Unformatted text preview: i.e. ) ( )) ( ) ( ( ) ( ) ( ) ( t z K t x t x K t f t x t x z I des p des +== Apply the Hurwitz conditions to prove the following points. a. If the controller is a simple Pcontroller (i.e. = I K ), the closed loop system is stable for all positive p K . b. If the integral controller is activated, the integral control gain must be smaller than the limit set by other parameters for stability. Assume that the feedback gains satisfy the stability condition. The desired position is constant: i.e. const x t x des des = = ) ( . a. Obtain ) ( lim t x x t ∞ → = for Pcontrol only. b. Obtain ) ( lim t x x t ∞ → = for PIcontrol. [4] 811...
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 Spring '08
 Tomizuka
 Mechanical Engineering, Order ODE, Feedback Homework Set, identical characteristic roots

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