I have a LTI system which I am modeling using scipy.signals. But I get different results when using TransferFunction or StateSpace. Besides the magnitudes for both the bode plot and the step response being different, the StateSpace representation add two more zeros on the LTI system I know are not there. I know for a fact the two descriptions should be equivalent (at least I think I do), because I re did the math several times. Could someone please help me explain what is happening?
the for the transfer function:
from params import *
numeratorthetaact = [Kt*Jl/(L*Jl*Ja), Kt*(betal+betac)/(L*Jl*Ja), Kt*kc/(L*Jl*Ja)]
denominatorthetaact = [1.0,
(L*betac*(Ja+Jl))/(Jl*Ja) + R/L,
(Ja+Jl)*(L*kc+R*betac)/(Jl*Ja*L) + (Kt*Kb)/(Ja*L),
(R*kc*(Ja+Jl))/(L*Jl*Ja) + (betac*Kt*Kb)/(L*Jl*Ja),
(kc*Kt*Kb)/(L*Jl*Ja),
0.0]
tfact = TransferFunction(numeratorthetaact, denominatorthetaact)
sysact = lti(tfact.num, tfact.den)
print "Zeros: ", sysact.zeros
print "Poles: ", sysact.poles
t, swact = step(sysact, T = time)
freqrad = numpy.multiply(frequency, 2.0*numpy.pi)
wrad, magact, phaseact = sysact.bode(w=freqrad)
whz = numpy.multiply(wrad, 1.0/(numpy.pi*2.0))
p.subplot(3,1,1)
p.plot(t, swact, label="Step Galvo")
p.legend()
p.subplot(3,1,2)
p.semilogx(whz, magact, label="Freq Galvo")
p.legend()
p.grid()
p.subplot(3,1,3)
p.semilogx(whz, phaseact, label="Phase Galvo")
p.legend()
p.grid()
p.show()
The code for StateSpace
from params import *
matrixA = numpy.array([[-(betaa+betac)/Ja, -kc/Ja, betac/Ja, kc/Ja, Kb/Ja],
[1.0, 0, 0, 0, 0],
[betac/Jl, kc/Jl, -(betal+betac)/Jl, -kc/Jl, 0],
[0, 0, 1.0, 0, 0],
[-Kb/L, 0, 0, 0, -R/L]])
matrixB = numpy.array([[0],
[0],
[0],
[0],
[1.0/L]])
matrixC = numpy.array([[0, 1.0, 0, 0, 0]])
matrixD = 0.0
ssact = StateSpace(matrixA, matrixB, matrixC, matrixD)
sysact = lti(ssact.A, ssact.B, ssact.C, ssact.D)
print "Zeros: ", sysact.zeros
print "Poles: ", sysact.poles
t, swact = step(sysact, T = time)
freqrad = numpy.multiply(frequency, 2.0*numpy.pi)
wrad, magact, phaseact = sysact.bode(w=freqrad)
whz = numpy.multiply(wrad, 1.0/(numpy.pi*2.0))
p.subplot(3,1,1)
p.plot(t, swact, label="Step Galvo")
p.legend()
p.subplot(3,1,2)
p.semilogx(whz, magact, label="Freq Galvo")
p.legend()
p.grid()
p.subplot(3,1,3)
p.semilogx(whz, phaseact, label="Phase Galvo")
p.legend()
p.grid()
p.show()
The resulting plots:
StateSpace vs TransferFunction
It is also worth mentioning that i get a BadCoefficients: Badly conditioned filter coefficients (numerator): the results may be meaningless "results may be meaningless", BadCoefficients) error when running the StateSpace code.
Thank you
