2018 06 12 midterm

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Control Systems (Prof. Casella) Final Mid-Term Exam – June 12th, 2018 (revised text) Surname:.............................................. Name: ................................................... Reg. Number:............................... Signature:...................................... Notices:  This booklet is comprised of 6 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 the feedback control system shown in the figure. Define the control sensitivity transfer function Q(s) and discuss its role in determining the dynamic performance of the system. Question 2 With reference to the same diagram of Question 1 and assuming jm > 40°, discuss the relationship between the crossover frequency wc of the loop transfer function L(s) = C(s)G(s) and the bandwidth of the transfer function between the set point y° and the controlled output y. C(s) y° - G(s) y n d u Question 3 Consider the following control system (time constants are given in seconds), where C(s) is a PI controller with Kp = 10, Ti = 50: 3.1 Compute the steady-state errors corresponding to unit step changes of the set point y° and of the disturbance d. 3.2 Compute the crossover frequency and the phase margin of the control system. Then, plot an approximated diagram of the step response of the controlled variable y to a step change of…