_state[1], long_state[2], lat_state[2]]), alpha=alpha0, beta=beta0)\n", + " long_stateB = np.copy(long_state)\n", + " lat_stateB = np.copy(lat_state)\n", + " long_stateB[0] = v[0]\n", + " long_stateB[1] = v[2]\n", + " long_stateB[2] = r[1]\n", + " long_stateB[3] += theta0\n", + " lat_stateB[0] = v[1]\n", + " lat_stateB[1] = r[0]\n", + " lat_stateB[2] = r[2]\n", + " return long_stateB.real, lat_stateB.real" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Reference conditions\n", + "alpha = np.arctan2(trimmed_state.velocity.w, trimmed_state.velocity.u)\n", + "beta = np.arcsin(trimmed_state.velocity.v/nl.norm(trimmed_state.velocity.vel_body))\n", + "u, v, w = body2wind(trimmed_state.velocity.vel_body, alpha, 0)\n", + "theta0 = trimmed_state.attitude.theta*1.0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Longitudinal case" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can pick any perturbation from the equilibrium. Here I chose something along the eigenvectors of A_long.\n", + "The result will be a weighted sum of eigenvector*exp(eigenvalue*t). The weights are determined by the initial condition." + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "long_perturbation = (long_vec.T[2] + long_vec.T[3])/1000" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "C = nl.lstsq(a=long_vec,b=long_perturbation.real)[0].real" + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "T = 100;\n", + "t_long = np.linspace(0,T,1000)\n", + "N = len(t_long)\n", + "X_long = np.zeros((N,4))\n", + "for i in range(N):\n", + " x_stab = (long_vec*np.exp(long_val*t_long[i])).dot(C)\n", + " X_long[i,:] = linear_stab_2_body(long_state=x_stab.real, alpha0=alpha, u0=u, theta0 = theta0)[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Lateral case" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again we can pick any perturbation" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "lat_perturbation = (lat_vec.T[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "C = nl.lstsq(a=lat_vec,b=lat_perturbation.real)[0].real" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "t_lat = np.linspace(0,10,100)\n", + "N = len(t_lat)\n", + "X_lat = np.zeros((N,4))\n", + "for i in range(N):\n", + " x_stab = (lat_vec*np.exp(lat_val*t_lat[i])).dot(C)\n", + " X_lat[i,:] = linear_stab_2_body(lat_state=x_stab.real, beta0=beta, alpha0=alpha, u0=u, theta0 = theta0)[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Longitudinal case" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We perturbate the trimmed state and run the simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Perturbate the trimmed state\n", + "trimmed_state.cancel_perturbation()\n", + "p = linear_stab_2_body(long_state=long_perturbation.real, alpha0=alpha)[0]\n", + "trimmed_state.perturbate(np.array([p[0],0,p[1]]), 'velocity')\n", + "trimmed_state.perturbate(np.array([0,p[2],0]), 'angular_vel')\n", + "trimmed_state.perturbate(np.array([p[3],0,0]), 'attitude') # /!\\ Convention theta, phi, psi" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "trimmed_state.save_to_json('long_perturb.json')" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment.update(trimmed_state)\n", + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)\n", + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "time: 0%| | 0/100 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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RDcOoZkxwKUWBtewc0Po0lVTzRErDMKoV0y1WijKycsiiAUFykivkrHmui2EY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\nM56yweVkiEhZuA8SJQu75uR3ql0v2DVHk3WLGWOMiTgLLsY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9llLqlFJqD7DLV1+xdfru6eOrA1+dQ8/xjKDnOOFiv/KmWxvCJZN08O5Puxlr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\nTF2RitU4ezjJ4jnJdcY6vrB+S7yxmww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7Ujyrzx+owCas6BA/Rl7fG4DmcoiXvt9sJhMahlFjmQBSDnEpmTTWI5xSb45z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\nNnpcSibdbZvIVgdr3Fdhr4D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AegIjre+3Wk1VTuARYDqwDNgN5L/jOIBwoA8wApgsIo0A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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Longitudinal