2021 06 18 exam

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Control Systems (Prof. Casella) Written Exam – June 18th, 2021 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 Explain how to assess the stability of a given equilibrium of a nonlinear system described by means of state-space equations. Discuss the similarities and differences with the stability criterion for LTI systems described by transfer functions. Question 2 Discuss how LTI systems can be used as filters in signal processing, what are the main types of filters and what are their possible applications. Question 3 Consider the system represented in the figure, which is part of a recuperated closed-cycle oxy-combustion power generation system. The two compressors on the left pump an oxygen flow w1 and a carbon dioxide flow w2 into a recuperator, where they are preheated. The two flows w3 and w4 leaving the recuperator react with a fuel flow rate w5 in a burner and are expanded in a gas turbine with flow rate w6. Assuming ideal gas and nearly constant temperatures in the recuperator, neglecting the pressure losses in the circuit, and assuming choked…