2023 06 16 midterm

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Control Systems (Prof. Casella) Final Mid-Term Exam – June 16th, 2023 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 control system shown in the figure. Discuss why direct disturbance compensation can be much more effective than feedback control to reject fast changes of the disturbance d. Question 2 Consider the feedback control system represented in the figure. Using Bode’s stability criterion, determine for which values of Kp the closed-loop system is asymptotically stable. C(s)y° - G(s)u y° d H(s) C(s) y° - G(s) yu n G (s)=20 e−100s (1+10 s)(1+s) H (s)=5 e−100s (1+10 s) C ( s)= K p G (s)= 10 s (1+10 s)(1+ s)(1+0.1 s) (1+20 s)(1+ 2 s)(1+0.2 s) Question 3 Consider the following filter F(s) 3.1 Draw the Bode plots for modulus and phase of its frequency response 3.2 Classify the type of filter and determine what is its bandwidth 3.3 Compute the asymptotic amplitude of the filter output when the input is a sinusoidal signal with amplitude 5 and frequency 0.5 Hz. F ( s)= 10 s (1+10 s)(1+0.1 s)(1+0.04 s) Question 4 Consider the following…