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Symmetric_flight.py
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Symmetric_flight.py
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# -*- coding: utf-8 -*-
"""
Created on Wed Mar 7 11:11:44 2018
@author: xx
"""
from Cit_par import *
#from Cit_par_changing import changing_constants
from WeightBalance import cg
from numpy import*
from control.matlab import*
import matplotlib.pyplot as plt
import warnings
import matplotlib.cbook
warnings.filterwarnings("ignore",category=matplotlib.cbook.mplDeprecation)
"""
#begin short period
hp0 =7000*0.3048
V0 =188.92*0.51444
alpha0 =5*pi/180
th0 =0*pi/180
fuel_used_LEngine=504.276941303232
fuel_used_REngine=520.152402665631
m =cg(4100-(fuel_used_LEngine+fuel_used_REngine),0)[0]
changing_constants=changing_constants(hp0,V0,alpha0,th0,m)
muc = changing_constants[0]
mub = changing_constants[1]
CL = changing_constants[2]
CD = changing_constants[3]
CX0 = changing_constants[4]
CZ0 = changing_constants[5]"""
#symmetric case
#------original state space system---------------------------------------
#dimension having
C1_symmetric=matrix([[-2*muc*c/(V0**2) ,0, 0 ,0],
[0,(CZadot-2*muc)*c/V0,0,0],
[0,0,-c/V0,0],
[0,Cmadot*c/V0,0,-2*muc*KY2*c**2/V0**2]])
C2_symmetric=matrix([[CXu/V0,CXa,CZ0,CXq*c/V0],
[CZu/V0,CZa,-CX0,(CZq+2*muc)*c/V0],
[0,0,0,c/V0],
[Cmu/V0,Cma,0,Cmq*c/V0]])
C3_symmetric=matrix([[CXde],[CZde],[0],[Cmde]])
A_symmetric=linalg.inv(-C1_symmetric)*C2_symmetric
B_symmetric=linalg.inv(-C1_symmetric)*C3_symmetric
C_symmetric=identity(4)
D_symmetric=zeros((4,1))
sys_symmetric=ss(A_symmetric,B_symmetric,C_symmetric,D_symmetric)
#dimensionless
C1_sym_dimless=matrix([[-2*muc*c/V0,0,0,0],
[0,(CZadot-2*muc)*c/V0,0,0],
[0,0,-c/V0,0],
[0,Cmadot*c/V0,0,-2*muc*KY2*c/V0]])
C2_sym_dimless=matrix([[CXu,CXa,CZ0,CXq],
[CZu,CZa,CX0,(CZq+2*muc)],
[0,0,0,1],
[Cmu,Cma,0,Cmq]])
C3_sym_dimless=matrix([[CXde],[CZde],[0],[Cmde]])
A_sym_dimless=linalg.inv(-C1_sym_dimless)*C2_sym_dimless
B_sym_dimless=linalg.inv(-C1_sym_dimless)*C3_sym_dimless
C_sym_dimless=identity(4)
C_sym_hybrid=matrix([[V0,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,V0/c]])
D_sym_dimless=zeros((4,1))
#true dimensionless output
sys_sym_dimless=ss(A_sym_dimless,B_sym_dimless,C_sym_dimless,D_sym_dimless)
#dimensionless computation but dimension having output
sys_sym_hybrid=ss(A_sym_dimless,B_sym_dimless,C_sym_hybrid,D_sym_dimless)
#------------state space expanded for altitude approximation----------------
temp_a=A_sym_dimless
temp_b=matrix([[0],[0],[0],[0]])
temp_c=matrix([[0,-V0,V0,0,0]]) #Assumption: Speed stays constant:V=V0; u=0=const
a_sym_dimless=vstack((hstack((temp_a, temp_b)),temp_c))
temp_d=B_sym_dimless
temp_e=matrix([[0]])
b_sym_dimless=vstack(((temp_d),temp_e))
c_sym_dimless=matrix([[V0,0,0,0,0],
[0,1,0,0,0],
[0,0,1,0,0],
[0,0,0,V0/c,0],
[0,0,0,0,1],
[0,-V0,V0,0,0]])
d_sym_dimless=zeros((6,1))
sys_extended=ss(a_sym_dimless,b_sym_dimless,c_sym_dimless,d_sym_dimless)
print (linalg.eig(A_asym_dimless)[0])
#---state space computation------------------------------------------------------
