MECH466 - Lecture16-BodeDiagrams-2009W

# 10 0 2 10 1 10 0 10 1 10 2 10 100 product of basic

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Unformatted text preview: 0 0 -2 10 2008/09 -1 10 0 10 MECH466 : Automatic Control 1 10 2 10 13 2008/09 Bode plot of a 2nd order system MECH466 : Automatic Control 14 Bode plot of a time delay resonance 1 20 0.5 0 0 -20 Resonant freq. -0 . 5 -1 -2 10 -40 -60 -1 10 0 10 10 -1 10 0 10 1 10 2 Huge phase lag! 0 1 10 -2 0 0 0 0 Peak gain -4 0 0 0 -50 -6 0 0 0 -2 10 -100 -200 -1 10 MECH466 : Automatic Control -1 10 0 10 1 10 2 The phase lag causes instability of the closed-loop closedsystem, and thus, the difficulty in control. -150 2008/09 10 0 10 1 10 15 2008/09 MECH466 : Automatic Control 16 4 Sketching Bode plot An advantage of Bode plot Basic functions Basic Bode plot of a series connection G1(s)G2(s) is Bode the addition of each Bode plot of G1 and G2. Constant gain Constant Differentiator and integrator Differentiator Double integrator Double First order system and its inverse First Second order system Second Time delay Time Gain Gain Phase Phase Product of basic functions Product We use this property to design C(s) so that We C(s) G(s)C(s) has a “desired” shape of Bode plot. ) ” G(s)C(s desired 1. Sketch Bode plot of each factor, and 2. Add the Bode plots graphically. Main advantage of Bode plot! 2008/09 MECH466 : Automatic Control 17 2008/09 Short proofs MECH466 : Automatic Control 18 Example 1 Use polar rep...
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