L10-1 - Classical Control Design Guidelines & Tools (L10.1)...

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1 Classical Control Design Guidelines & Tools (L10.1) Douglas G. MacMynowski Control & Dynamical Systems Jan 5, 2009 1 California Institute of Technology Transfer Functions G K y n d r e Nov 30, 2009 D. G. MacMynowski CDS 110a 2
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2 Design Guidelines 1. Design the loop transfer function L=GK, not the closed-loop a) L large: good performance b) L small: good robustness 2. Steady-state error based on L(0) a) Zero steady-state error to step requires integrator in L(s) b) Zero steady-state error to ramp requires two integrators c) Note that more than two integrators is harder • Conditionally stable (finite negative gain margin) 3. Cross-over with slope of -1 Nov 30, 2009 D. G. MacMynowski CDS 110a 3 = 0 then there is no crossover = -1 then phase is -90 = -2 then phase is -180 Zero phase margin a) Behaviour near crossover is what influences stability b) Usual problem is losing phase (higher order dynamics, filters, time delays,…) Guidelines, cont’d 4. Phase margin required for both robustness and performance a) Typically want 30 < PM < 60 (30 is typically absolute minimum, |S| generally no advantage to more than 60) b) Can trade bandwidth for phase margin Higher bandwidth faster response Lower phase margin worse overshoot Nov 30, 2009 D. G. MacMynowski CDS 110a 4
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3 Guidelines, cont’d 5. Main design tools: a) Lead: Adds phase, maximum phase m added at E.g. b Lag m b/a 30 ~3 45 ~6 60 ~14 c) PID: Nov 30, 2009 D. G. MacMynowski CDS 110a b) Lag: a/b = increase in error constant Use for steady-state performance May not need all three terms For second order system G(s)=(s 2 + 2  s + 2 ) -1 need derivative term to ensure slope is -1 if crossover is above For simple system G(s) = 1, then integral gain may suffice Guidelines, cont’d 6. Don’t get too close to RHP zero:
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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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L10-1 - Classical Control Design Guidelines & Tools (L10.1)...

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