2022 07 11 exam

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Control Systems (Prof. Casella) Written Exam – July 11th, 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 simple frictionless pendulum, where the input variable is a horizontal force applied to the point mass and the output is the angle formed by the pendulum with a vertical axis. The pendulum is in the lower equilibrium conditions with a zero applied force and a zero angle. Based on the general definition of external stability, explain whether the equilibrium is asymptotically stable, simply stable or unstable. Question 2 Consider the control system shown on the right. Assume that the system is subject to significant process disturbances d and measurement noise n. Discuss the trade-offs in system performance when choosing a low or a high cross-over frequency for the controller d C(s) y° - G(s) yu n Question 3 The equations shown on the right describe the dynamic behaviour of the penstock-nozzle system in Pelton hydropower plant, where w is the mass flow rate through the penstock, Po is the penstock outlet pressure, Phyd is the hydraulic…