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Control Systems (Prof. Casella) Written Exam – July 2nd, 2015 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 With reference to feed-back control systems, explain why the input-output dynamic behaviour of the plant to be controlled is crucial for the system performance. Also explain why, on the other hand, a very precise knowledge of that dynamic behaviour is not required, if the controller is designed properly. Question 2 Briefly explain why the stability of a linear system with transfer function G(s) is completely determined by its poles. Then, state precisely under which conditions such system will be asymptotically stable, simply stable, or unstable. Question 3 Consider a one-dimensional spring-mass mechanical system, in which a body of mass M is connected to the ground by a spring and by a damper, and subject to an external force F. Contrary to a standard spring-mass harmonic oscillator, the spring has a nonlinear force-displacement characteristic, where the force grows more than proportionally to the spring deformation. The equations describing the…