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# 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 ( ) 1 0.5 20 100 100 G s s s 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 D s K K KD s s Ts α + + = = = + + (1) The plant is given by: 2 2 1 ( ) 1 0.5 20 100 100 G s s s s s =

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