UNIVERSITI TUN HUSSEIN ONN MALAYSIA
PROJECT: Transient Response Analysis with Matlab
SEMESTER 1
SESSION 2020/2021
COURSE NAME
: CONTROL SYSTEM/INSTRUMENTATION
& CONTROL
COURSE CODE
: BNR 37502/20703
SECTION
: 1, 2 & 3
DATE
: 11 NOVEMBER 2020
DURATION
: 6 WEEKS
INSTRUCTION
: ANSWER ALL QUESTIONS
TOTAL MARKS:
⁄40
BNR 37502/20703
INTRODUCTION
I.
-
Transfer functions (TF) are frequently used to characterize the input-output relationships or systems.
The applicability of the concept of the Transfer Function (TF) is limited to Linear Time-Invariant (LTI)
differential equation systems.
The transfer function (TF) of a LTI differential-equation system is defined as the ratio of the Laplace
transform (LT) of the output (response function) to the Laplace transform (LT) of the input (driving function)
under the assumption that all initial conditions are zero.
A. STEP RESPONSE.
-
The step function plots the unit step response, assuming zeros initial conditions.
The basic syntax is “step (sys)”, where sys is the Linear Time-Invariant (LTI) object.

The basic syntax commands are summarized below:
Command (Basic Syntax)
>> step(sys)
>> step(sys,tf)
>> step(sys,t)
>> [y,t]=step(sys,…)
>> step(sys1, sys2,…,t)
Use:
- generates a plot of a unit step response and displays a response
curve on the screen.
- The computation time interval ∆𝑡 and the time span of the response
𝑡𝑓 are determined automatically by MATLAB
- generates a plot of a unit step response and displays a response
curve on the screen for the specified final time 𝑡𝑓.
- The computation time interval ∆𝑡 is determined automatically by
MATLAB
- generates a plot of a unit step response and displays a response
curve on the screen for the user specified time 𝑡 where 𝑡 = 0: ∆𝑡: 𝑡𝑓
- Returns the output 𝑦, and the time array 𝑡 used for the simulation
- No plot is drawn.
- The array 𝑦 is 𝑝 × 𝑞 × 𝑚 where 𝑝 𝑖𝑠 length (𝑡), 𝑞 is the number of
outputs, and 𝑚 is the number of inputs.
- Plots the step response of multiple LTI systems on a single plot.
- The time vector 𝑡 is optional.
- You can specify line color, line style and marker for each system.
PS:


The steady state response and the time to reach that steady state are automatically determined.
The steady state response is indicated by horizontal dotted line
2
BNR 37502/20703
B. IMPULSE RESPONSE.
-
The impulse function plots the unit impulse response, assuming zeros initial conditions.
The basic syntax is “impulse (sys)”, where sys is the Linear Time-Invariant (LTI) object.

The basic syntax commands are summarized below:
Command (Basic Syntax)
Use:
- generates a plot of a unit impulse response and displays a response
curve on the screen.
>> impulse(sys)
- The computation time interval ∆𝑡 and the time span of the response
𝑡𝑓 are determined automatically by MATLAB
- generates a plot of a unit impulse response and displays a response
curve on the screen for the specified final time 𝑡𝑓.
>> impulse(sys,tf)
- The computation time interval ∆𝑡 is determined automatically by
MATLAB
- generates a plot of a unit impulse response and displays a response
>> impulse(sys,t)
curve on the screen for the user specified time 𝑡 where 𝑡 = 0: ∆𝑡: 𝑡𝑓
- Returns the output 𝑦, and the time array 𝑡 used for the simulation
- No plot is drawn.
>> [y,t]=impulse(sys,…)
- The array 𝑦 is 𝑝 × 𝑞 × 𝑚 where 𝑝 𝑖𝑠 length (𝑡), 𝑞 is the number of
outputs, and 𝑚 is the number of inputs.
- Plots the impulse response of multiple LTI systems on a single plot.
>> impulse(sys1, sys2,…,t)
- The time vector 𝑡 is optional.
- You can specify line color, line style and marker for each system.
PS:


