Description
1 Objective
The main goal of this assignment is to become familiar with Simulink environment and start
working with the cart stations.
2 Your responsibility
Your duty is to answer all questions which have been asked throughout this assignment and submit
all your answers in addition to matlab codes and Simulink results.
3 Model Description
The equation of motion of a DC motor can be described by:
Jm
¨θ + (b +
KtKe
Ra
)
˙θ =
Kt
Ra
va
where θ is the shaft angle (in radians) of the motor and va is the applied voltage.
The system parameters are as follows:
• Jm = 0.01kgm2 be the inertia of the rotor and the shaft.
• b = 0.001Nmsec be the viscous friction coefficient
• Ke = 0.02V sec be the back emf constant
1
• Kt = 0.02Nm/A be the motor torque constant.
• Ra = 10Ω be the armature resistance
Note that this document uses SI units for which Ke = Kt
.
4 Questions
1. Implement the transfer function you derived in previous lab ( θ(s)
va(s)
) in simulink. You can use
blocks Transfer Fcn from continuous library, scope from Sinks library, and Signal Generator,
and Step, from Sources library. [10 marks] (In order to include the diagrams you can use
Print To File)
2. Using Step, find the rise-time and steady-state response of the system to a unit step function.
[5 marks]
3. Using Signal Generator or Sine Wave, measure response of the system to sine waves of
amplitude 1 and frequencies w = [0.1, 1, 10, 100, 1000]. [5 marks] Using these data, plot
Bode diagram(gain diagram) of the system. [10 marks] Using the transfer function and bode
command, plot the theoretical Bode diagram and then compare it with the diagram you
found by experiments. [10 marks]
Hint: Note that you have to use w = log10(input frequencies) as the x-axis and 20*log(gains)
as y- axis to draw your data points Bode diagram.
4. Implement the unity Feedback loop in Simulink. Repeat the steps of Q2 to derive the
Bode diagram of the feedback system. [10 marks] Using the closed-loop transfer function
you derived in previous session, plot the Bode diagram of the closed-loop system then plot
experimental bode diagram and theoretical one in one figure. [10 marks]
5. Implement a proportional controller in simulink. By changing the amount of proportional
gain K, find the corresponding K for which we get rise-time of 4 seconds. [10 marks]
6. Experimenting different proportional gains K in Simulink, find the proportional gain K for
which get, 20% overshoot. [10 marks]
7. Using a derivative block, and an integrator block, implement a PID controller for the system.
Suppose we name the gain block before the derivative block Kd, and the gain block before
the integrator block Ki
, and proportional gain Kp, observe the output of the system to unit
step function for different combinations of Ki
, Kd, Kp ∈ {0.1, 1, 10}(by different combinations
we mean fixing two of the gains and iterating over the last one). [15 marks]
2
Using the above experiment describe intuitively the impact of increment in Kd, Ki(individually),
on the step response of the system. [15 marks]
8. Setting Kd = 0, Find the step response of the system. [5 marks]
9. Setting Ki = 0, Find the step response of the system. [5 marks]
10. Follow instructions of the Lab Manual, observe the output of the system to a sine wave[It
would be checked by the TA]
11. Using a ruler find the correct linear position gain.(Convert the sensor’s output to the position
in mm)
12. Using previous linear position gain, plot the step-response of the system.[10 marks]
Hint: In order to bring the data out of Simulink environment you can use the To Workspace
block.
13. Alter the Simulink model such that you can observe velocity as output of the system.( V (s)
va(s)
),
and then plot the step-response. [10 marks]
14. Explain why the observed velocity on the scope is noisy.[5 marks]
3