1. ERT 210 DYNAMICS AND PROCESS CONTROL CHAPTER 11 – MATLAB TUTORIAL
Prepared by:
Puan Hairul Nazirah Abdul Halim

2. Transfer function
To model a transfer function in MATLAB, define the numerator and denominator polynomials as 1-row matrices first.
Then use the ‘ tf ’ command in Matlab.

3. Example 1 Transfer function is given by:
Model the transfer function in MATLAB.
Solution
Using MATLAB, define the denominator and numerator as matrices:
>> num = 1;
>> den = [1 2 3];
>> G = tf(num,den)
OR >> G = tf(1, [1 2 3])

4. Example 2 Model the following transfer function in MATLAB. Solution
Using MATLAB, define the denominator and numerator as matrices:
>> num = 1;
>> den = [1e-9 1e-6 1];
>> G = tf(num,den)
OR >> G = tf(1, [1e-9 1e-6 1])

5. Exercise 1 1) 2)

6. Model interconnections
Multiple models can be manipulated using normal mathematical functions (addition and multiplication)
For models in series, multiply them
For models in parallel, add them

7. Model interconnections

8. Model interconnections

9. Model interconnections
Example 3
Given that
Find the total transfer function if both of them are:
a) Connected in series (multiply)
b) Connected in parallel (add)

10. Model interconnections
Solution
>> G1 = tf([1 4], [1 3 2])
>> G2 = tf(1, [1 5])
>> G_series = G1*G2
>> G_parallel = G1+G2

11. Model interconnections
Example 4
For feedback loop above, overall transfer
function is

12. >> gl = tf ([1 4] , [1 3 2])
>> g2 = tf (1, [1 5]);
>> g_closed = feedback(gl,g2)

13. Example 5 In the diagram above, it is given that
Find the overall transfer function using MATLAB

14. Solution
>> g1=tf(1, [1 2]);
>> g2=tf([1 3] , [1 4 5]);
>> g3=tf(4, [1 0]);
>> g4=tf(10, [1 10]);
>> g12=g1+g2;
>> g123=g12*g3;
>> g_overall=feedback(g123,g4);

15. Refer to Appendix C – Use of MATLAB in Process Control

16. COMPUTER SIMULATION
WITH SIMULINK

17. Consider a dynamic system consisting of a single output Y and two inputs U and D:
Y(s) =Gp(s) U(s) + Gd(s) D(s)
Where:
Then, draw a Simulink block diagram (Figure C.1).

18. Figure C.1 Simulink block diagram

19. Figure C. 2. Response for simultaneous unit
Figure C.2 Response for simultaneous unit step change at t = 0 in U and D from the simulink diagram in Fig. C1

20. Figure C.4 Closed loop diagram

21. Closed-loop response with Setpoint Changes
Click block D
Set the Final Value to 0 (zero)
Click Ysp
Set te Final Value to 1 (one)
Set the Stop time = 50 (In the simulation parameter menu)
Click Start from the Simulation menu
Type plot(t,y) to view the response.

22. Figure C.5 Unit set-point response for the closed-loop system in Fig. C4 with
P = 1.65, I = 0.23, D = 2.97

23. Figure C.5 Unit set-point response for the closed-loop system in Fig.C4 with P = 1.65, I = 0.23, D = 2.97

24. Closed-loop response with Disturbance Changes
Click block Ysp
Set the Final Value to 0 (zero)
Click D
Set the Final Value to 1 (one)
Set the Stop time = 50 (In the simulation parameter menu)
Click Start from the Simulation menu
Type plot(t,y) to view the response.

25. Figure C. 6. Closed loop response for a unit
Figure C.6 Closed loop response for a unit step disturbance (Stop time = 50)

26. Figure C. 6. Closed loop response for a unit
Figure C.6 Closed loop response for a unit step disturbance (Stop time = 150)

27. Tuning by Ziegler-Nicholas Method
What is Kcu and Pu?
Calculate Kc, τI and τD for PID setting.