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Control Systems (Prof. Casella) Written Exam – July 19th, 2017 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 Give the most general definition of what a dynamical system is. Then, write down the state-space equations of a generic nonlinear time-invariant dynamical system, explaining why it fits the general definition. Question 2 Draw the block diagram of a cascaded control system. Explain what are the design criteria for the controller blocks and when is this control structure advantageous compared to a standard feedback controller. Question 3 Consider a high-temperature electrical heater, in which a metallic body is heated up by an electrical current passing through it. Assuming a uniform temperature distribution in the body, neglecting the convective heat transfer with respect to the radiative heat transfer, and assuming a black-body behaviour, the following model can be written: E =McT ˙E =Q−Qr Qr=σ S (T 4 −T e 4 ) where E is the thermal energy stored in the body, M is its mass, c is its specific heat, Q is the thermal power dissipated by Joule…