Question

A block() d,agram 억 a pos s Show har hon Cot ol servomech awisnm a, use Wadlal tu sketch the Root locus Versus K fbr kT-O (kr cstla tachometer Redback) to k: 4. tur these oco hous estimak bu transient espouse paror 9. 0., and tse r k:4, uhe Walob to skatoh tu root lotus versus k.

Answer 1

MATLAB code is given below in bold letters. clc; close all; clear all; % define the laplace variable s s = tf('s'); % define the loop transfer function L = 1/(s*(s+1)); % define the gain k = 0:0.01:10; % plot the root locus figure; rlocus(L,k); From the abvoe root locus plot, it is observed that for gain k = 4, the percent overshoot is 44.4% damping ratio = 0.25. rise time = (pi-acos(0.25)) / (wn*sqrt(1-0.25^2)) =   0.9416 seconds. settling time = 4/ (zeta*wn) = 4/(0.25*2) = 8 seconds. Question c MATLAB code: % loop transfer function for obtaing rootlocus with respect to KT is given below L = s/(s^2+s+4); % plot the root locus figure; rlocus(L); Root Locus 1.5 0.5 0.5 -2 -2.5 43.5 -3-2.5 -21.5 -1 0.5 0 0.5 Real Axis (seconds)