Scf s 1 c p scs has favorable properties eg easy

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Unformatted text preview: .s/ Ta .s/ To keep F .s/ stable, Tref .s/ must then satisfy the following two conditions: 1. all nonminimum-phase zeros of Ta .s/ must be zeros of Tref .s/ too (otherwise, they will be poles of F .s/) 2. pole excess of Tref .s/ must not be smaller than that of Ta .s/ (otherwise, F .s/ will be improper) Outline "Flexible" loops Pendulum on cart DC motor with flexible transmission 2-degrees-of-freedom controller configuration 2DOF example: DC motor with flexible transmission Remember this? DC motor Load with the plant transfer function 5. s C 40/.s C 40/2 P .s/ D 2 e .s C s C 156:25/.s 2 C 3:172s C 1936/ 0:1s and control objectives: I I complete steady-state rejection of step disturbances, dampened output response. Controller and disturbance response We designed (nonminimum-phase) 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/ which resulted in the following closed-loop system from d to y : Bode diagrams of Sd .s/ and P .s/ 25 20 15 10 Output responses to step disturbance (Sd .s/ and P .s/) 2.5 2 1.5 Magnitude (dB) 0 -5 -10 -15 Amplitude 0 1 2 5 1 0.5 0 -20 -25 -1 10 10 10 Frequency (rad/sec) 10 -0.5 0 0.5 1 Time (sec) 1.5 2 Step response with 1DOF controller With y n d P .s/ u ym C.s/ e r we have the following closed-loop system from r to y : Bode diagrams of T .s/ and P .s/ 2.5 20 Output responses to step reference (T .s/ and P .s/) 2 10 1.5 Magnitude (dB) 0 Amplitude 1 2 3 -10 1 -20 0.5 -30 0 -40 0 10 10 10 Frequency (rad/sec) 10 -0.5 0 0.5 1 Time (sec) 1.5 2 Not that great transients. . . 2DOF design: simple split (Cb .s/ D 1) In this case . s C 40/.s 2 10:2s C 72:25/e 0:1s Ta .s/ D T .s/ 2 Tinv .s/; .s C 14:89s C 283:5/.s 2 C 11:37s C 2985/ where Tinv .s/ is some (stably) invertible tra...
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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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