Question

9. A control system is given by the following state-space representation -8 101 [2 dt 1-6 00 y [1 0 0]x Please do the following: a. Find its transfer function representation. b. Calculate its zeros and poles c. Write a Scilab program to draw the step response and impulse response graphs in the same window with the step response graph in the upper half the window and the impuise response graph in the lower half the window. The time interval is: 0 s t s 6 with step size 0.05.

this problem needs to be done using SciLab

Answer 1

part a:

A = [-8 1 0;-16 0 1;-6 0 0];
B = [2;8;6];
C = [1 0 0];
D = 0;

SS = syslin('c',A,B,C,D); //defining state space
TF1 = ss2tf(SS); //finding state from transfer function

o/p:

--> TF1
TF1 =

2   
6 + 8s + 2s
-----------------
2 3
6 + 16s + 8s + s   

part b:

[z,p,k]=tf2zp(TF1); //finding zeros and poles and gain k

o/p:

--> z
z =

-3.
-1.

--> p
p =

-5.0861302
-2.4280067
-0.4858631

part c

t = 0:0.05:6;

subplot(211);
plot(t,csim('step',t,TF1));

subplot(212);
plot(t,csim('imp',t,TF1))

output:

0.6 0.4 0.2 0 02 0.4 0 D.8 1.2 14 1. 1.8 2 2.2 24 2.8 2.8 33.23.4 3.6 38 42 4.4 46 .8 52 6.4 58 6.86 0.5 20.4 0.6 0.8 1 1.2 1.4 1.8 1.8 2 2.2 2.4 2.8 2.8 33.2 3.4 3.6 3.8 4 424448486526.4 0.0 e