Specialized course Process Control at Norwegian University of
Life Sciences (NMBU), Spring 2018
Compulsory exercise to lessons in Lecture 1
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.
1.
Some feedback control basics: Open the simulator Temperature
Control of Liquid Tank.
a.
Use the PI(D) controller. What happens to the stability of the control
system if the process time-delay is relatively large?
b.
Use the PI(D) controller. Include random temperature measurement noise
with max amplitude of 0.2 deg C. The D-term of the controller can be
activated by increasing Td from 0 to one quarter of the integral time (Ti),
which is the ratio between Td and Ti according to Ziegler and Nichols. Compare
the behaviour of the control signal using PI controller and PID controller.
With PID controller, select a filter time-constant so that you become content
with the noise level in the control signal.
c.
Use the On/off controller. Is the mean value of the control error zero
or non-zero?
2.
Simulation of transfer function: In Chapter 2 of the textbook
Basic Dynamics and Control, a mathematical model of a mass-spring-damper system
is presented.
a.
Derive the transfer function, H(s), from force F to position y.
b.
Try to replicate the responses shown in Figure 2.8 in the textbook by using
the lsim function in Matlab.
c.
Implement a simulator of H(s) in Simulink, and try again to replicate
the responses shown in Figure 2.8 in the textbook. The simulation should be
run using the sim function in a Matlab
script. Also in that script, the model parameters should be defined (the
Simulink block diagram should contain no numerical values), and the responses
should be plotted using the plot
function (but you may also include Scopes in the block diagram).
3.
Simulation of state-space model
represented as a block diagram: See Exercise 2.3 in the Basic Dynamics and Control exercise book.
a.
Implement a simulator of the system in Simulink using a fixed-step
solver (e.g. the ode1 solver which implements Euler forward numerical
integration). Use the MATLAB Function
block to calculate the time-derivatives of the state variables, and use Integrator Limited blocks to
integrate these time-derivatives (i.e. to calculate the levels). Set
appropriate max and min levels (on the integrators). Select proper parameter
values yourself. You can assume zero initial state (levels).The simulation
should be run using the sim function
in a Matlab script. Also in that script, the model parameters should be
defined (the Simulink block diagram should contain no numerical values), and
the responses should be plotted using the plot function (but you may also include Scopes in the block
diagram).
b.
Run a simulation where u2 is kept constant, while u1 is changed as a
step from zero to a proper nonzero value at some point of time larger than
zero. Plot the responses in levels h1 and h2 in one plot and u1 in another
plot (using the subplot command).
c.
Verify that the simulated levels are equal to the analytically
calculated levels under steady-state (static) conditions.
Updated 22 December 2017 by Finn Aakre Haugen, course teacher.
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