MECH466 - Lecture20-FrequencyResponseShaping-2009@

gscs desired 200809 mech466 automatic control 5

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Unformatted text preview: lot. ) ” G(s)C(s desired 2008/09 MECH466 : Automatic Control 5 2008/09 MECH466 : Automatic Control 6 Effect of gain C(s) on L(jω) Bode plot of a gain (review) dB 100 In case of K>1, 50 Gain increases Gain uniformly, but phase does not change. 0 -50 -100 -2 10 Typically, Typically, deg (Steady state) L(0) (Steady (Speed) ωg (Speed) (Stability & (Stability overshoot) PM 2008/09 MECH466 : Automatic Control 7 2008/09 -1 10 0 10 1 10 2 10 3 10 -100 -120 -140 -160 -180 -2 -1 10 10 MECH466 : Automatic Control PM 0 10 1 10 2 10 3 10 8 2 Bode plots of lead and lag C(s) Straight-line approximations dB Lead compensator dB +20 +20 Lag compensator 20 -5 10 Lead (z<p) 0 15 -10 5 0 -2 10 -1 10 0 10 1 10 MEMORIZE THESE -15 SHAPES!!! -20 2 10 3 10 -2 10 60 0 10 1 10 2 10 3 10 +45 -45 dB dB -20 -20 20 -1 10 +45 0 40 deg deg -40 -20 Lag (p<z) deg 0 -2 10 -1 10 2008/09 0 10 1 10 2 10 PHASE LEAD 3 10 -60 -2 10 deg -1 10 MECH466 : Automatic Control 0 10 1 10 2 10 PHASE LAG -45 3 -45 10 9 2008/09 +45 MECH466 : Automatic Control 10 Effect of a lag C(s) on L(jω) Guideline of lead/lag design 0 Gain+lag -5 Lead • Decreasing ωg -10 -15 -20 -2 10 Lag -1 10 0 10 1 10 2 10 3 10 0 -20 -40 Lead -60 -2 10 -1 10 0 10 1 10 2 10 Destabilizing effect 2008/09 MECH466 : Automatic Control 11 2008/09 3 10 Select z much (at least 1 decade) less than ωg MECH466 : Automatic Control 12 3 Lag+gain C(s) design Guideline of lead/lag design 100 Gain+lag 50 Lead 0 -50 PM: 28 deg at ωg=47 rad/s -100 -2 10 -1 10 0 10 1 10 2 10 Lag 3 10 -100 -120 Lead -140 -160 PM: 27 deg at ωg=47 rad/s PM -180 -2 10 2008/09 -1 10 0 10 1 10 2 10 MECH466 : Automatic Control 3 10 13 Effect of a lead C(s) on L(jω) 20 2008/09 14 Example of a lead C(s) design Increasing ωg 15 MECH466 : Automatic Control 20 0 10 -20 5 0 -2 10 -1 10 0 10 1 10 2 10 PM: 28 deg at ωg=47 rad/s 3 10 60 -40 -60 1 10 40 3 10 -100 20 2 10 -120 0 -2 10 -140 -1 10 0 10 1 10 2 10 Stabiliz...
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