Question

6. Given the following transfer function, IAs 12) 100s $2 +4s 20 (a) realize the filter using the canonical form (Direct Form II). (b) determine its state equation description (c) suppose (t)2u(t), determine the solution to the state equation in the Laplace domain, and in the time domain using Matlab

Answer 1

Given transfer function H (s) = 100 s/s^2 + 4s + 20 canonical form (Direct Forms II) for the given transfer function is given by H (s) = 100 (s + 2) - 200/(s + 2)^2 + (4)^2 H (s) = 100 (s + 2)/(s + 2)^2 + (4)^2 - 200/(s + 2)^2 + (4)^2 for s + a/(s + a)^2 + (b)^2 doubleheadarrow 1 e^- a T_s cos b T_s z^- 1/1 2 e^- a T_s cos b T_s z^- 1 + e^- 2 a T_s z^- 2 b/(s + a)^2 + (b)^2 doubleheadarrow e^- a T_s sin b T_s z^- 1/1 - 2 e^- a T_s cos b T_s z^- 1 + e^- 2a T_s z^- 2 using impulse invariant method let us consider T_s = 1 100 (s + 2)/(s + 2)^2 + (4)^2 rightarrow 100 [1 - e^- 2 cos 4 z^- 1/1 - 2 e^- 2 cos 4 z^- 1 + e^- 2 (2) z^- 2]