11 - PolePlacement11 filled

11 - PolePlacement11 filled - ME 575 Handouts 1 ME575...

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Unformatted text preview: ME 575 Handouts 1 ME575 Session 11 Pole Placement School of Mechanical Engineering Purdue University Slide 1 POLE PLACEMENT DESIGN POLE PLACEMENT DESIGN Motivation Motivation A systematic procedure to synthesize a controller for A systematic procedure to synthesize a controller for SISO LTI systems to place closed SISO LTI systems to place closed-loop poles of nominal loop poles of nominal system at certain desired locations system at certain desired locations Polynomial Approach Polynomial Approach General Formulation General Formulation No constraint on the controller to be used No constraint on the controller to be used Practical Constraints Practical Constraints Controller with integrator Controller with integrator Controller with stable pole/zero cancellation Controller with stable pole/zero cancellation PID Controller via Pole Placement PID Controller via Pole Placement ME575 Session 11 Pole Placement School of Mechanical Engineering Purdue University Slide 2 Closed Closed-Loop Characteristic Loop Characteristic Eq Eq . Controller Plant R(s) Y(s) + C G o o o o Go C Go C G (s)C(s) T(s) 1 G (s)C(s) characteristic eq: 1 G (s)C(s) D (s)D (s) N (s)N (s) = + + = + = C C Go o Go let N (s) C(s) , D (s) N (s) G (s) D (s) = = ME 575 Handouts 2 ME575 Session 11 Pole Placement School of Mechanical Engineering Purdue University Slide 3 Basic Idea of Pole Placement Basic Idea of Pole Placement Specify desired characteristic polynomial: Specify desired characteristic polynomial: Equate desired polynomial with polynomial given Equate desired polynomial with polynomial given by by C(s C(s ) and ) and G o (s (s ): ): Match coefficients and solve Match coefficients and solve CL CL CL CL CL CL n n 1 c c c c CL n n 1 1 c n 1 2 n D (s) s s s (s p )(s p )...
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This note was uploaded on 12/09/2011 for the course ME 575 taught by Professor Meckl during the Fall '10 term at Purdue University-West Lafayette.

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11 - PolePlacement11 filled - ME 575 Handouts 1 ME575...

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