2022 06 17 midterm

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Control Systems (Prof. Casella) Final Mid-Term Exam – June 17th, 2022 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 Explain why the bandwidth of a linear feedback control system is limited in case the plant to be controlled has a non-minimum phase dynamic response and how to determine that limit. Question 2 Consider the feedback control system represented in the figure, where G(s) is an asymptotically stable transfer function with a dominant pole of time constant T. Explain why step changes of the set point changes cause overshoots in the manipulated variable if the crossover frequency of the control system is larger than 1/T. C(s)y° - G(s)u y° Question 3 Consider a filter with transfer function F(s) 3.1 Pick the appropriate values for parameters m, a, b, T1, T2, T3 such that the harmonic components of a signal passing through it are • unchanged if their frequency w < 10 rad/s, except for those with w  1 rad/s • attenuated if their frequency is w > 10 rad/s • completely removed from the signal at w = 1 rad/s 3.2 Draw the Bode plots of the frequency…