2023 07 10 exam

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Control Systems (Prof. Casella) Written Exam – July 10th, 2023 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 Consider a generic linear time-invariant SISO dynamical system, described by its transfer function.. State under which conditions the unit step response asymptotically approaches a constant value. Then, state under which additional conditions that value is actually zero. Question 2 Explain why controlling systems that have an open-loop step response showing an undershoot is in general difficult. Question 3 The equations shown on the right describe the temperature dynamics in an insulated pipe modelled by three finite volumes, assuming perfect insulation, negligible wall heat capacity, and a liquid fluid with constant density. w is the fluid mass flow rate, hj are the specific enthalpy values at each volume boundary, c is the constant specific heat capacity of the fluid, and M is the constant total mass of fluid in the pipe. 3.1 Write down the system equations in standard state-space form, considering T0 and w as inputs and T3 as output. 3.2…