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# lec14-handout-6up - 6.003 Signals and Systems Lecture 14...

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6.003: Signals and Systems Lecture 14 October 29, 2009 1 6.003: Signals and Systems CT Feedback and Control October 29, 2009 Feedback and Control Continuous-time feedback has many applications. Examples: improve performance of an op amp circuit. control position of a motor. reduce sensitivity to unwanted parameter variation. reduce distortions. stabilize unstable systems magnetic levitation inverted pendulum Feedback and Control Reducing sensitivity to unwanted parameter variation. Example: power amplifier F 0 MP3 player power amplifier 8 < F 0 < 12 speaker Changes in F 0 (due to changes in temperature, for example) lead to undesired changes in sound level. Feedback and Control Feedback can be used to compensate for parameter variation. F 0 MP3 player K β + power amplifier 8 < F 0 < 12 speaker X Y H ( s ) = KF 0 1 + βKF 0 If K is made large, so that βKF 0 1 , then H ( s ) 1 β independent of K or F 0 ! Feedback and Control Feedback reduces the change in gain due to change in F 0 . F 0 MP3 player 100 1 10 + 8 < F 0 < 12 X Y 0 10 20 0 10 20 8 < F 0 < 12 F 0 Gain to Speaker F 0 (no feedback) 100 F 0 1 + 100 F 0 10 (feedback) Check Yourself F 0 MP3 player K β + power amplifier 8 < F 0 < 12 speaker X Y Feedback greatly reduces sensitivity to variations in K or F 0 . lim K →∞ H ( s ) = KF 0 1 + βKF 0 1 β What about variations in β ? Aren’t those important?

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6.003: Signals and Systems Lecture 14 October 29, 2009 2 Crossover Distortion Feedback can compensate for parameter variation even when the variation occurs rapidly.
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