Question

Please solve parts (a) and (b) neatly and show problem solving. Ignore reference to part 1, but please still plot the root loci.

For the system given in Figure 1 a) Design a PD compensator with the transfer function: to give a dominant root of the closed-loop characteristic equation of the compen- sated system at s -1+j1 (i.e., a settling time Ts of less than 6 seconds and a maximum overshoot Mo of less than 10%). Required Pre-Practical work] (b) Indicate the locations of the compensated system's closed-loop poles. Plot the root loci of the compensated system in the same window as Graph 1 (defined in Part 1(a)). Comment on the change of the closed-loop system stability. 21 G(s) M Figure l A servo control svstem

Answer 1

Dominanr LS.loni 180 tan 25 USc 01 A 28 21 (s 3335) 4 Kp_ 0-1428× 1.3335:11905

I have used MATLAB to plot the closed loop locations of the poles and the root locus plot.

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define the laplace variable s
s = tf('s');

% define the controller transfer function
Gc = 0.1428*(s+1.3335);

% define the plant transfer function
Gp = 21/(s*(s+1)*(s+3));

% plot the closed loop system poles
figure;
pzmap(feedback(Gc*Gp,1));

% root locus plot
figure;
rlocus(Gc*Gp);

pole zero map:

Pole-Zero Map 0.8 0.6 0.4 to 8 0.2 2 0.2 0.4ト -0.6 -0.8 㟖 0.5 1.5 -2 2.5 Real Axis (seconds)

root locus:

Root Locus 6 4 2 -6 0.5 -8 3.5 0.5 2.5 -3 Real Axis (seconds)

the closed loop poles are stable from the root locus plot.