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2002final_partc

2002final_partc - 16.060 Principles of Automatic...

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16.060 - Principles of Automatic Control (F’02) Final Exam Part C C-1) You are given ± 10 100 s ² 1 ³ ± ³ s G ± s s ² 1 ³± 1 . s ² 1 ³ a) Sketch the log G vs log Z b) Sketch the G vs. log Z . What is the value at Z =10 r/s ? C-2) For the open loop system ± s k ² 4 ³ ± ³ s G 2 ± s ² 2 ³± s ´ 4 ³ ± s ² 8 s ² 32 ³ figure (a) is the pole zero diagram and figure (b) is the Nyquist diagram showing 3 regions of interest: A, B & C Figure (a) Figure (b) a) Fill in table C-2 b) Sketch the branches which correspond to region C, the root locus
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C-3) Figure C-3 is the Bode diagram of a certain G(s). What is the expression for G(s)? C-4) Given K ± 1 ² s ³ 2 ± ³ s G ± 1 ´ s ³ 2 a) Sketch the Nyquist plot and the root locus for k>0 and k<0. For the Nyquist plot use G(s)/k. Clearly show 0+, +j f , -j f , 0- and the direction of increasing frequency. b) There will be four regions of interest (A,B,C,D left to right) in the Nyquist plot. Mark them. c) Show the r ´ O branches which correspond to regions B and D. C-5) Estimate the phase margin and crossover frequency specifications to which a loop gain
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