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lecture11

# lecture11 - MAE 171A Dynamic Systems Control Lecture 11...

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MAE 171A: Dynamic Systems Control Lecture 11: Control Design Using Root Locus Goele Pipeleers

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Situation In Lecture 10 P, D, I, PD, PID controllers analysis of their advantages and disadvantages In Lecture 11: Root Locus problem formulation basic characterization 4 root locus drawing rules In This Lecture controller design using root locus 1
Additional Controller Structures Lead Compensator D ( s ) = K s + z s + p , where z < p variation of the PD controller: D ( s ) = k s + z z + p = K p s + z s/p + 1 let p → ∞ and adjust K = k d p to preserve DC-gain, then D ( s ) k d ( s + z ) improves the transient response 2

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Lag Compensator D ( s ) = K s + z s + p , where p < z variation of the PI controller: let p 0 , then D ( s ) k 1 + z s improves the steady-state response 3
Control Design Problem D ( s ) G ( s ) u y w r v Problem: given the system G ( s ) , compute a controller D ( s ) such that a set of specifications are met 4

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Example Used Throughout This Lecture D ( s ) G ( s ) u y r e system G ( s ) = 1 s ( s + 1) specifications: step response: M p 20% t r 0 . 3 s ramp response: | e ss | ≤ 0 . 015 5
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