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Control Systems (Prof. Casella) Written Exam – June 30th, 2016 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 Define the external stability and asymptotic stability of the equilibria of a single-input, single- output dynamical system. Question 2 With reference to a single-input, single-output linear time invariant system, discuss the relationship between the eigenvalues of the A-matrix and the poles of the transfer function between the input and the output. Question 3 Consider the turbine system in a large Rankine cycle power plant with reheat. The system is described by these equations, where wHP and wLP are the high and low pressure turbine flow rates, Y are the turbine admittances, P are the pressures, r is the steam density, P are the produced mechanical powers, and h are the specific enthalpies of steam at the turbine inlets and outlets . Assume that PHP and YLP are constants and that the changes in the specific enthalpy differences are much smaller than the changes in the flow rates, so that h1, h2, h3, and h4 can also be considered as constants.…