Linear Matrix Inequalities in Control

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Synthesis (11) H-inf loop shaping z1 W1 w - y K u G d + W3 z3 z Basic idea: W1 ( s) S( s) W ( s) T( s) 3 1 The sensitivity functions: L( s) S( s) T( s) G( s) K( s) ( I ( I G( s) K( s)) 1 ( I L( s)) 1 G( s) K( s)) G( s) K( s) I 1 S( s) ( I 1 L( s)) L( s) KSO materiały do wykładu 2008/09 70 Optimisation setup: w min K u T P K w z Synthesis (12) H-inf loop shaping y ( s) z1 z3 z „Clever” selection of the zinf z1 z3 y x z y z w P u C x W1 0 I D u WG 1 W3G G Ax Buu Bww C x D uu D ww C x D u D w z y yu zu yw D w zw w u KSO materiały do wykładu 2008/09 71 Demo no.9 Optimiser: SeDuMi Preprocesor: YALMIP G ( s) 1 G ( s) 2 G ( s) 3 1 a 2 s ( s a) G0 ( I ); 1 2 2 2 s ( s 2s ) G0 ( I ); 1 s 1 b s e ; 2 2 s s b s G0 ( I ); filters W 1 and W 3 1 2 2 3 KSO materiały do wykładu 2008/09 72 ( s) 1 ( s) ( s) 3 2 s ; s a 2 s 2s 2 s 2s 2s ; b s 2 ; Design controller by the loop shaping method taking into account all possible neglected dynamics. 24
Synthesis (13) Model predictive control (MPC) • For actual plant state x(k), find next M control u(k) steps (by optimisation), knowing next N (future) reference values. M
Page 1 and 2: Linear Matrix Inequalities (LMI) in
Page 3 and 4: Optimisation approach (2) scalar si
Page 5 and 6: Optimisation approach (8) Analysis
Page 7 and 8: Computer tools support • Matlab
Page 9 and 10: LMI Primer (5) The Schur complement
Page 11 and 12: Basic LMI tools for control (2) Sta
Page 13 and 14: Basic LMI tools for control (8) Bou
Page 15 and 16: Optimiser: SeDuMi Demo no.3 Preproc
Page 17 and 18: Analysis (4) Robust stability - exa
Page 19 and 20: Scope of the lecture • Control -
Page 21 and 22: Synthesis (5) Design of static, sta
Page 23: Demo no.7 Optimiser: SeDuMi Preproc
Page 27 and 28: Synthesis (18) Gain Scheduled H-inf
Page 29 and 30: Optimiser: SeDuMi Demo no.11 Prepro

Linear Matrix Inequalities in Control

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