# Loop shaping before we start some observations are in

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Unformatted text preview: tions are in order: 1. Static gain P .s/jsD0 and velocity gain 1 P .s/jsD0 are both zero. s 2. Gain at sub-resonance frequencies (! &lt; 2) is pretty low. Thus, plant filters out low-frequency disturbances well (no help required2 ). Also, 3. gain at over-resonance frequencies (! &gt; 50) is low. Thus, plant filters out high-frequency noise also well (no help required). Therefore, I we only need to interfere around the resonance (i.e., in 2 &lt; ! &lt; 50). fact we cannot do much. For example, static gain can only be increased by canceling the poles at the origin, which is obviously illegal. 2 In Loop shaping: proportional gain Comparison of these two plots Nichols chart of L.s/ D P .s/ 60 60 Nichols chart of L.s/ D P .s/ 40 40 Open-Loop Gain (dB) 20 Open-Loop Gain (dB) 20 0 0 -20 -20 -40 -40 -60 0 45 90 135 180 225 Open-Loop Phase (deg) 270 315 360 -60 -180 -135 -90 -45 0 45 Open-Loop Phase (deg) 90 135 180 shows clearly that negative gain (positive feedback) is preferable. Note that I loop gain has two crossover frequencies in this case, which means that we have two regions of interest for loop phase (arg L. j!/). Loop shaping: keeping far from the critical point If we keep the plant's first crossover ( 2:64) and want phase margin of 50i , Nichols chart of L.s/ D 60 P .s/ 60 225:35.sC5:85/ Nichols chart of L.s/ D P .s/ .sC500/.sC1:188/ 40 40 Open-Loop Gain (dB) 20 Open-Loop Gain (dB) 20 System: L Phase Margin (deg): -50.3 Delay Margin (sec): 2.05 At frequency (rad/sec): 2.64 Closed Loop Stable? Yes 0 0 System: L Phase Margin (deg): 123 Delay Margin (sec): 0.15 At frequency (rad/sec): 14.3 Closed Loop Stable? Yes -20 -20 -40 -40 -60 -180 -135 -90 -45 0 45 Open-Loop Phase (deg) 90 135 180 -60 -180 -135 -90 -45 0 45 Open-Loop Phase (deg) 90 135 180 we need to add phase lag around !c ! This promts the choice C.s/ D 1=Clead .s/; for !m D !c and max D 41:5i (and then adding a lowpas...
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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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