A temperature control system can be modelled by the following transfer function G(s), where – s e W...

Question

A temperature control system can be modelled by the following transfer function G(s), where – s e W represents a pure time delay in the system and t=1. You are
	
Document Preview: Assignment 1 1 
 
Assignment 1 
Due date: 7 April 2017 
Value: 20% 
Total marks: 200 
Penalty for late submission: 5% per day 
 
A temperature control system can be modelled by the following transfer function G(s), 
– s
e
where  represents a pure time delay in the system and t=1. You are required to 
implement a digital PID controller to track the temperature setting without error. 
 s
Cs () 5e
Gs () 
Ms () s 5
1. Analytically find the open-loop system response c(t) to a unit step input and plot 
the response. 
(30 marks) 
2. Based on sampling theorem, determine a suitable sample interval T for the rest of 
the assignment. (Hint: Use Bode plots of G(s) to determine the system’s cut-off 
frequency. At cut-off frequency the magnitude plot is about 3dB below the 
magnitude of the low frequency. The cut-off frequency can be considered as the 
highest frequency component. Choose k = t/T as an integer for calculation 
convenience). 
(40 marks) 
3. Derive the discrete-time system transfer function G (Z) from G(s). 
HP
–sk

(Hint:Ze G s  z Z Gs , where kT  / , and keep T as a parameter until

the final results are available). 
(30 marks) 
4. Design a digital Proportional (P) controller to form a unit feedback control system, 
and optimise its parameter P with respect to the performance criterion IAE using 
the steepest descent minimisation process. Simulate the P controller system and 
M
plot its response for a unit step input (The performance criterion IAE | e | ). 
 k
k 0
(Please provide the plots that show the initial and the final/optimal responses).  
(50 marks) 
  
© University of Southern Queensland2 ELE3105 – Computer controlled systems

5. If the P controller is replaced with a PID controller, using the steepest descent 
minimisation process again to optimise the PID controller with respect to the 
M
performance criterion IAE | e | for a unit step input. (Please also provide the 
 k
k 0
plots that show both the initial and the final/optimal responses)....

David · Accepted Answer

Assignment 1 
Solution 1 : 
Analytical solution:
Therefore the Inverse laplace of above function with time delay        
 ( )  (     (   )) (   ) 
The plot is given below.  
MATLAB Code: 
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 
%%                             Assignment 1                              %% 
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 
delay  time with 
)5(
5
)5(
5
)5(
5
)5(
5
)(1
)()()()(:1
11 

























ss
L
ss
eL
ss
e
ss
e
s
sG
s
sGsRsGsCAss
s
s
s
%% Cleanup the workspace 
clc; 
clear; 
close all; 
%% Program starts here 
%% Verification of Analytical step Response 
tau=1; 
num = 5; 
den = [1 5]; 
P = tf(num,den,'InputDelay',tau); 
P0 = tf(num,den); 
step(P,'r');

A temperature control system can be modelled by the following transfer function G(s), where – s e W represents a pure time delay in the system and t=1. You are Document Preview: Assignment 1 1...

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment