AERO 371 – Modelling and Control Systems - 1/3 - Midterm Exam, 08:45 – 10:00, March 10, 2026
CONCORDIA UNIVERSITY
GINA CODY SCHOOL OF ENGINEERING AND COMPUTER SCIENCE
DEPARTMENT OF MECHANICAL, INDUSTRIAL AND AEROSPACE ENGINEERING
AERO 371 – Modelling and Control Systems
Midterm Instructor: Youmin Zhang Date: March 10, 2026
____________________________________________________________________________________
Answer all two (2) questions. Time: 08:45 - 10:00 Location: H 411
Please put your name and ID number in all pages.
For all questions:
Justify clearly all your steps; Clearly show all equations and mathematical steps.
Answers without mathematical steps and/or justifications will be given a mark of zero.
Good Luck !
Problem 1 [20 marks]
Assume that the automotive suspension system we have solved in Quiz #1 (showed also as Figure 1
below) has following s-domain formulation between input 𝑦𝑦0 and output 𝑦𝑦2 as given below:
s+3
Y 2 ( s) = 2
Y 0 (s)
s + 3s + 2
1) Based on the Final Value Theorem of Laplace Transform (without solving for time response),
calculate the steady-state output (final value) of 𝑦𝑦2 subject to a road condition change as a unit
step function as disturbance/input y0 (t ) = 1(t ) for t > 0;
2) a) Calculate and show an approximate sketch of the system response y2 (t ) by using Laplace
Transform method when the road condition is subject to a unit step disturbance/input y0 (t ) = 1(t )
for t > 0 under zero initial condition of output 𝑦𝑦2; b) Identify the transient and steady-state terms
of the response you obtained;
3) If the road condition is subject to a unit impulse disturbance/input, calculate the system output
response and show an approximate sketch of the system output response in this case;
4) a) Calculate system response y2 (t ) as in 2) when the road condition is subject to a unit step
disturbance/input y0 (t ) = 1(t ) for t > 0 but under non-zero initial condition with output
=y2 (0) 1,=y 2 (0) 0 ; b) Identify the forced and free (non-forced) response terms you obtained
(Optional: 5 bonus marks if you solve this sub-question correctly).
(t)
Figure 1: An automotive suspension system
, AERO 371 – Modelling and Control Systems - 2/3 - Midterm Exam, 08:45 – 10:00, March 10, 2026
Problem 2 [20 marks]
Assume that the transfer function model of the above system is given by:
Y 2 (s) s +1
G (s)
= = 2
Y 0 ( s) s + 6s + 8
1) Determine system poles and zeros and sketch the pole-zero plot. Judge the stability of the system
and explain your answer;
2) What are the values of damping ratio ( ζ ) and natural frequency ( ωn ) of the above system? How
do the damp ratio and natural frequency changes affect the dynamic performance of the system?
3) Calculate and show an approximate sketch of the system response y2 (t ) when the system is
subject to a unit step input y0 (t ) = 1 for t > 0. Identify the transient and steady-state terms of the
response. If a step input y0 (t ) = 2 for t > 0 is used as system input, what changes will have in the
above step response?
4) List the four fundamental characteristics to represent the performance of a physical/dynamic
system, which we have described during the lectures. Write and mark the five performance
specifications on the sketched step response you obtained in 3);
5) What are the values of damping ratio ( ζ ) and natural frequency ( ωn ) if the above system changes
to = Y 2 (s) s + 1 with a new parameters design/choice in the system?
G (s) = 2
Y 0 ( s) s + 4s + 8
Compare with the original system, please explain (without solving the time response) how about
the changes of the system performance (Optional: 5 bonus marks if you solve this sub-question
correctly).
CONCORDIA UNIVERSITY
GINA CODY SCHOOL OF ENGINEERING AND COMPUTER SCIENCE
DEPARTMENT OF MECHANICAL, INDUSTRIAL AND AEROSPACE ENGINEERING
AERO 371 – Modelling and Control Systems
Midterm Instructor: Youmin Zhang Date: March 10, 2026
____________________________________________________________________________________
Answer all two (2) questions. Time: 08:45 - 10:00 Location: H 411
Please put your name and ID number in all pages.
For all questions:
Justify clearly all your steps; Clearly show all equations and mathematical steps.
Answers without mathematical steps and/or justifications will be given a mark of zero.
Good Luck !
Problem 1 [20 marks]
Assume that the automotive suspension system we have solved in Quiz #1 (showed also as Figure 1
below) has following s-domain formulation between input 𝑦𝑦0 and output 𝑦𝑦2 as given below:
s+3
Y 2 ( s) = 2
Y 0 (s)
s + 3s + 2
1) Based on the Final Value Theorem of Laplace Transform (without solving for time response),
calculate the steady-state output (final value) of 𝑦𝑦2 subject to a road condition change as a unit
step function as disturbance/input y0 (t ) = 1(t ) for t > 0;
2) a) Calculate and show an approximate sketch of the system response y2 (t ) by using Laplace
Transform method when the road condition is subject to a unit step disturbance/input y0 (t ) = 1(t )
for t > 0 under zero initial condition of output 𝑦𝑦2; b) Identify the transient and steady-state terms
of the response you obtained;
3) If the road condition is subject to a unit impulse disturbance/input, calculate the system output
response and show an approximate sketch of the system output response in this case;
4) a) Calculate system response y2 (t ) as in 2) when the road condition is subject to a unit step
disturbance/input y0 (t ) = 1(t ) for t > 0 but under non-zero initial condition with output
=y2 (0) 1,=y 2 (0) 0 ; b) Identify the forced and free (non-forced) response terms you obtained
(Optional: 5 bonus marks if you solve this sub-question correctly).
(t)
Figure 1: An automotive suspension system
, AERO 371 – Modelling and Control Systems - 2/3 - Midterm Exam, 08:45 – 10:00, March 10, 2026
Problem 2 [20 marks]
Assume that the transfer function model of the above system is given by:
Y 2 (s) s +1
G (s)
= = 2
Y 0 ( s) s + 6s + 8
1) Determine system poles and zeros and sketch the pole-zero plot. Judge the stability of the system
and explain your answer;
2) What are the values of damping ratio ( ζ ) and natural frequency ( ωn ) of the above system? How
do the damp ratio and natural frequency changes affect the dynamic performance of the system?
3) Calculate and show an approximate sketch of the system response y2 (t ) when the system is
subject to a unit step input y0 (t ) = 1 for t > 0. Identify the transient and steady-state terms of the
response. If a step input y0 (t ) = 2 for t > 0 is used as system input, what changes will have in the
above step response?
4) List the four fundamental characteristics to represent the performance of a physical/dynamic
system, which we have described during the lectures. Write and mark the five performance
specifications on the sketched step response you obtained in 3);
5) What are the values of damping ratio ( ζ ) and natural frequency ( ωn ) if the above system changes
to = Y 2 (s) s + 1 with a new parameters design/choice in the system?
G (s) = 2
Y 0 ( s) s + 4s + 8
Compare with the original system, please explain (without solving the time response) how about
the changes of the system performance (Optional: 5 bonus marks if you solve this sub-question
correctly).
