2019 06 19 exam

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Control Systems (Prof. Casella) Written Exam – June 19th, 2019 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 the superposition principle for linear, time-invariant dynamical systems. Explain why it makes the analysis of the system response to inputs easier than in the general case of nonlinear systems. Question 2 Draw the block diagram of a cascaded feedback control system. Explain in which cases it can be advantageous over a standard feedback controller and what are the tuning criteria for its components. Question 3 Consider an open vertical cylindrical tank, where two incoming mass flow rates of water w1 and w2 at temperatures T1 and T2 are mixed. An outlet mass flow rate wo at temperature T is then drawn from the bottom of the tank. Assuming a constant specific heat capacity c and de = dh = cdT, where e and h are the specific energy and enthalpy of the liquid, the system is described as: 3.1 Write the system equations in standard state-space form, considering w1, w2, wo, T1 and T2 as inputs and l, T as states and outputs. 3.2 Compute the…