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Control Systems (Prof. Casella) Written Exam – June 30th, 2017 Surname:.............................................. Name: ................................................... Reg. Number:............................... Signature:...................................... Notices:  This booklet is comprised of 7 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 State how to determine the stability of a single-input single-output linear time-invariant dynamical system described by its transfer function G(s). Then, explain why in this case stability is an attribute of the system and not of its individual equilibria. Question 2 Consider the control system represented by the following block diagram. There are two sets A and B of properties of this system. All properties in set A can be achieved simultaneously, as well as all properties in set B, while there is a trade-off between each property in set A and each property in set B. Tag the following properties as belonging to set A or B. __ Fast response of controlled output y to changes of set point y° __ Good rejection of disturbance d __ Good rejection of disturbance n __ Large value of crossover frequency wc __ Wide bandwidth of transfer function between the set point y° and the controlled output y __ Small sensitivity of the control variable u to changes…