Pm in this example to increase pm by gain in

Unformatted text preview: -150 -200 -250 10 2008/09 -2 10 -1 10 0 10 1 MECH466 : Automatic Control 10 2 21 2008/09 MECH466 : Automatic Control Bode plot for C(s)=0.286 22 Step responses 50 1.4 Low freq. gain 0 decreases. 1.2 -50 1 -100 10 -2 10 -1 10 0 10 1 10 0.8 2 Uncompensated (C(s)=1) Uncompensated (C(s)=1) 0.4 K=0.286 (PM=50deg) 0.2 -150 0.6 Gain compensated -100 K=0.158 (PM=65deg) -200 -250 10 2008/09 -2 10 -1 10 0 MECH466 : Automatic Control 10 1 10 0 0 2 23 2008/09 K=0.455 (PM=35deg) 5 10 MECH466 : Automatic Control 15 24 6 Phase-lag compensator (review) Phase-lag C(s) design We try to design phase-lag C(s) which gives phaseC(s) • PM 50deg • Low frequency gain same as the original plant. dB 0 -20 -5 1. To satisfy low frequency requirement, adjust DC gain of OL system by a constant gain K. -10 -15 -20 -2 10 deg -1 0 10 10 1 2 10 C(s) C(s) 3 10 10 Analysis for C(s)=1 Analysis C(s)=1 0 -40 -45 2008/09 -1 0 10 10 1 2 10 3 10 MECH466 : Automatic Control Plant 10 25 2008/09 After Step 1 OK Controller Stable Stable PM at least 12 deg PM GM at least 3.5 dB GM -20 -60 -2 10 G(s) G(s) MECH466 : Automatic Control 26 Phase-lag C(s) design 2. Find the frequency ωg (which will become gain crossover frequency after compensation) where 50 0 -50 -100 10 -2 10 -1 10 0 10 1 10 2 In this example, -100 -150 -200 -250 10 2008/09 -2 10 -1 10 0 MECH466 : Automatic Control 10 1 10 Note: The reason of +5 deg is explained later. Note: 2 27 2008/09 MECH466 : Automatic Control 28 7 A...
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