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Control Systems (Prof. Casella) Final Mid-Term Exam – June 25th, 2016 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 system shown in the figure. State Bode’s criterion for the asymptotic stability of the closed-loop system. Question 2 Define what non-minimum phase linear dynamical systems are. Then, discuss how this property of of a process to be controlled influences its controller design and performance. L(s) u - y Question 3 Consider the following control system (time constants are given in seconds), where C(s) is a real PID controller with Kp = 0.4, Ti = 200, Td = 30, N = 6: 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 the set point y°. H (s)= 20 (1+1000 s) H(s) C(s)y° - G(s) y n d G(s)= 50 (1+1000 s)(1+30 s)(1+10 s) u 3.3 Compute the asymptotic amplitude of the oscillations…