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MECH 466 - Lecture21-LeadLagDesigninFrequencyDomain-2009W

5 db gm 0 50 100 10 2 10 1 10 0 10 1 10 2 100 lead

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Unformatted text preview: 00 10 -2 10 -1 10 0 10 1 10 2 -100 Lead These values are too small for good transient response! -150 -200 -250 10 2008/09 MECH466 : Automatic Control 7 2008/09 -2 10 -1 MECH466 : Automatic Control 10 0 10 1 10 2 8 2 Gain compensation Bode plot for C(s)=0.286 50 PM is specified to be 50 deg. PM In this example, to increase PM by gain In compensation, we need to lower the gain curve. Low freq. gain 0 decreases. -50 -100 10 -2 10 -1 10 0 10 1 10 2 Uncompensated (C(s)=1) Uncompensated (C(s)=1) -100 Gain compensated -150 -200 -250 10 2008/09 MECH466 : Automatic Control 9 Step responses -2 10 2008/09 -1 10 0 10 1 10 2 MECH466 : Automatic Control 10 Phase-lag compensator (review) 1.4 dB 1.2 0 1 -20 0.8 -5 -10 -15 0.6 K=0.455 (PM=35deg) 0.4 K=0.286 (PM=50deg) 0.2 -20 -2 10 deg K=0.158 (PM=65deg) 0 0 0 10 1 10 2 3 10 10 0 -20 -40 5 10 15 -45 -60 -2 10 2008/09 -1 10 MECH466 : Automatic Control 11 2008/09 -1 10 MECH466 : Automatic Control 0 10 1 10 2 3 10 10 12 3 Phase-lag C(s) design After Step 1 OK We try to design phase-lag C(s) which gives phaseC(s) • PM 50deg • Low frequency gain same as the original plant. 50 0 -50 1. To satisfy low frequency requirement, adjust DC gain of OL system by a constant gain K. -100 10 C(s) C(s) Analys...
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