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Unformatted text preview: s filter for high-frequency roll-off). Loop shaping: keeping far from the critical point (contd) The resulting controller, C.s/ D jSd . j!/j 60 225:35.sC5:85/ , .sC500/.sC1:188/ does its job rather well: Output response to a short pulse disturbance 10 40 5 20 Magnitude (dB) 0 Amplitude 0 -20 -5 -40 -10 -60 -1 10 0 1 2 3 10 10 Frequency (rad/sec) 10 10 0 0.5 1 1.5 2 2.5 Time (sec) 3 3.5 4 4.5 5 Loop shaping: keeping far from the critical point (contd) The resulting controller, C.s/ D jSc . j!/j 10 225:35.sC5:85/ , .sC500/.sC1:188/ does its job rather well: Control signal for a short pulse disturbance 0 0 -0.5 -10 Magnitude (dB) Amplitude 0 1 2 3 -1 -20 -1.5 -30 -2 -40 -2.5 -50 -1 10 10 10 Frequency (rad/sec) 10 10 0 0.5 1 1.5 2 2.5 Time (sec) 3 3.5 4 4.5 5 Loop shaping: let's play with !c We may want to I I increase damping/accelerate response--by decrease of the first !c , or decrease control efforts--by increase of the first !c . Nichols charts of L.s/ !c D 2=3 60 40 Open-Loop Gain (dB) !c D 1 20 0 -20 -40 !c D 4 -60 -180 -135 -90 -45 0 45 Open-Loop Phase (deg) 90 135 180 Loop shaping: let's play with !c (contd) Bode diagrams of Sd .s/ 60 Output responses to a short pulse disturbance 10 40 !c D 4 20 Magnitude (dB) 5 0 Amplitude 0 -20 -5 -40 !c D 1 -60 -1 10 10 0 !c D 2=3 10 Frequency (rad/sec) 1 -10 3 10 2 10 0 0.5 1 1.5 2 2.5 Time (sec) 3 3.5 4 4.5 5 Loop shaping: let's play with !c (contd) Bode diagrams of Sc .s/ 40 Control signals for a short pulse disturbance 0 !c D 2=3 30 !c D 1 20 -2 10 Magnitude (dB) -4 Amplitude 0 -6 -10 -20 -8 -30 !c D 4 -10 -40 -12 -50 -1 10 10 0 10 Frequency (rad/sec) 1 10 2 10 3 0 0.5 1 1.5 2 2.5 Time (sec) 3 3.5 4 4.5 5 What can we learn from this example? Shaping flexible loops is characterized by I over-emphasizing resona...
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This note was uploaded on 06/30/2011 for the course MECHANICAL 034406 taught by Professor Leonidmirkin during the Spring '10 term at Technion.

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