Question

Suppose that a system is shown in Figure 2. Based on for loop, write a piece of MATLAB code to calculate the closed loop poles for 03K35 and plot the outputs where the poles are represented by "W" letter. Find the interval of K parameter for stability using Routh-Hurwitz method. Calculate the poles of the closed loop transfer function where K attains the minimum value such that the system is stable. Figure 2: A unity feedback closed loop system

Please solve it with step by step MATLAB code, thank you!

Answer 1

The characteristic equation must be formulated in such a way that rootlocus can be drawn from it.

ie. (s^3+5*s^2+(k-3)*s+k) = (s^3+5*s^2-3*s) + k ( s+1) =0 => 1+k(s+1)/(s^3+5*s^2-3*s) =0

The loop transfer function that needs to be considered for the rootlocus plot is G(s) = (s+1)/(s^3+5*s^2-3*s).

MATLAB code is given below in bold letters.

clc;
clear all;
close all;

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

% define the plant
G = (s+1)/(s^3+5*s^2-3*s);

% define gain K
k = 0:0.1:100;

% plot the root locus
figure;
rlocus(G,k);

Root Locus 10 -2 E 4 -2 -3 .4 -5 -6 Real Axis (seconds)

noMial vw 3 RH Tablu 3 K-3 So For stabruG K-K-3 >0