Control System Design & Analysis

Control System Design & Analysis
Coursework Specification
Objectives
To investigate the control of a process using P and PI controllers
To gain experience of using a software package for computer simulation of control systems
Introduction
The process to be controlled is a liquid level process consisting of 2 storage tanks.
The process dynamics are described by the following transfer function:
where
H
G  s =
H
2
 s 
M  s 
=
K

T
1
s+1

2
2
is the level in tank 2 and M is the input to the inflow valve of tank 1.
Choose values for your process parameters using your date of birth:
K = day of birth (in range 1 to 31)
T
1
= month of birth (in range 1 to 12)
Method
1. Open Loop Step Response
a) Simulate the process transfer function with a unit step change in input.
b) Take required measurements from the response in a) for use in the Ziegler-Nichols open loop PID
tuning method.
2. P control
a) Design a P controller gain (Kc) for the process using your results in part 1 and Ziegler-Nichols
open loop method. Simulate the closed loop P control response to a unit step input.
A PID block can be used to simulate the controller, shown in the following example diagram.
Transfer Fcn is the process. PID, Multiplexer (MUX) and Sum simulation blocks are used.
Note The PID block implements a parallel form of the controller:
This should be compared to the standard form:
G
c
 s=K
c
G
11 /T
c
i
 s=K
sT
d
P
K
s
, to enter the correct
values for the block.
b) Adjust Kc and simulate the response to achieve a percent overshoot (%OS) of between 10 to
20%.
c) Choose one other value for Kc to show the effect of changing this parameter on the controlled
response. Include:
I
i. a plot of this step response,
ii. a table comparing the percent overshoot (%OS), settling time and steady state error for
the three values of gain used in parts 2a, b and c.
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General Note: To get a more accurate simulation (more data points, smoother plots), set the Max.
Step Size (Simulation → Simulation Parameters menu on SIMULINK model) from ‘auto’ to a
smaller value, e.g. 0.1.
sK
D
s
[20]
3. PI control
a) Design a PI controller (Kc and Ti) for the process using your results in part 1 and Ziegler-Nichols
open loop method. Simulate the closed loop PI control response to a unit step input.
Compare the response with the previously designed P controller in terms of %OS, settling time and
steady state error.
b) Adjust Kc if required to achieve a percent overshoot (%OS) of between 10 to 20%. With this
value of Kc, choose two other values for Ti to show the effect of changing the integral action time
(Ti) on the controlled response. Include:
i. plots of the step responses (max. 3),
ii. a table comparing the percent overshoot (%OS), settling time and steady state error for
the three values of Ti used.
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4. Effect of an input disturbance
Add a step disturbance at the input of the process. (Use a ‘Sum’ block to add the disturbance to the
controller output). This will simulate a change in the input flow to tank 1.
With the controller set point set at 0 (no change), apply a unit step change in the disturbance and
obtain the two output responses when using the P and PI controllers. Use the previous controller
settings from 2b and 3b which achieve approximately 10-20 %OS for a set point change. Measure
and compare the maximum output response, settling time and steady state error for the two
controllers in this test.
In your discussion, can either controller remove the effect of the disturbance in steady state?
[20]
Presentation [10]
Bonus marks (e.g. overall quality, conciseness, clarity, good discussions, additional relevant
investigations,…) [10]
Report
Submit a report in PDF format on Blackboard by the deadline.
Include a separate section for each of the main parts above. Each section should include (where
appropriate) methods used and explanations, appropriate diagrams (e.g. SIMULINK (or SCILAB)
diagrams, simulation results) and a discussion of the results.