2023 06 16 exam

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Control Systems (Prof. Casella) Written Exam – June 16th, 2023 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 generic time-invariant nonlinear dynamical system, given in state-space form. Explain how to compute the stability of its equilibria. Question 2 Describe the phenomenon of integral wind-up in linear controllers and why it should be avoided by properly implemented control systems. ˙x(t)= f ( x(t) ,u(t)) y(t)= g ( x(t) , u(t)) Question 3 The equations shown on the right describe the dynamic response of the power output in a steam Rankine cycle with reheat, operated at constant boiler pressure. wh and wl are the steam flow rates through the high and low pressure turbines, pr the reheater steam pressure, Ph, Pl, and P the high-pressure, low- pressure, and total turbine power outputs, Mr is the mass of vapour contained in the reheater tubes (assumed as a function of pr), and q is the partial arc opening degree of the high-pressure turbine in per-unit. The design parameters w0, pr0, Ph0, and Pl0 are all constants. 3.1 Write down the system…