2002final_parta

2002final_parta - 16.060 Principles of Automatic Control...

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16.060 Principles of Automatic Control Fall 2002 Final Exam Part A: Put your working and answers in the booklet provided. Question A.1 20 points Consider the plant 2 1.25 1.25 () (0 . 5) . 1.25 Gs sj ss == + −+ + ++ a) The desired closed-loop performance specifications are: 8 n ζω = 0.707, = . Where should the closed-loop poles be located? b) Using root-locus techniques, design a PD controller that satisfies the above performance requirements. c) What will be the steady-state error of your compensated system to a unity step input?
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Question A.2 20 points Consider the system represented by the following pole/zero diagram, where the pole at the origin represents a step input. The system has unity gain (i.e. the steady-state input/output gain is 1). X X X j1 -j1 step input -10 X s not to scale -1 a) Calculate the magnitude of all residues. b) What is the time constant associated to each mode? c) Write down an exact expression for the step response. d) Is there a dominant transient mode? If so, which mode is dominant? Justify your answer.
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2002final_parta - 16.060 Principles of Automatic Control...

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