Department of Mechanical Engineering
Control Systems Theory
Student Name:
Student ID:
Spring 2025
H.W. # 1
NOTE: The homework is part of your training and does not affect your grade. You can use (and I recommend
using) different software programs (e.g., MATLAB/Simulink, SciLab) to solve the problems and verify your
analytical answers. I also recommend using AI (with some caution) to enhance your understanding and assist in
solving the problems.
Question 1: Consider the following closed loop control systems
-
The room temperature control system
The aircraft altitude control system
Determine the following appearing in them and draw the closed loop diagram of the system
-
Plant
Input
Output
Disturbances
Sensors
Actuators
Measurement noises
Question 2: Solve the following differential equations,
𝑑𝑦
+ 2𝑥𝑦 = 0
𝑑𝑥
𝑥
𝑎𝑛𝑑
𝑑𝑦
+ 2𝑦 = sin(𝑥)
𝑑𝑥
𝑦(0) = 3
𝑎𝑛𝑑
𝜋
𝑦( ) = 0
2
Question 3: Solve the following ODEs analytically, Use MATLAB to draw 𝑦(𝑡) and compare their results. In all
cases 𝑦(0) = 1 and 𝑦̇ (0) = 0.5. Discuss about the
-
Damping and oscillatory behaviors,
Stability
𝑑2 𝑦
𝑑𝑦
+ 2 𝑑𝑡 + 5𝑦 = 0
𝑑𝑡 2
𝑑2 𝑦
𝑑𝑦
+ 5 𝑑𝑡 + 6𝑦 = 0
𝑑𝑡 2
𝑑2 𝑦
𝑑𝑦
− 2 𝑑𝑡 + 𝑦 = 0
𝑑𝑡 2
Question 4: Solve the following ODEs assuming 𝑦(0) = 1 for 𝑎 = −2, −1, 1, 2 and 𝑏 = 0, 2 Use MATLAB to
draw 𝑦(𝑡) and compare their results.
𝑑𝑦
+ 𝑎𝑦 = 𝑏
𝑑𝑥
Discuss about the
-
Transient response (which one is faster)
Stability