2022 04 11 midterm

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Control Systems (Prof. Casella) Midterm Exam – Apr 11th, 2022 Name:.............................................. Surname:................................................... 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 Define the open-loop and closed-loop control strategies. Then, comment on how and to which extent they can manage uncertainty (unknown disturbances and uncertainty on dynamic behaviour) Question 2 Consider a number of SISO nonlinear systems, each linearized around a certain equilibrium. Based on the transfer functions between the input and the output of the linearized systems, classify the stability of the corresponding equilibria of the nonlinear system. Asym. stable Simply stable Unstable Can’t say s+1 s3 −10 s2 + s     s+3 s2 +10     s+3 s2 −10     s+4 ( s+10)2 (s+3)2     s+1 s( s+1)     1 s2 ( s2 +1)     1+10 s− s2 ( s+10)3 ( s+2)2 ( s+1)     1 s4 +2 s2 +1     Question 3 For each of the following four diagrams indicate what is the transfer function, among those listed below, of which they are the step response. (1) 2 s+1 s+2 (2) 2 s+2 s+1 (3) 2 s+2 (4) (5) 50 s2 +3 s+2 (6) 9 s2 +s+9 (7) 9 s2 +2 s+9 (8) (9) s+3 s2…