L8-1_loopsyn

# L8-1_loopsyn - CDS 101/110a Lecture 8-1 Frequency Domain...

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1 CDS 101/110a: Lecture 8-1 Frequency Domain Design Douglas MacMynowski 15 November 2010 Goals: Describe canonical control design problem and standard performance measures Show how to use “loop shaping” to achieve a performance specification Work through a detailed example of a control design problem Reading: Åström and Murray, Feedback Systems, Ch 11 Advanced : Lewis, Chapter 12 Frequency Domain Performance Specifications Specify bounds on the loop transfer function to guarantee desired performance C ( s ) P ( s ) + + d y eu r Tracking BW SS Steady state error: zero frequency (“DC”) gain Bandwidth: assuming ~90˚ phase margin PC > 100/X -1 D. MacMynowski, Caltech CDS CDS 101/110, 15 Nov 10 2 sets crossover freq Tracking: X % error up to frequency t determines gain bound (1 + PC > 100/ X )

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2 Relative Stability Relative stability: how stable is system to disturbances at certain frequencies? System can be stable but still have bad response at certain frequencies Typically occurs if system has low phase gnitude (dB) Bode Diagrams -40 -20 0 20 40 margin get resonant peak in closed loop overshoot; poor step response Solution: specify minimum phase margin. Typically 45˚ or more Phase (deg); Mag -60 10 -1 10 0 10 1 10 2 -300 -200 -100 0 100 Step Response 1.5 From: U(1) D. MacMynowski, Caltech CDS CDS 101/110, 15 Nov 10 3 Time (sec.) Amplitude 0 0.5 1 1.5 2 2.5 3 0 0.5 1 To: Y(1) Frequency (rad/sec) Magnitude (dB) -60 -40 -20 0 20 10 -1 10 0 10 1 10 2 M r Overview of Loop Shaping Performance specification Steady state error Tracking error Bandwidth 0 50 Relative stability Approach: “shape” loop transfer function using C ( s ) P ( s ) + specifications given L ( s ) = P ( s ) C ( s ) -100 -50 -100 0 100 D. MacMynowski, Caltech CDS CDS 101/110, 15 Nov 10 4 - Use C ( s ) to choose desired shape for L ( s ) Important: can’t set gain and phase independently
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## This note was uploaded on 01/04/2012 for the course CDS 101 taught by Professor Murray,r during the Fall '08 term at Caltech.

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L8-1_loopsyn - CDS 101/110a Lecture 8-1 Frequency Domain...

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