Ch: Model Conversion from State Space to Transfer Function and Zero-Pole-Gain

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