Loop shaping adding integrator first to satisfy step

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Unformatted text preview: Gain (dB): 2.33 Phase (deg): -224 Frequency (rad/sec): 12.5 -810 -720 -630 -540 -450 -360 Open-Loop Phase (deg) -270 -180 -90 0 It makes sense to locate resonances as far from critical points as possible, so I phase lags at ! D 12:5 should be 136i and at ! D 44 -- 156i Also, we need to increase gain at the second resonance. Loop shaping: adding phase lag This is achieved by adding two RHP zeros to controller: Bode diagram of 0:025 s 30 25 20 Magnitude (dB) 15 10 5 0 -5 -10 -15 -90 2 1:28:5sC8:52 s 20 Nichols chart of P .s/ 0:025 s 2 1:28:5sC8:52 s 15 Open-Loop Gain (dB) 10 5 0 -135 Phase (deg) -180 -5 -225 -10 -270 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 This is PID controller: CPID .s/ D 0:255 1 1 0:1412s 0:098s ; which is not proper. Loop shaping: adding lowpass filter To "properize" the controller, we may want to add lowpass filter. Bode diagram of 0:025 s 30 25 20 Magnitude (dB) 15 10 5 0 -5 -10 -15 -90 2 1:28:5sC8:52 s.s=110C1/ 20 Nichols chart of P .s/ 0:025 s 2 1:28:5sC8:52 s.s=110C1/ 15 Open-Loop Gain (dB) 10 5 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 This LPF, however, I adds too much phase lag around the fifth crossover. This results in the loop, which is too close to the third critical point. So, we need to look for an additional phase lead there. Notch filters The system of the form 2 s 2 C 2n !n s C !n F .s/ D 2 ; 2 s C 2d !d s C !d n < d ; is called the notch filter if !n D !d and skewed notch filter if !n !d . Bode diagrams of notch 0 s 2 C2n sC1 s 2 C2d sC1 Bode diagrams of skewed notch 10 5 2 s 2 C2!n sC!n 2 s 2 C2!d sC!d Magnitude (dB...
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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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