Lecture26 - Summary Compensator design using the Root Locus State Space controller plant R(s G c(s compensator sensor transducer G p(s C(s

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Lecture 26 – Wednesday, Nov. 7 2.004 Fall ’07 Summary: Compensator design using the Root Locus; State Space Root Locus sketching rules (negative feedback) Rule 1: # branches = # open-loop poles Rule 2: symmetrical about the real axis Rule 3: real-axis segments are to the left of an odd number of real-axis finite open-loop poles/zeros Rule 4: RL begins at open-loop poles ( K =0), ends at open-loop zeros ( K = ) Rule 5: Asymptotes: real-axis intercept σ a , angles θ a Rule 6: Real-axis break-in and breakaway points Rule 7: Imaginary axis crossings (transition to instability) σ a = P nite poles P nite zeros # nite poles # nite zeros θ a = (2 m +1) π # nite poles # nite zeros m =0 , ± 1 , ± 2 ,... Found by setting K ( σ )= 1 G ( σ ) H ( σ ) ( σ real) and solving d K ( σ ) d σ =0 forreal σ . Found by setting KG ( j ω ) H ( j ω 1 and solving Re £ ( j ω ) H ( j ω ) ¤ = 1 , Im £ ( j ω ) H ( j ω ) ¤ .
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This note was uploaded on 02/23/2012 for the course MECHANICAL 2.004 taught by Professor Derekrowell during the Fall '08 term at MIT.

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Lecture26 - Summary Compensator design using the Root Locus State Space controller plant R(s G c(s compensator sensor transducer G p(s C(s

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