note12 - MEEN 364 Notes for session on December 1, 2004....

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MEEN 364 Notes from Session on December 1, 2004 Notes for session on December 1, 2004. 1) Problem 6.57, p. 483 from the textbook “Feedback control of dynamic systems”, 4 th edition by Franklin et al.: For a unity feedback system with 2 2 1 () 10 . 5 20 100 100 Gs ss s s = ⎛⎞ ++ ⎜⎟ ⎝⎠ 1 + a) A lead compensator is introduced with α = 1/5 and a zero at 1/T = 20. How must the gain be changed to obtain crossover at ω c = 31.6 rad/sec, and what is the resulting value of K v ?. b) With the lead compensator in place, what is the required value of K for a lag compensator that will readjust the gain to the original K v value of 100? c) Place the pole of the lag compensator at 3.16 rad/sec, and determine the zero location that will maintain the crossover frequency at ω c = 31.6 rad/sec. Plot the compensated frequency response on the same graph. d) Determine the PM of the compensated design. Solution: a) The compensator is given by: 1 1 1 20 1 1 100 s Ts Ds K K KD s s Ts α + + === + + ( 1 ) The plant is given by: 2 2 1 . 5 20 100 100 s = 1 + In order to obtain crossover at ω c = 31.6 rad/s with the lead compensator, let

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This note was uploaded on 04/18/2010 for the course MEEN 364 taught by Professor Staff during the Spring '08 term at Texas A&M.

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note12 - MEEN 364 Notes for session on December 1, 2004....

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