case\n", + "plt.plot(t_long, X_long[:,0], '.', label='eigenvalue analysis')\n", + "plt.plot(r_long.u, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Horizontal velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_long, X_long[:,1], '.', label='eigenvalue analysis')\n", + "plt.plot(r_long.w, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Vertical velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_long, X_long[:,2], '.', label='eigenvalue analysis')\n", + "plt.plot(r_long.q, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_long, X_long[:,3], '.', label='eigenvalue analysis')\n", + "plt.plot(r_long.theta, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch angle\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Lateral case\n", + "plt.plot(t_lat, X_lat[:,0], '.', label='eigenvalue analysis')\n", + "plt.plot(r_lat.v, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Lateral velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_lat, X_lat[:,1], '.', label='eigenvalue analysis')\n", + "plt.plot(r_lat.p, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Roll rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_lat, X_lat[:,2], '.', label='eigenvalue analysis')\n", + "plt.plot(r_lat.r, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Yaw rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_lat, X_lat[:,3], '.', label='eigenvalue analysis')\n", + "plt.plot(r_lat.phi, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Heading angle\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1285.3154166 , 0. , -677.908975 ],\n", + " [ 0. , 1824.9309607 , 0. ],\n", + " [ -677.908975 , 0. , 2666.89390765]])" + ] + }, + "execution_count": 105, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "aircraft.inertia\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# References" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dynamics of Flight, Stability and Control, Etkin and Reid" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/validation/PyFME vs Simulink - batch of cases.ipynb b/validation/PyFME vs Simulink - batch of cases.ipynb new file mode 100644 index 0000000..97b1ffb --- /dev/null +++ b/validation/PyFME vs Simulink - batch of cases.ipynb @@ -0,0 +1,624 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# PyFME Validation: comparing response versus Matlab model" + ] + }, + { + "cell_type": "code", + "execution_count": 238, + "metadata": {}, + "outputs": [], + "source": [ + "from pyfme.aircrafts import LinearB747, Cessna172, SimplifiedCessna172\n", + "from pyfme.models import EulerFlatEarth\n", + "from pyfme.models.state import AircraftState\n", + "import numpy as np\n", + "# nl = np.linalg\n", + "import matplotlib.pyplot as plt\n", + "from pyfme.environment.atmosphere import SeaLevel\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant\n", + "from pyfme.environment import Environment\n", + "from pyfme.utils.trimmer import steady_state_trim\n", + "from pyfme.models.state.position import EarthPosition\n", + "from pyfme.simulator import Simulation\n", + "from pyfme.utils.export import results2matlab\n", + "from scipy.io import savemat, loadmat\n", + "from pyfme.utils.coordinates import wind2body, body2wind\n", + "from pyfme.utils.input_generator import Constant, Doublet, Ramp\n", + "from json import load as jload\n", + "from copy import deepcopy as cp\n", + "plt.style.use('ggplot')\n", + "from scipy.interpolate import interp1d as itp\n", + "import pickle" + ] + }, + { + "cell_type": "code", + "execution_count": 218, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Running a PyFME simulation and save it to a MATLAB readable file" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We start by defining the airplane and the environment." + ] + }, + { + "cell_type": "code", + "execution_count": 128, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = SimplifiedCessna172()" + ] + }, + { + "cell_type": "code", + "execution_count": 129, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "atmosphere = SeaLevel()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()\n", + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate a serie of states on which to test" + ] + }, + { + "cell_type": "code", + "execution_count": 130, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}\n", + "tstate, cont = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 131, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "N = 100;\n", + "omega = np.random.normal(loc=1,scale=.5,size=(N,3)) * np.random.choice([-1,1],(N,3), replace=True)\n", + "euler = 60*np.pi/180*np.random.normal(loc=1,scale=.5,size=(N,3)) * np.random.choice([-1,1],(N,3), replace=True)\n", + "velocity = np.random.normal(loc=[50, 5, 5],scale=.5,size=(N,3)) * np.random.choice([-1,1],(N,3), replace=True)\n", + "velocity[:,0] *= np.sign(velocity[:,0])\n", + "states = []\n", + "for case_id in range(N):\n", + " state = cp(tstate)\n", + " state.velocity._vel_body = velocity[case_id, :]\n", + " state.angular_vel._euler_ang_rate = omega[case_id, :]\n", + " state.attitude._euler_angles = euler[case_id, :]\n", + " states.append(state)\n", + " state.save_to_json(f'{case_id}.json')" + ] + }, + { + "cell_type": "code", + "execution_count": 228, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Bd/R2bCIislq9u6H2Ao4BnjGzPyVl5wAXAW5mE4lvCJxQp/hERDK5/aGzuj/g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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(omega[:,:]*180/np.pi,40,stacked=True)\n", + "plt.xlabel('rotation rates in deg/s')\n", + "plt.ylabel('number of occurences')\n", + "plt.title('distribution of initial roll rates')\n", + "plt.legend(('roll','pitch','yaw'))\n", + "plt.show()\n", + "\n", + "plt.hist(euler[:,:]*180/np.pi,40,stacked=True)\n", + "plt.xlabel('euler angles in degrees')\n", + "plt.ylabel('number of occurences')\n", + "plt.title('distribution of initial attitudes')\n", + "plt.legend(('roll','pitch','yaw'))\n", + "plt.show()\n", + "\n", + "vel = velocity*1.0\n", + "vel[:,0]/=10\n", + "plt.hist(vel,40,stacked=True)\n", + "plt.xlabel('velocities in m/s')\n", + "plt.ylabel('number of occurences')\n", + "plt.title('distribution of velocities')\n", + "plt.legend(('u / 10','v','w'))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "We finally pick a particular time serie of controls and run the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 132, + "metadata": {}, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=cont['delta_elevator']),\n", + " 'delta_aileron': Ramp(t_init=1,T=2, A=.2, offset=cont['delta_aileron']),\n", + " 'delta_rudder': Constant(cont['delta_rudder']),\n", + " 'delta_t': Constant(cont['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 133, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "T = 3 # seconds" + ] + }, + { + "cell_type": "code", + "execution_count": 134, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: -1.018 rad, phi: -1.910 rad, psi: -1.009 rad \n", + "u: 50.52 m/s, v: -3.92 m/s, w: -5.04 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: 0.00 rad/s², Q_dot: 0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 134, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "state" + ] + }, + { + "cell_type": "code", + "execution_count": 141, + "metadata": {}, + "outputs": [], + "source": [ + "results = {}\n", + "for case_id in range(N):\n", + " state = states[case_id]\n", + " environment.update(state)\n", + " system = EulerFlatEarth(t0=0, full_state=state)\n", + " sim = Simulation(aircraft, system, environment, controls, verbose=False)\n", + " results[case_id] = sim.propagate(T)" + ] + }, + { + "cell_type": "code", + "execution_count": 242, + "metadata": {}, + "outputs": [], + "source": [ + "with open('batch_results.pkl','wb') as f:\n", + " pickle.dump(file=f,obj=results)\n", + "# r = pickle.load(open('batch_results.pkl','rb'))" + ] + }, + { + "cell_type": "code", + "execution_count": 136, + "metadata": {}, + "outputs": [], + "source": [ + "nT = int(T/sim.dt)\n", + "t= np.arange(nT)*sim.dt\n", + "controls4matlab = np.ones((nT,4));\n", + "for it in range(nT):\n", + " controls4matlab[it,0] = controls['delta_aileron']._fun(t[it])\n", + " controls4matlab[it,1] = controls['delta_elevator']._fun(t[it])\n", + " controls4matlab[it,2] = controls['delta_rudder']._fun(t[it])\n", + " controls4matlab[it,3] = controls['delta_t']._fun(t[it])\n", + "savemat('controls.mat',{'c': controls4matlab, 'dt':sim.dt})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We save the controls in a Matlab file" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Run the same simulation in Simulink" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The simulink bloc diagram used for comparison uses exactly the same model to compute forces and moments (the method aircraft.compute_forces_and_moments() was translated directly to Matlab). The entire equations of motion integration is done with the %6DOF (Quaternion) % Simulink bloc from the aerospace blocset. Verifying against this tool allows to make sure that there are no mistake in the way the EulerFlatEarth equations of motion are written, and in the way they are integrated.\n", + "\n", + "We run the Simulink model and load the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 143, + "metadata": {}, + "outputs": [], + "source": [ + "matlab_rslt = {}\n", + "for case_id in range(N):\n", + " with open('../../matlab_comparison/results' + str(case_id) + '.json','r') as f:\n", + " mat_states = jload(f)\n", + " mat_states = {k:np.array(el) for k,el in mat_states.items()}\n", + " matlab_rslt[case_id] = mat_states" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Compare outputs" + ] + }, + { + "cell_type": "code", + "execution_count": 256, + "metadata": {}, + "outputs": [], + "source": [ + "getname={'Euler':['phi','theta','psi'], 'Omega_body':['p','q','r'], 'V_body':['u', 'v', 'w']}\n", + "unit = {'Euler':'deg', 'Omega_body':'deg/s', 'V_body':'m/s'} \n", + "legend = {'Euler':('roll','pitch','yaw'), 'Omega_body':('roll','pitch','yaw'), 'V_body':('u','v','w')} \n", + "factor = {'Euler':180/np.pi, 'Omega_body':180/np.pi, 'V_body':1}\n", + "name = {'Euler':'euler angles', 'Omega_body':'rotation rates', 'V_body':'velocities'} \n", + "def getMSE(keyword, idx):\n", + " name = getname[keyword][idx]\n", + " error = np.zeros(N)\n", + " for case_id in range(N):\n", + " nc = len(results[case_id].u)\n", + " matlab_calc = itp(matlab_rslt[case_id]['t'], matlab_rslt[case_id][keyword][:,idx])\n", + " error[case_id] = np.sum(abs(results[case_id][name] - matlab_calc(results[case_id].index)))/nc\n", + " return error*factor[keyword]" + ] + }, + { + "cell_type": "code", + "execution_count": 257, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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XokvoC54IU0Df56lknQerqufgKgrzlU1VzZednQ1DQ0M9JNJW3DngipadnV1o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\nlT8W4FIQOjzOsrh+imovb2XJV+DWrVv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XEmvQoAG2b9+OmTNnol69ehg9erR0CWPgyXUhwsLC0KxZMyxfvhxTpkzB4MGD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\nuLu7w8LCAu3bt0d8fLyxYxERUQ1X4w9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isLAQp06dwttvv4233noLFy5cUDoKEVGN06lTJ6xcuRIdO3ZEx44dsXHjRrRs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\nZMT/B5eBJgGPJrUyAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for keyword in getname.keys():\n", + " err = (getMSE(keyword,i) for i in range(3))\n", + " error = np.vstack(err)\n", + " plt.hist(error.T, 30, stacked=True);\n", + " plt.title('Distribution of absolute errors on ' + name[keyword] + ' for all trajectories')\n", + " plt.ylabel('number of occurences')\n", + " plt.xlabel('Error in ' + unit[keyword])\n", + " plt.legend(legend[keyword])\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Show examples" + ] + }, + { + "cell_type": "code", + "execution_count": 147, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "case_id=19" + ] + }, + { + "cell_type": "code", + "execution_count": 148, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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1E20LfcQyZ+vaWC3Cf7ztseLlEdt8AIbMz2112vDQ4FcqTLL682+V5XzkGIxd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\nfp8KtM+lzM1AmjHmT2PMX0Aa0PIsXvO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LciCQI+I02Ivh+W9+YZDtGzxYTHTfAGhrXamiGtUrFhCecA1ikzmf8Y6x1Jcd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\nh+rVq2uohzkRoXr16sX6Zhb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LHtcjB1UySiIYMoD6+e5HAbuKaiMiDqAG8Gcxty0R0xLjad8sApddaFTnLD65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\nlAoZSd1aUM1l50NvR360GvK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ckgDXUpVHGgBKBYnsxeQ+c5rxt6wRREsa74Y9RW32kpaeqRPGVInTAFAqiGx7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\nqQrq/wGr+IN1ud+3WwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Longitudinal values\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['V_body'][:,0], '.', label='Simulink output')\n", + "plt.plot(results[case_id].u, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Horizontal velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['V_body'][:,2], '.', label='Simulink output')\n", + "plt.plot(results[case_id].w, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Vertical velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['Omega_body'][:,1], '.', label='Simulink output')\n", + "plt.plot(results[case_id].q, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['Euler'][:,1], '.', label='Simulink output')\n", + "plt.plot(results[case_id].theta, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch angle\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 149, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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W6B00aBBXX301TZs2ZfTo0bz66qt07NiRrl27snv3buDYpX937txJQkLCcedauHAh3bp1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\nvQBoGV+rStbOwWr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6rVnrtmKDNieDkJxlbaoOU1lYMBhTiIKm48iWOyjinW/o4mwjUvxtz6iXjRrN\nGrc1a9zWpLit2EdDsscpwMLCVEwWDMZcoPwT++UXwWG6ONtybh3kW8IlE4CDWpsNbnM2aDTr3RZs\n0OhAF9T/wsJOujPBZsFgTAkVFhQhZNFOdtHJ2UGMpNLB+ZbWspcQ8QFwRGuywY1mg7ZgvducjRrF\nLm2M4uT5nNYRNZn/u8Sy3BRjAAsGY0rd+NmbeXXJzvO2CSODNrKHGCeVGNlJjJNKG9lDmPivQXFS\nw9iql7HFbcZmbcYWtxlb9TKOUTPP59jRUKYsWDAYUw4KmqojvxCyuFz2coXzLW1lD+1kN22d3dQP\nHAUF/iOhNrvN2BIIi83ajFS9BDff3kW9Gl5Sfl/oqT7GFMiCwZggKUpYgNKYw7RzdtNWdufct5R9\neMUF4LSG5OxdbNHL2KxRbHEv4wi183ySjV2YorJgMKYCOddJd/mFkkkr+S5nryI7NBrJsZw2+7UB\nW9zL2KLNcga8d+vFNnZhCmXBYEwFd64JAQvSiKO0c3bRNhAY7WQPrWQvoYGB7mNag00a7R/sDoTF\nTm16VleUzQtVvVkwGFNJFXY0VLbcYxcxkkqM8y3tZDc1xH+tq3QNZZNGscGNZp3bkjXamm/1EnIf\nQmtjFtWLBYMxVUzsk/M4kp513jYefLSQ/cTIt/4jo5xvaS+7qC3pABzSWqwNnJi3RlvztduSU7lm\nmg3xCE8OsxPzqioLBmOqgaKMXTi4tJLv/Cfmif/kvFaOf/4onwobNZrlbntWuG1Z5bY969DZ4rDD\nbSsmCwZjqqminG9RlxN0drbTxfmGrs5WOss2wiQLV4WNGsVytz279WIABA3c/48PhzOEcEZDOUMI\np/Hfn9RwjlCTo1qL49Q4a0A8P9tDKV8WDMaYHOebFwr8J+Z1drbTTTbT3dlMF2cbYYHpPorLp8Ix\nanJIa7NfG/A9Df332oDvtBE7tAnfacRZA+QAkfXCWZrUt0TrN2ezYDDGnNf5xixCyaQW6TnPNefe\nv9/gxSWMDMIkk3AyCCOTcMmgJqepy0nqyknqygnqcYKGcowmcohL5BCNOZxzngb4z9X4VpuwXZuy\nzY1knTZnnduSQ9TJU0+412HyL7oTF1XgBSJNEVkwGGMuSNFOzCsZDz4acZTL5EdaOvtpKftoJd/R\nUvZxmaThiP/3aK82IsVtxXK3HcvcK9ipTcjdmWXXxCgeCwZjTFAU9XDb/GqSToyk0tHZQSdnJ12c\nb2gqhwD/SX3L3CtY4OvCYrdTniOp7ES+orNgMMZUaIXvoShR8gMJzkZ6OBtJcDbQQE5wRkP4rxvD\nPPdK5vq6cpyLADsSqigsGIyl3urgAAAX6UlEQVQxlc57K3bzxCfryXLPfs+Dj3j5hgGeVVzjSSZS\nDnBaQ5jrXsmHvt4sc6/IOQrK9iIKZsFgjKkSrvzTfNJOZOR7VekkO7jes4RhnmXUlVPs1Ub8K6s/\n7/uuzjkXI6JWKKse61/+RVdQ5RIMItIAmApEA6nAjap6uIB2c4HuwFJVHZrr9YlAbyD7DJ1bVTWl\nsPVaMBhTPRV0jkYYGVzjJHOT5wsSPJs4oeF84Evkbd9A9gbOxbA9CL/yCoa/AodUdbyIJAH1VXVc\nAe36AhcBdxUQDJ+p6kcXsl4LBmNMQSHRXlK53TubYc5XOLjMcHvwz6yfkqpN8AjseGZIkKqtGMor\nGLYCiaq6X0SaAItUtc052iYCD1gwGGNKW/4joRpziNu8c7jFM58Qsngs6zam+K6u9uFQ1GA4//nq\nhWusqvsBAvcXF+