Higher Colleges of Technology
MCE 4603 – Control Systems -Lab 5
Faculty of Engineering Technology and Science
Academic Year
Semester
Course Code - Name
Program
Instructor Name
Lab Instructor
Lab Title
Date
Students HCT ID
2019 – 2020
☒ Fall
☐ Spring
☐ Summer
MCE 4603 – Control System
Mechanical Engineering Technology
Dr. Ismail Ladipo
Jamil Fayyad
Lab 4: Routh Hurwitz Stability using Matlab
07/04/2020
Student Names
Abdulla Adil - H00373075
Abdulla Yaqoob - H00373072
Yousef Salim - H00353277
Hussain Ali – H00367159
CRN
For Evaluator’s Use Only:
Object of Evaluation
Max. Marks
Obtained
Approved by:
Lab 5: Control Systems
Part A
Part B
Part C
20
40
30
Date:
Performance
Evaluation
10
Total
100
Higher Colleges of Technology
MCE 4603 – Control Systems -Lab 5
Introduction:
The Routh-Hurwitz criterion shows that all systems can be stable only if all the roots in the first column have
the same sign and there is no same sign or the sign is changed. The first column is equal to the number of roots
in the characteristic equation in the right half of the map. That is, it is equal to the number of roots that have a
positive real part.
Objective:
The objective of this exercise is to study system stability using Routh-Hurwitz Approach.
List of Resources
 Matlab
 Experience Controls Mobile Application
System under Test:
Given the unity feedback systems below.
Part 1 (Analysis):
Obtain the following:
a. The Forward Path Transfer Function “G(s)”
b. The Feedback Transfer Function “H(s)”
c. The Open loop Transfer Function “O(s)”
d. The System Closed Loop Transfer Function “T(s)”
e. The System Characteristic Equation.
Lab 5: Control Systems
Higher Colleges of Technology
MCE 4603 – Control Systems -Lab 5
Part 2 (Calculation): Students Homework
a. Show manually (by hand on a paper) range of K for stability.
Lab 5: Control Systems
Higher Colleges of Technology
MCE 4603 – Control Systems -Lab 5
Part 3 (Simulation)-Laboratory:
Using Matlab, obtain the following:
a. Develop an m-file to compute the closed loop function
b. Range of Gain “K” where the system is stable
Lab 5: Control Systems
Higher Colleges of Technology
MCE 4603 – Control Systems -Lab 5
Part 4 (Mobile application)-NOT GRADED
Download the “Experience Controls Application” on your mobile:
a. Click on “Review System Stability”, answer questions from 1 to 8 and check your answers.
b. Click on “Routh-Hurwitz”, read Routh-Hurwitz Criterion and check your understanding by answering all questions.
c. This application will help you review different subjects, try it.
Lab 5: Control Systems
Higher Colleges of Technology
MCE 4603 – Control Systems -Lab 5
Part 5 (Conclusion)
In part 2 we applied Routh Hurwitz law to know the range of K for stability by using the given function and we
found that the overall K range for stability was K>4. while in part 3 of the experiment, we learned how to
develop an m-file to compute the closed-loop, also we knew the range of gain for K where the system is stable
or where it's unstable so in the graph from the zero in the x-axis all the variables on right hand in the S plain
will give you unstable system and anything on the left-hand side from the zero it's going to give us a stable
system.
References
www.javatpoint.com. 2021. Control System Routh Hurwitz Stability Criterion - javatpoint. [online] Available at:
<https://www.javatpoint.com/control-system-routh-hurwitz-stability-criterion> [Accessed 1 November 2021].
Report Requirements:
A. Report must be typed
B. Report must include all calculation details
C. Report must include Matlab script file
D. Report must include simulation results, Graphs with measurement and title shown.
E. Report must include your conclusion (part 5)
Lab 5: Control Systems