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Control Systems (Prof. Casella) Written Exam – July 22nd, 2015 Answer Sheet 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 Define the frequency response of a linear, time-invariant system. Then, state how it can be used to determine the system response to a sinusoidal input in the time domain. If the system has transfer function G(s), then the frequency response of the system is the complex function G(jw), where the real frequency w goes from 0 to infinity. If the system is asymptotically stable, then the asymptotic response of the system's output to a sinusoidal input u(t) = A cos(wt + f) is y(t) = |G(jw)| cos(wt + f + arg(G(jw))). Question 2 Explain the phenomenon of integral wind-up in linear controllers and how it can be avoided. See lecture notes. Question 3 Consider a thermo-hydraulic system in which a volume V of well-mixed fluid exchanges heat with a wall that is kept at a constant temperature Tw by some external means. A mass flow rate wi of fluid at temperature Ti enters the volume, and a mass flow rate of fluid wo leaves it. The heat transfer…