2019 04 15 midterm

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Control Systems (Prof. Casella) Midterm Exam – Apr 15th, 2019 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 Consider a room heating system, in which the temperature of the water sent to the radiators is a function of the outside temperature, while the flow rate is fixed. Discuss whether the control strategy of the system is open-loop or closed-loop. Then, discuss if this changes with the installation of thermostatic valves on the radiators. Question 2 Assess the stability of the systems described by the following transfer functions: Asym. stable Simply stable Unstable 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( s2 +1)    1 s2 ( s2 +1)    1 s(s2 +1)2    1 s4 +2 s2 +1    Question 3 Consider the systems shown in the figures 1.A and 1.B, in which a ball that can roll without any friction is sitting in equilibrium condition. The input of the system is a force applied to the ball in the horizontal direction, while the output is the horizontal displacement of the ball center. Based on physical intuition…