The steady state response and the time to reach that steady state are automatically determined.
The steady state response is indicated by horizontal dotted line
3
BNR 37502/20703
II.
QUESTIONS
0.045
Q1. For the following second order system: 𝑇(𝑠) = 𝑠2 +0.025𝑠+0.045;
Using Matlab, to find:
a. The pole locations
(1 mark)
b. Damping ration 𝜉
(1 mark)
c. Un-damped natural frequency 𝜔𝑛
(1 mark)
d. Plot the poles on s-plane using Matlab
(3 marks)
e. Plot the step response using MATLAB.
(2 marks)
f. Based on your calculation, what is the type of response? Overdamped, underdamped,
undamped or critically damped? Why?
(2 marks)
Q2. For 𝒎 = 𝟎. 𝟏𝟎 𝒌𝒈, 𝒃 = 𝟎. 𝟒 𝑵 − 𝒔⁄𝒎, 𝒌𝟏 = 𝟔𝑵⁄𝒎, 𝒌𝟐 = 𝟒𝑵⁄𝒎 of the following
mechanical system in Figure Q(2):
Figure Q(2)
4
BNR 37502/20703
a. Draw the free body diagram (FBD)
(2 marks)
𝑋(𝑠)
𝑌(𝑠)
b. Derive the transfer function 𝐺(𝑠) = 𝑃(𝑠) and 𝐹(𝑠) = 𝑃(𝑠)
(4 marks)
c. On a single plot, obtain the response 𝑥(𝑡) and 𝑦(𝑡) for 𝑝(𝑡) a step input of
magnitude 10 𝑁
(3 marks)
d. On a single plot, obtain the response 𝑥(𝑡) and 𝑦(𝑡) for 𝑝(𝑡) an impulse input of
magnitude 10 𝑁
(3 marks)
e. Comment your results (plots) obtained in c and d.
(2 marks)
PS:
-
Write your report in 3-4 pages (Follow the Report Format)
-
For the Final Score (out of 25), the weightage system will be applied to the marks obtained.
End of questions.
5
(16 marks)
Report Assessment Rubrics
Faculty:
FACULTY OF ENGINEERING TECHNOLOGY
Programme:
BND/BNE
Course:
CONTROL SYSTEM / INSTRUMENTATION AND CONTROL
Code:
BNR 37502 / 20703
POPBL Activity: Implementation of Lean Concept into Automotive Maintenance activities
CLO 2, 4:
Limited/ No
Proficiency
Some Proficiency
Proficiency
High Proficiency
1
2
3
4
#REF!
Project Analysis and
Simulation
Project Report
Criteria
1.Able to employ Matlab for
interactive computations.
2. Able to generate plots and
export this for use in reports and
presentations.
3. Able to program scripts and
functions using the Matlab
development environment
4. Able to construct a function of
vector magnitude from Matlab
5. Able to perform vector plot (2D
and 3D) according to problem
given
6. Able to construct and
consolidate each computational
function to compute electric force
due to multiple charges
Subcriteria
(Project1):Reproduce matlab code for basic computation [Reproduce]
Level
P2 Guided
Response
Weight
Score
Able to produce
No be able to
basic coding for
Able to produce most Perfectly produce most
produce basic
Matlab function but of the basic coding for of the basic coding for
coding for matlab
very limited
Matlab function
Matlab function
function
proficiency
4
1.25
5
Project 2: Display final outcome screenshot from coding [Display]
P2 Set
Not able to
display screen
shot from matlab
output
Display partially
screen shot from
matlab output
Display most of the
screen shot from
matlab output
Display all screen shot
from matlab output
4
1.375
5.5
Project 2: Construct coding for computational function to compute
response of a function due to multiple forces [Construct]
C3 Mechanism
(basic proficiency)
Not able to
construct
appropiate
coding
Construct only
partial part of the
coding for matlab
function
Contruct highly
accurate coding for
required Matlab
function
Perfectly construct
matlab coding for
computational purposes
4
1.75
7
Display most of the
Graph from matlab
output
Display all required
graph from matlab
output
4
1.375
5.5
4
0.5
2
6.25
25
Project 2: Able to display 3D graph outcome [Display]
Project 2: Sketch manual calculation and compare with computed coding
[Manipulate]
P2 Set
C3 Mechanism
(basic proficiency)
Not able to
Display partially 3D
display 3D graph
graph from matlab
from matlab
output
output
Not be able to
demonstrate
manual
calculation
Demonstrate some
proficiency to
manually calculate
Demonstrate good
Perfect manual
proficiency of manual
calcuation wihtout error
calculation
Total