So we need to look for an additional phase lead there

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Unformatted text preview: ) Magnitude (dB) Phase (deg) 0 1 -5 0 -5 -10 -15 -20 -10 -15 -20 90 -25 90 45 Phase (deg) 45 0 0 -45 -45 -90 -1 10 10 Frequency (rad/sec) 10 -90 -1 10 10 Frequency (rad/sec) 0 10 1 Skewed notch vs. lead Skewed notch lead controller has more narrow phase lead region, yet I the (magnituge) price we pay for leading phase is lower than in the standard lead controller case. Bode diagrams of skewed notch lead and standard lead 4 3 2 Magnitude (dB) Phase (deg) 1 0 -1 -2 -3 -4 30 20 10 0 -10 1 10 10 Frequency (rad/sec) 2 10 3 Loop shaping: the final controller Thus, PID + lowpass filter + skewed notch filter result in: Bode diagram of final C.s/ 20 10 5 0 Nichols chart of final L.s/ Magnitude (dB) 15 -10 Open-Loop Gain (dB) -5 10 5 -90 0 Phase (deg) -180 -5 -270 -10 -360 0 10 10 1 10 Frequency (rad/sec) 2 10 3 -1080 -990 -900 -810 -720 -630 -540 -450 -360 Open-Loop Phase (deg) -270 -180 -90 0 for C.s/ D 3.s 2 10:2s C 72:25/.s 2 C 40s C 1600/ : s.s C 80/.s 2 C 70s C 2500/ Loop shaping: the final controller (contd) Closed-loop responses: Bode diagram of Sd .s/ 25 20 Output responses to step disturbance 2.5 2 15 10 1.5 Magnitude (dB) 0 -5 -10 -15 Amplitude 5 1 0.5 0 -20 -25 -1 10 10 0 10 Frequency (rad/sec) 1 10 2 -0.5 0 0.2 0.4 0.6 0.8 1 Time (sec) 1.2 1.4 1.6 1.8 2 Outline "Flexible" loops Pendulum on cart DC motor with flexible transmission 2-degrees-of-freedom controller configuration 2DOF example: DC motor with flexible transmission Closed-loop vs. open-loop configurations d y n d P .s/ u ym C.s/ e r y P .s/ u C.s/ r Closed-loop control necessary when I I I plant P .s/ unstable disturbance attenuation required modeling uncertainties are substantial Open-loop control sufficient for tracking of r when I plant P .s/ stable and uncertainty level (disturbances / modeling errors) is low noise n level high and its spectrum not sufficiently separated from that of r Open-loop control advantageous for...
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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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