L9-1_pid

L9-1_pid - CDS 101/110a: Lecture 9-1 PID Control Douglas...

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1 CDS 101/110a: Lecture 9-1 PID Control Douglas MacMynowski 22 November 2010 Goals: Show how to use “loop shaping” using PID (Proportional + Integral + Derivative) to achieve a performance specification Reading: Åström and Murray, Feedback Systems, Ch 10 Advanced : Lewis, Chapters 12-13 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, 22 Nov 10 2 - Use C ( s ) to choose desired shape for L ( s ) Important: can’t set gain and phase independently Frequency (rad/sec) 10 -1 10 0 10 1 10 2 -300 -200
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2 Overview: PID control PID P ( s ) + y eu -1 r Intuition Proportional term: provides inputs that correct for “current” errors Integral term: ensures steady state error goes to zero Derivative term: provides “anticipation” of upcoming changes A bit of history on “three term control” First appeared in 1922 paper by Minorsky: “Directional stability of automatically steered bodies” under the name “three term control” A l l i d t h t “l l d i t i ( l ii t i )l d b d td t d t h D. MacMynowski, Caltech CDS CDS 101/110, 22 Nov 10 3 Also realized that “small deviations” (linearization) could be used to understand the (nonlinear) system dynamics under control Utility of PID PID control is most common feedback structure in engineering systems For many systems, only need PI or PD (special case) Many tools for tuning PID loops and designing gains Proportional Feedback Simplest controller choice: u = k p e Effect: lifts gain with no change in phase
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L9-1_pid - CDS 101/110a: Lecture 9-1 PID Control Douglas...

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