Question

DP6.3 A unity negative feedback system with K(s 2) s(1 Ts)(1 + 2s) G,(s)G(s) has two parameters to be selected. (a) Determine and plot the regions of stability for this system. (b) SelectT and K so that the steady-state error to a ramp input is less than or equal to 25% of the input magnitude. (c) Determine the percent overshoot for a step input for the design selected in part (b)

I understand most o f the problem. I manly need help with the plots for part a and c. My teacher requires me to use matlab to plot them.

Answer 1

3 3 t K 2-Y (21T)

S CIts) (14%)
matlab code for step response:

clc;

clear all;

close all;

s=tf('s');

g=2*(s+2)/(s*(s+1)*(1+2*s));% plant and controller transfer function

step(feedback(g,1));grid % step response of compensated system

Step Response System untitied Peak ampinude: 1.81 Overshoot ( Artime (seconcs):2.T 1 A 12 Systemc untitied Setting time (seconds):107 System: unttied Hise time (seconds: 0.909 0.4 50 100 150 Time Iseconds)