ECIV 360 Chapter 3B Linear Control Systems

ECIV 360 Chapter 3B Linear Control Systems - Part 2 Linear...

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1 ECIV 360 Civil Engineering Systems Prof. Bill X. Yu Spring, 2009 Part 2 Linear Control Systems (cont.) Background on linear control system design Active column Components of active control system Target of Control System Design 0 ) 0 ( ) ( ) ( ) ( ) ( tion Representa Space State ) ( ) ( ) ( ) ( ) ( : Equation Motion z z t Hf t Bu t Az t z t Ef t Du t Kx t x C t x M  dt t Ru t u t Qz t f t T 0 T ) ( ) ( ) ( ) ( z J index e Performanc
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2 Target of Control System Design  n consumptio energy control : R ess effectiven control reduction/ response : Q matrix te semidefini : R and ) ( ) ( ) ( ) ( z J index e Performanc 0 T Q dt t Ru t u t Qz t f t T Open versus Close Loop Control  Equation Riccati matrix solving by determined is P(t) where 2 1 control optimal linear For : Example gain control : G z z(0) ), ( ) ( ) ( z z(0) , ) ( ) ( ) ( 1 0 0 P(t)z(t) B R - G(t)z(t) u(t) t Hf t z BG A t z t Hf t Az t z T Control Principles 0 ) 0 ( ) 0 ( ), ( cos 4 ) ( ) ( ) ( 2 ) ( 0 2 0 0 x x t u m k t x t x t x
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ECIV 360 Chapter 3B Linear Control Systems - Part 2 Linear...

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