MznhaRdSLydxEJO1cjEblTRJJFJDktLa249RpjqqD5v0skdfwQ7u7VAoAfaMAz\nWaPpdWYCX7ox/Mn7Nr2cr/EpXP7o7CBXW/EVuscgIguASwp461HgXVWtl6vtYVUt8NTEc+wxNAG+\nB0KB14EdqvpUYUXbHoMx5nxW7zrMDa8sw8V/fsSHoU9xmfzIdRlPsk0jq+1046W2x6Cq/VQ1poDb\nJ8APgR/37B/5Hy+kSFXdr35ngHeArheyvDHGFCQuqj47xw+hV+tGnKQGt2U8QDphvBbyN2pziiPp\nWdzy1opgl1lhlbQraSYwJvB4DPDJhSycK1QEGAFsKGE9xhiTY9Lt3RgR25Tvacg9GfdxmaTxfMgr\nCC5Lth1g9a6zDqI0lDwYxgP9RWQb0D/wHBGJF5E3sxuJyH+BD4G+IrJXRLL34SaLyHpgPdAI+FMJ\n6zHGmDwmjOxMbGRdkrUtf84axTWe1dzt+QyA619ZFuTqKiY7wc0YUy34Z5PN5J8h/2Sws4KbMx9m\nmRtTrcYbyuuoJGOMqRRSfj8AR4RxmXeyU5syIeRlGnDMxhsKYMFgjKk2Prw7gVOEc1/mvdTlBM+G\nvAaojTfkY8FgjKk24qLq06t1IzZrFM9kjaKvZy1jPJ8DcOOrNt6QzYLBGFOtTLq9G/VqeJnoG8BC\nX2ce8b5HO9mFT/1nUBsLBmNMNZTy+wEIwoOZd3GUmvwt5BVCyGJb2kneW7E72OUFnQWDMaZaevqn\nHThEHR7OvJ12zm7u9U4H4JHp64NcWfBZMBhjqqVR3ZoRG1mXhW4c03w9+ZXnE2LEP1vrVeMXBrm6\n4LJgMMZUWzPuvYpQj/Bk5s0coC7PhbxGKJnsPXK6WncpWTAYY6q19+/8CceoRVLmHbR19vD/Al1K\nj1XjLiULBmNMtZZ9COsitzPTfD25y/MprWQvLjDixaXBLi8oLBiMMdXepNu74XWEpzNHc5IaPB3y\nNoJLyt6j1fLENwsGY4wBnhoewyHq8EzWTXRztnC9ZwkAN7+5PMiVlT8LBmOMwX+UUuuImnzo681K\ntw2PeN+jAcc4lekyfvbmYJdXriwYjDEmYP7vEgGHRzNvpxbpPOx9D4BXl+wMal3lzYLBGGNyuatX\nC7ZpJG/5BnGDdwkdZQdAtZqB1YLBGGNySRrcjpqhHl7MGkGa1uX3IZOobjOwWjAYY0w+k27vxgku\n4q9ZPyfO2cYwxz/z6q1vV4+9BgsGY4zJJy6qPrGRdfnI14t1bnMeDnmfGpzm+BlftTgjukTBICIN\nRGS+iGwL3NcvoE2siHwlIhtFZJ2I/DzXe81FZEVg+akiElqSeowxprTMuPcqwOEPmWNoIoe42/sp\nAE98UvXPiC7pHkMSsFBVWwMLA8/zOwXcoqpXAAOBCSJSL/DeX4C/B5Y/DNxewnqMMabU3NWrBWv0\ncj71decXntlEcJgslyp/+GpJg2E48G7g8bvAiPwNVPUbVd0WeLwP+BGIEBEBrgY+Ot/yxhgTLEmD\n2xHiEZ7LupEQsvi192Og6h++WtJgaKyq+wEC9xefr7GIdAVCgR1AQ+CIqmYF3t4LXFrCeowxplQ9\nOSyGXXoJ7/muZqTnPzSX/QDcP2VtkCsrO4UGg4gsEJENBdyGX8iKRKQJ8C9grKq6gBTQTM+z/J0i\nkiwiyWlpaReyamOMKbZR3ZpRJ9zLP7Ou4wwh/M77AQAzUvYFubKyU2gwqGo/VY0p4PYJ8EPgBz/7\nh//Hgj5DROoAs4DHVDV74pEDQD0R8QaeRwLn/JNW1ddVNV5V4yMiIoq+hcYYU0LvjO3KAerypm8I\nQz0rck56q6p7DSXtSpoJjAk8HgN8kr9B4Eij6cAkVf0w+3VVVeA/wPXnW94YY4ItLqo+TeqE8UbW\nYA5qbR70TgWq7l5DSYNhPNBfRLYB/QPPEZF4EXkz0OZGoBdwq4ikBG6xgffGAb8Vke34xxzeKmE9\nxhhTJl4cHccJLuKVrGH09GwgXrYAVXOvQfz/ca9c4uPjNTk5OdhlGGOqmZ/8eQFHjh1lSdj9bHGb\ncXPmIwCkjh8S5MqKRkRWq2p8Ye3szGdjjCmiF0fHkU44r2VdW6X3GiwYjDGmiLLHGib7+pKmdXLO\na6hqYw0WDMYYcwHOtddQlabltmAwxpgLkD3BXvZew33e6QAs2XYgyJWVHgsGY4y5QDPuvYp0wnkr\nazC9POu5Qr4Fqs5YgwWDMcYUQ/smtZns68cxrcEvAzOvVpWxBgsGY4wphj+O6MBxLmKyrx+DnBU0\nkx+AqjHzqgWDMcYUQ/YRSm9nDSQLD3d6PgPgjf9W/plXLRiMMaaYXhwdRxr1mebryQ2eJURwBJ9S\n6a/yZsFgjDHFFBdVn9phHl73DSWELG71zgXg6VmbglxZyVgwGGNMCTw8uD2p2oQ57pX8n2cBNTjN\nyQwfq3cdDnZpxWbBYIwxJTCqWzNCHOHtrEHUlVNc51kKwG+npgS5suKzYDDGmBK6/armrNbLWec2\nZ6xnLoLLrkOngl1WsVkwGGNMCSUNboeIf6+hlbOPns56oPKe8GbBYIwxpWB4p6bMcrvzo9ZjrMc/\nCP1JJT3hzYLBGGNKwYSRncnEy7+z+tHH8zUt5TuUynnCmwWDMcaUkotrh/Kery9n1MsYz+cAvLW0\n8p3wZsFgjDGl5P5+bThAXT51E7jO819qkk6mW/lOeLNgMMaYUjKqWzNqh3n4V1Y/aslpRni+BOBv\n87cGubILU6JgEJEGIjJfRLYF7usX0CZWRL4SkY0isk5Efp7rvYki8q2IpARusSWpxxhjgu3hwe35\nWluywY3m/zwLAOXAiYxgl3VBSrrHkAQsVNXWwMLA8/xOAbeo6hXAQGCCiNTL9f6DqhobuFXeM0KM\nMQb/XoNHhMm+vrRzdtNFtgGV69DVkgbDcODdwON3gRH5G6jqN6q6LfB4H/AjEFHC9RpjTIV1baem\nzPQlcFxrMNq7EICZlejQ1ZIGQ2NV3Q8QuL/4fI1FpCsQCuzI9fLTgS6mv4tI2HmWvVNEkkUkOS0t\nrYRlG2NM2ZkwsjMnqcEMXw+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JmLkqsBVVQU3DX6kQlN0ZXN5ucZDq3Jk1ifnuBEbZl/Cu8xmu5BfSMk7RbOKy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\nsjt/13mvYbHnJu61fUodORx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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Lateral case\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['V_body'][:,1], '.', label='Simulink output')\n", + "plt.plot(results[case_id].v, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Lateral velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['Omega_body'][:,0], '.', label='Simulink output')\n", + "plt.plot(results[case_id].p, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Roll rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['Omega_body'][:,2], '.', label='Simulink output')\n", + "plt.plot(results[case_id].r, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Yaw rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['Euler'][:,0], '.', label='Simulink output')\n", + "plt.plot(results[case_id].phi, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Heading angle\")\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/validation/PyFME vs Simulink.ipynb b/validation/PyFME vs Simulink.ipynb new file mode 100644 index 0000000..2aa4feb --- /dev/null +++ b/validation/PyFME vs Simulink.ipynb @@ -0,0 +1,438 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# PyFME Validation: comparing response versus Matlab model" + ] + }, + { + "cell_type": "code", + "execution_count": 116, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.aircrafts import LinearB747, Cessna172, SimplifiedCessna172\n", + "from pyfme.models import EulerFlatEarth\n", + "import numpy as np\n", + "# nl = np.linalg\n", + "import matplotlib.pyplot as plt\n", + "from pyfme.environment.atmosphere import SeaLevel\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant\n", + "from pyfme.environment import Environment\n", + "from pyfme.utils.trimmer import steady_state_trim\n", + "from pyfme.models.state.position import EarthPosition\n", + "from pyfme.simulator import Simulation\n", + "from pyfme.utils.export import results2matlab\n", + "from scipy.io import savemat, loadmat\n", + "from pyfme.utils.coordinates import wind2body, body2wind\n", + "from pyfme.utils.input_generator import Constant, Doublet, Ramp\n", + "from json import load as jload" + ] + }, + { + "cell_type": "code", + "execution_count": 117, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Running a PyFME simulation and save it to a MATLAB readable file" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We start by defining the airplane and the environment." + ] + }, + { + "cell_type": "code", + "execution_count": 118, + "metadata": {}, + "outputs": [], + "source": [ + "aircraft = SimplifiedCessna172()" + ] + }, + { + "cell_type": "code", + "execution_count": 119, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "atmosphere = SeaLevel()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()\n", + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then pick a the trim position. We save the trimmed state into a json file." + ] + }, + { + "cell_type": "code", + "execution_count": 120, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}\n", + "trimmed_state, trimmed_controls = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ")\n", + "environment.update(trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 121, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "trimmed_state.save_to_json('ini_state.json')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "We finally pick a particular time serie of controls and run the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Ramp(t_init=1,T=2, A=.2, offset=trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 126, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment.update(trimmed_state)\n", + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)\n", + "sim = Simulation(aircraft, system, environment, controls,verbose=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 127, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "T = 10 # seconds" + ] + }, + { + "cell_type": "code", + "execution_count": 128, + "metadata": {}, + "outputs": [], + "source": [ + "results = sim.propagate(T)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We save the controls in a Matlab file" + ] + }, + { + "cell_type": "code", + "execution_count": 129, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "N = int(T/sim.dt)\n", + "t= np.arange(N)*sim.dt\n", + "controls4matlab = np.ones((N,4));\n", + "for it in range(N):\n", + " controls4matlab[it,0] = controls['delta_aileron']._fun(t[it])\n", + " controls4matlab[it,1] = controls['delta_elevator']._fun(t[it])\n", + " controls4matlab[it,2] = controls['delta_rudder']._fun(t[it])\n", + " controls4matlab[it,3] = controls['delta_t']._fun(t[it])\n", + "savemat('controls.mat',{'c': controls4matlab, 