2022 06 17 exam answers

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Control Systems (Prof. Casella) Written Exam – June 17th, 2022 ANSWERS SHEET Question 1 Consider a building heating system where the room temperature controller sends hot water to the heating elements at a temperature that is linearly dependent on the measured outside air temperature. Is this an open-loop or closed-loop control strategy? Motivate your answer and explain what are its potential shortcomings and how to avoid them by changing the control strategy. The measured outside temperature is a disturbance for the process, so the proposed controller adopts an open-loop control strategy. The main shortcoming of this strategy is that it is insensitive to all other disturbances (e.g. solar radiation, heat dissipated by human occupants and machines, etc.) that affect the room temperature, as well as to uncertainty in the system behaviour (e.g. water pumps not working as intended, clogging, etc.). These shortcomings can be overcome by adding some kind of feedback control in each thermal zone of the building, that acts on the heating input (e.g. by opening and closing valves) as a function of the difference between the temperature set point and the actual temperature; in other words, install thermostats. Question 2 Draw the block diagram of a cascaded control system and explain what are the tuning criteria for the inner and outer controller. See lecture notes. Question 3 The equations shown on the right describe the dynamic behaviour of a Pelton turbine with moment of inertia J and radius R, rotating at an angular velocity w and driving an electrical generator absorbing a power Pe. The turbine is fed by a jet of water with hydraulic power Ph and constant speed u. The efficiency h of the turbine depends on the ratio between the blade speed wR and the fluid speed u; the…