1. No category

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.
1