2022 06 17 exam

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Control Systems (Prof. Casella) Written Exam – June 17th, 2022 Surname:.............................................. Name: ................................................... Reg. Number:............................... Signature:...................................... Notices:  This booklet is comprised of 7 sheets – Check that it is complete and fill in the cover.  Write your answers in the blank spaces with short arguments, including only the main steps in the derivation of the results.  You are not allowed to leave the classroom unless you hand in the exam paper or withdraw from the exam.  You are not allowed to consult books or lecture notes of any kind.  Please hand in only this booklet at the end of the exam – no loose sheets.  The clarity and order of your answers will influence how your exam is graded. 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. Question 2 Draw the block diagram of a cascaded control system and explain what are the tuning criteria for the inner and outer controller. 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 maximum efficiency h0 is…