rlocusdesign

rlocusdesign - Root-Locus Design Example System...

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Unformatted text preview: Root-Locus Design Example System Configuration Closed-loop System Block Diagram System Dynamic Model 2 1 1 1 1 2 1 2 1 1 2 2 2 3 2 2 2 1 1 1 1 1 1 i q H H H A R R A R A H H H A R R A R Take the following numerical data + +- = + +- = 1 3 2 1 2 1 1 2 1 2 2 1 1 1 2 2 4 6 4 2 3 i R R , R , A , A then H H H q H H H = = = = = +- =- + + = System Dynamic Model (continued) 1 2 i 2 1 2 1 Taking Laplace transform yields ( s 6 )H ( s ) 4H ( s ) Q ( s ) ( s 3 )H ( s ) 2H ( s ) ( s 3 )H ( s ) H ( s ) 2 and substitution results in s 3 )( s 3 ) +- = +- = +- = +- = + + +- + + =- + + =- + + =- + + = = + 2 i 2 2 i ( s 3 )( s 3 ) 4 H ( s ) Q ( s ) 2 Hence H ( s ) 2 G( s ) Q ( s ) s 9s 10 + + + + + + + + - =- =- =- = = = = = = = = = + + + + + + + + Performance Specifications (i) Percent overshoot (ii) Steady state error to step p M 2% 0.78 = e( ) 5% Might have other requirements such as rise time Proportional (P) Control Law n=[2];d=[1 9 10]; n=[2];d=[1 9 10]; >> g=tf(n,d); >> g=tf(n,d); rlocus(g); rlocus(g); c A T 2 Open-loop transfer function: 2K K K G( s ) s 9s 10 = + + + + + + + + grid grid Proportional (P) Control Law (continued) c A T c A T A T Controller gain computation 11.6 K K K 11.6 K K K Check if the performance specifications for steady state error is satisfied:...
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rlocusdesign - Root-Locus Design Example System...

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