L8-1_loopsyn

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 )
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online