# LAB 6 ```Lab Title:
Sketch Root Locus Plots in MATLAB
Course:
90(A) EC
Group No:
02
Group Members:
N/C Zain Ul Abidin (172105)
Maryam (17090012)
Prepared by:
Submitted to:
Date Submitted:
11 February 2020
Given a unity feedback system that has the forward transfer function
𝐺 𝑠 = 𝐾(𝑠+2) / (𝑠^2−4𝑠+13)
do the following:
(a) Sketch the root locus.
(b) Find the imaginary-axis crossing.
(c) Find the gain, K, at the jω-axis crossing.
(d) Find the break-in point.
(e) Find the angle of departure from the complex
poles.
Solution
s = tf('s')
G = tf([1 2],[1 -4 13])
RLocusGui(G)
s=
s
Continuous-time transfer function.
G=
s+2
-------------s^2 - 4 s + 13
Xfer Function Info
Completed Root Locus
Cross Imag. Axis
Changing K Changes Closed Loop Poles
Angle of Departure
Break-Out and In Points on Real Axis
Given the unity feedback system of Figure below,
find the angle of departure from the complex poles and sketch
the root locus.
Also, do the following:
(a) Find the imaginary-axis crossing.
(b) Find the gain, K, at the jω-axis crossing.
(c) Find the break-in point.
SOLUTION
Completed Root Locus
Angle of Departure
Choose Pole Location and Find K
Break-Out and In Points on Real Axis
Locus does not cross imaginary axis.
```