Description

15MH302J – LINEAR AND DIGITAL CONTROL SYSTEMS
EXERCISE 4 ROOT LOCUS
LAB PREREQUISITES:
Exercise 1 to 3
PREREQUISITE KNOWLEDGE:
Fundamentals of MATLAB programming OBJECTIVES:
The objective of this exercise is to plot the root locus of given system and determine the gain for obtaining the different peak overshoots using MATLAB and SIMLINK PRELAB:
Draw the roots locus for the given open loop transfer function.

READINGS:
Introduction to Root Locus:
Application of the many classical and modern control system design and analysis tools is based on mathematical model. MATLAB can be used with systems given in the form of transfer function description. We are interested in how MATLAB can assist us in determining
• the number of branches.
• the starting and ending points of all the branches.
• the intersections of the root loci with the imaginary axis and the corresponding value of K.
• the system’s oscillating frequency associated with the gain K.
• the breakaway points.
• the value of K at breakaway point.
For any given system G(s) the following figure illustrates a closed loop proportional control.

15MH302J

The root locus of an (open-loop) transfer function is a plot of the locations (locus) of all possible closed loop poles with proportional gain K and unity feedback.

PROGRAMS, OBSERVATIONS AND INFERENCES
1. Write the Matlab codes for drawing root locus of the given open loop system G(s)= and
draw the output response for the desired poles selected from the root locus.

2. Write the Matlab program for calculating the gain for the given peak over shoot value and also draw the step response for the calculated gain value.

15MH302J
PROGRAM
clc; clear all; close all; num=[1]; den=[1 3 2 0]; sys=tf(num,den) cl_sys=feedback(sys,1) figure(1); step(cl_sys); figure(2); rlocus(num,den);
z=input(‘Enter the value for zeta’); w=input(‘Enter the value for omega n ‘); sgrid(z,w);
[k,poles]=rlocfind(num,den); new_clsys=feedback(sys*k,1) figure(3);
step(new_clsys);

15MH302J
RESULTS & INFERENCES:
Evaluation
Component Maximum Marks Marks Obtained
Pre-lab Tasks 10
In-Lab Tasks 20
Post-lab Tasks 10
Bonus Tasks 10
(This page must be the last page of the exercise)