2019 06 11 midterm

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Control Systems (Prof. Casella) Final Mid-Term Exam – June 11th, 2019 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 sensitivity transfer function S(s) and discuss its role in determining the dynamic performance of the system, assuming that the phase margin jm > 40°. Question 2 Consider the control system represented in the diagram of Question 1. Explain whether or not it is possible to increase the rejection of the effects of disturbance d on the controlled output y, without also increasing the effect of the sensor noise n on the controlled output y. C(s) y° - G(s) y n d u Question 3 Considering the following block diagram A( s)= 2 s B( s)= 1−s 1+10 s 3.1 Compute the transfer functions between the input u and the outputs y and v. 3.2 Determine for which values of the parameter K the system is asymptotically stable and shows an undershoot in the step response of the output y. C (s)=5 1+10 s 1+ s u K - A(s) C(s) B(s)- yv Question 4 Consider the following control system (time constants…