Question

4 bloclk diagaa poiton Coutral servome ch awism s Shown he , use Wodlal tu sketch the Root locus ver sus k tor kr0 (k s t tachometer Reelback |bTuckale onth. Iocus 억 (a) かǐ not location s Corresponding 1 to k: 4. r灿ese locohous estimak bu trans ient espouse paramekr e 9. 0., and ell. 白和r k, 4, use Wallab to skatehtlu-root locus versus kT please alse wnke wwich ow t gug to iu denowka, nonuhaho

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);

Root Locus -2 -3 -4 0.2 -0.8 0.6 -0.4 0.2 Real Axis (seconds)

Root Locus System: L Gain: 4 Pole: -0.51.94i Damping: 0.25 Overshoot(%): 44.4 Frequency (rad/s) 2 -1 -2 .4 -0.6 0.4 -0.2 0.2 -0.8 Real Axis (seconds)

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)