state_feedback

state_feedback - State Feedback Controller Design 1. Linear...

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Unformatted text preview: State Feedback Controller Design 1. Linear state-space models 2. State feedback control 3. Illustrative example 4. Chemical reactor example 5. Integral state feedback control 6. Simulink example Linear State-Space Models Linear deviation model State-space representation 1 1 1 1 20 2 2 1 21 2 1 21 2 10 1 1 1 11 1 1 11 1 ) ( ) ( ) ( n n m nm n n nn n n m m n n m m n n x x u b u b x a x a dt dx x x u b u b x a x a dt dx x x u b u b x a x a dt dx = + + + + + = = + + + + + = = + + + + + = m m n n R u u u R x x x dt d = = = + = 2 1 2 1 ) ( u x x x Bu Ax x Open-Loop Stability State-space matrices Linear system stability Steady-state point: Origin is asymptotically stable if and only if Re[ i ( A )] < 0 for i = 1, 2, , n Origin is unstable if Re[ i ( A )] > 0 for any i nxm nm n m nxn nn n n R b b b b R a a a a = = 1 1 11 1 1 11 B A = = u x State Feedback Control Objectives Choose eigenvalues of closed-loop system Decrease response time of open-loop stable system Stabilize open-loop unstable system State feedback control law...
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This document was uploaded on 02/04/2012.

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state_feedback - State Feedback Controller Design 1. Linear...

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