Example 8 -- Model Conversion from State Space to Transfer Function and Zero-Pole-Gain
Given the system
.
X = AX + BU
Y = CX + DU
where
[-4.12 -17.4 -30.8 -60] [1]
A = [1 0 0 0 ], B = [0], C = [4 8.4 30.78 60], D = 0
[0 1 0 0 ] [0]
[0 0 1 0 ] [0]
find the transfer function, zeros and poles of the system.
Answer:
The transfer function of this system is
4*s^3 + 8.4*s^2 + 30.8*s + 60
---------------------------------------
s^4 + 4.12*s^3 + 17.4*s^2 + 30.8*s + 60
The zeros, poles and gain of the system are
zeros = -0.05 + 2.738156i, -0.05 - 2.738156i, -2.0
poles = -1.797086 + 2.213723i, -1.797086 - 2.213723i,
-0.262914 + 2.703862i, -0.262914 - 2.703862i
k = 4
Program in Ch
Output in Ch
Program in MATLAB
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