Uncertainty, Discretization and Saturation

Building Control and Automation, Spring 2015
Dr. R. Evins, Dr. C. Gaehler
Prof. J. Lygeros, Prof. R. Smith
Automatic Control Laboratory
ETH Zurich, ETL I28
8092 Zurich
Exercise set 4: Plant parameter uncertainty, discrete controllers
and saturation
Handing out:
Exercise 1
Monday, 30 March 2015
Plant parameter uncertainty
(1)
Consider a single-room building with parameter uncertainty. The room is equipped with a heating
system and regulated by a PI-controller with a Kp of 10 and a Ki of 0.003. The room temperature
is measured. The initial room temperature is 12◦ , the reference temperature of the room is 20◦
and the outside temperature is 16◦ . Simulate the single-room building assuming a thermal capacity
of C = 73.5 kJ/K and a thermal conductance to the outside of h = 10 W/K, a decrease of the
parameters by 25% and an increase of the parameters by 25% (thermal capacity and conductance).
Plot the step responses.
(2)
Simulate the cases from (1) without a PI-controller, but with an input heating power of 40 W
(feed-forward control). Compare the performance of the PI-controller to the feed-forward under the
aspect of parameter uncertainty.
Exercise 2
Discretization and Saturation
(1)
Consider the nominal case of the single-room building from above. The initial room temperature
is 12◦ , the reference temperature of the room is 20◦ and the outside temperature is 12◦ . The room
is equipped with a heating system and regulated by a P-controller with gain Kp = 30. Increase the
sampling time of the discrete model and observe the impact on the response. Compare it to the continous model. Hints: Get the Simulink Model discrete example.slx from the webpage. Open the
Simulink model to find out which variables must be specified in the MATLAB workspace. Use the
MATLAB command [tsim,xsim,ysim] = sim(’discrete example’,t sec,[],[t sec,ref,Tamb])
to execute the model.
(2)
Consider the nominal case of the single-room building from above with a PI-controller with gains
Kp = 30 and Ki = 0.004. The initial room temperature is 12◦ , the reference temperature
of the room is 23◦ and the outside temperature is 12◦ . Compare the performance of an unbounded PI-controller and a bounded PI-controller with u ∈ [0, 150]. Plot the response of the
two cases including the controller output and the actuator output. Hints: Get the Simulink
Model sat example.slx from the webpage. Open the Simulink model to find out which variables
must be specified in the MATLAB workspace. Use the MATLAB command [tsim,xsim,ysim] =
sim(’sat example’,t sec,[],[t sec,ref,Tamb]) to execute the model.
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