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Control Systems (Prof. Casella) Written Exam – July 22nd, 2015 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. Question 2 Illustrate the phenomenon of integral wind-up and how it can be avoided. 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 coefficient between the fluid and the wall is proportional to wo 0.8. It is assumed for simplicity that the fluid has constant density and that dh = de = c dT. The equations describing the system are the following, where M is the constant fluid mass, T the fluid temperature, c the constant fluid specific heat capacity, Q the heat flow to the fluid, and wnom the nominal value of the flow rate:…