#-------------------------------------------------------------------------------
#-------inputs-------------
t=arange(0,150,0.01)
ude=[0]*len(t) #input vector for elevator deflection
x0=[0,0.01,0,0]
#--which model is selected----------------------------------------------------
#sys=sys_symmetric #standard dimension having
sys=sys_sym_hybrid #dimless computation, dim having outputs
#sys=sys_sym_dimless #dimless outputs
#sys=sys_extended #dimension having, extended for approx. ROC and altitude
#--what Input is selected------------------------------------------------------
x0=matrix([[0],[0.1],[0],[0]])
y=lsim(sys,ude,t) #Using input vector
#y=impulse(sys,t) #Impulse input
#y=step(sys,t) #Step input
#y=initial(sys,t,x0)
# y[0][:,0]: u
# y[0][:,1]: alpha
# y[0][:,2]: theta
# y[0][:,3]: q
# y[0][:,4]: h - for u=0
# y[0][:,5]: ROC - for u=0
#y[1]: t
#-----Matrix analysis--------------------------------------------------------
#--------dimensionless system--------------------------------------------------
print()
print('Symmetric Flight:')
print()
eigenvalues_A_sym_dimless=linalg.eig(A_sym_dimless)[0]
print ('Eigenvalues of Short Period:',eigenvalues_A_sym_dimless[:-2] )
print ('Eigenvalues of Phugoid:',eigenvalues_A_sym_dimless[-2:] )
eigenvalues_A_sym=linalg.eig(A_symmetric)[0]
print ('Eigenvalues of Short Period:',eigenvalues_A_sym[:-2] )
print ('Eigenvalues of Phugoid:',eigenvalues_A_sym[-2:] )
print()
T12_A_sym_dimless=log(0.5)/real(array(linalg.eig(A_sym_dimless)[0]))
print ('T1/2 of Short Period:',T12_A_sym_dimless[0])
print ('T1/2 of Phugoid:',T12_A_sym_dimless[2])
print()
Period_A_sym_dimless=2*pi/imag(array(linalg.eig(A_sym_dimless)[0]))
print ('Period of Short Period:',Period_A_sym_dimless[0])
print ('Period of Phugoid:',Period_A_sym_dimless[2])
print()
damping=damp(sys,doprint=False)[1]
print ('Damping of Short Period:',damping[0])
print ('Damping of Phugoid:',damping[2])
print()
natfreq=damp(sys,doprint=False)[0]*sqrt(1-damp(sys,doprint=False)[1]**2)
print ('Nat. Frequency of Short Period:',natfreq[0])
print ('Nat. Frequency of Phugoid:',natfreq[2])
print()
print ('Frequency of Short Period:',natfreq[0] / sqrt(1 - damping[0]**2))
print ('Frequency of Phugoid:',natfreq[2]/ sqrt(1 - damping[2]**2))
print()
#----------plotting-----------------------------------------------------------
plt.figure(1)
#plt.subplot(321)
#plt.title('Input in Elevator (rad)')
#plt.plot(t,array(ude),color='m',label='i')
plt.subplot(321)
plt.title('Velocity V (m/s)')
plt.plot(t,y[0][:,0]+V0,color='c',label='u')
plt.subplot(322)
plt.title('Angle of Attack alpha (rad)')
plt.plot(t,y[0][:,1], color='r', label='alpha')
plt.subplot(323)
plt.title('Flight Path Angle theta (rad)')
plt.plot(t,y[0][:,2],color='b',label='theta')
plt.subplot(324)
plt.title('Pitch Rate q (rad/s)')
plt.plot(t,y[0][:,3],color='g',label='q')
"""
plt.subplot(716)
plt.title('Altitude (m)')
#plt.plot(t,y[0][:,4],color='y',label='h')
plt.subplot(717)
plt.title('Rate of Climb (m/s)')
#plt.plot(t,y[0][:,5],color='k',label='h')"""
#plt.show()