'dt':sim.dt})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Run the same simulation in Simulink" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The simulink bloc diagram used for comparison uses exactly the same model to compute forces and moments (the method aircraft.compute_forces_and_moments() was translated directly to Matlab). The entire equations of motion integration is done with the %6DOF (Quaternion) % Simulink bloc from the aerospace blocset. Verifying against this tool allows to make sure that there are no mistake in the way the EulerFlatEarth equations of motion are written, and in the way they are integrated.\n", + "\n", + "We run the Simulink model and load the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 130, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "dict_keys(['V_body', 'Omega_body', 'Euler', 't'])\n" + ] + } + ], + "source": [ + "with open('../../matlab_comparison/matlab_results.json','r') as f:\n", + " mat_states = jload(f)\n", + "mat_states = {k:np.array(el) for k,el in mat_states.items()}\n", + "print(f\"{mat_states.keys()}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Compare outputs" + ] + }, + { + "cell_type": "code", + "execution_count": 131, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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pmMc2DXSl4pzT5eY89jPDMZVWls3M9SXxqK9/tnvL9cJnfNBAVyqOOV1uLpVN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\n+6FV3gB65L61KslsFthmqrM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ksfA3xhwj2AHsohqDcx7iV63JePfTtJWfAOsAIoWFvzHmBMEOIIvq3JDzMDu1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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Longitudinal values\n", + "plt.plot(mat_states['t'], mat_states['V_body'][:,0], '.', label='Simulink output')\n", + "plt.plot(results.u, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Horizontal velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['V_body'][:,2], '.', label='Simulink output')\n", + "plt.plot(results.w, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Vertical velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['Omega_body'][:,1], '.', label='Simulink output')\n", + "plt.plot(results.q, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['Euler'][:,1], '.', label='Simulink output')\n", + "plt.plot(results.theta, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch angle\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 132, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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hDLX4DYid0osqnVmzZlXo6Ly0NKGriNN8xFQEl6cS3mIPp/Nowa0E55iXdSlk06h+HCKR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\nyHQb87rTP3SfnghVJ5NcszI/U5sMtyP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q2cHnmwks8p4Y5n6NOWah/v+tNOTy/DupxUGmuh+jHnlk5+5j+pc/RbhCYypP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\nNYllhQZ+o3mRRwt/Y4wBfhg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GKihNAEqFuaReTfPMJfSs+y/c4XrIP730aHrY1gLaJVQRaQJQSgF57wNY6m1F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\nUkqFqf8HmUlTeQiWl6EAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Lateral case\n", + "plt.plot(mat_states['t'], mat_states['V_body'][:,1], '.', label='Simulink output')\n", + "plt.plot(results.v, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Lateral velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['Omega_body'][:,0], '.', label='Simulink output')\n", + "plt.plot(results.p, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Roll rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['Omega_body'][:,2], '.', label='Simulink output')\n", + "plt.plot(results.r, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Yaw rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['Euler'][:,0], '.', label='Simulink output')\n", + "plt.plot(results.phi, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Heading angle\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}