Question

6, Fig. 4 shows three systems. System 1 is a positional servo system. System Π is a positional servo system with PD control action. System III is a positional servo system with velocity feedback. Compare the unit-step, unit-impulse, and unit-ramp responses of the three systems by using MATLAB. Which system is best with respect to the speed of response and maximum overshoot in the step response? R(s) C(s) #5s + 1) System I R(s) CI(s S1 +0.8)6-D) System II R(s) Cu(s 5s +1 0.8 System II Fig. 4

Answer 1

Matlab Code:

%system 1
G1 = tf(5,[5 1 0]);
G1 = feedback(G1,1);

%system 2
G2 = tf([0.8*5 5],[5 1 0]);
G2 = feedback(G2,1);

%system 3
G3 = tf(5,[5 1]);
G3 = feedback(G3,0.8);
I = tf(1,[1 0]);
G3 = feedback(G3*I,1);

%step
step(G1);hold all;
step(G2);hold all;
step(G3);
legend('system1','system2','system3');
hold off
%impulse
impulse(G1);hold all;
impulse(G2);hold all;
impulse(G3);
legend('system1','system2','system3');
hold off
%ramp
t = 0:0.1:50;
lsim(G1,t,t);hold all;
lsim(G2,t,t);hold all;
lsim(G3,t,t);
legend('system1','system2','system3');
title('unit ramp input response')

Step Response 1.8 system 1 system2 1.6 system3 1.4 1.2 E 0.8 0.6 0.4 0.2 0 0 10 20 30 40 50 60 Time (seconds)

Impulse Response system1 0.8 system2 system3 0.6 0.4 9 0.2 0.2 0.4 0.6 0.8 0 10 20 30 40 50 60 Time (seconds)

unit ramp input response 50 system 1 system2 45 system3 40 35 a 30 E 25 4 20 15 10 5 0 0 50 40 30 20 10 Time (seconds)

Clearly, system 1 has higher overshoot in the step response.

system 2 is faster since it reaches the value 1 quicker than others.