Specialized course Process Control at Norwegian University of
Life Sciences (NMBU), Spring 2018
Compulsory exercise to lessons in Lecture 2
For the
problems given below, send a short report presenting the results (plots and
calculations), and the Matlab scripts and the Simulink model to the teacher
in email no later than the deadline given in the lecture plan on the course
homepage. (Collect the files in a zip file, and send the zip file.)
1.
Controller tuning: Open the simulator Temperature
Control of Liquid Tank.
a.
Tune the controller as a PI controller using the Ziegler-Nichols’
method. Check the stability with the setpoint step response and also with a
disturbance step response (the ambient tank temperature can be regarded as
disturbance).
b.
As in Problem 1a, but use the Relaxed Ziegler-Nichols’ method.
c.
As in Problem 1a, but use the relay-method.
d.
As in Problem 1a, but use the Skogestad method.
e.
Find the gain margin GM and the phase margin PM of the control system
for (1) Ziegler-Nichols’ tuning (cf. Problem 1a) and for (2) Skogetad tuning
(1d). Are the values of GM and PM acceptable in each of the two cases?
2.
Implementation of a simulator of a
control system in Simulink:
a.
Implement in Simulink a simulator of the control system system containing
the components described below:
· The process is a time-constant
with time-delay system (i.e., time-constant system in series with a
time-delay). The process gain is 5, the process time-constant is 10 s, and
the time-delay is 2 s.
· An “input process disturbance” in
the form of a step signal that acts on the process input (i.e. the disturbance
is added to the control signal; most process disturbances are actually input
disturbances).
· A measurement filter in the form
of a time-constant filter with time-constant 1 s. Although you may implement
this filter using a transfer function block in Simulink, you shall here
implement the discrete-time filter algorithm in a MATLAB Function block.
· A PID controller. (You can use an
inbuilt PID controller block in Simulink.)
· Calculation of the IAE index.
Use a fixed step solver with time step of
0.01 s.
b.
Tune the PI controller with the Ziegler-Nichols’ method. Then, apply a
unit step in the process disturbance. What is the IAE index for time-interval
from zero until the response has virtually become constant?
c.
As Problem 2b, but now a PID controller.
d.
Probably, you will see here that the IAE index with the PID controller
is less than with the PI controller, indicating that PID is favourable. Despite
this, what is the reason why PI often often is preferred to PID in a
practical system? Illustrate with a simulation!
Updated 12 January 2018 by Finn Aakre Haugen, course teacher.
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