lec13 - 6.003: Signals and Systems CT Feedback and Control...

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Unformatted text preview: 6.003: Signals and Systems CT Feedback and Control October 27, 2009 Mid-term Examination #2 Tomorrow, October 28, 7:30-9:30pm, Walker Memorial. No recitations tomorrow. Coverage: cumulative with more emphasis on recent material lectures 112 homeworks 17 Homework 7 includes practice problems for mid-term 2. It will not collected or graded. Solutions are posted. Closed book: 2 pages of notes ( 8 1 2 11 inches; front and back). Designed as 1-hour exam; two hours to complete. Feedback and Control Feedback is pervasive in natural and artificial systems. We have previously investigated feedback in DT systems. Example: robotic steering + plant controller sensor x [ n ] y [ n ] n y [ n ] Feedback and Control Today: investigate continuous-time feedback and control. 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 Op-Amp Much of the utility of op-amps depends on their having high gain. Ideal op-amp: lim K V + V V o = K ( V + V ) K Op-Amp The gain of an op-amp depends on frequency. 10 2 10 3 10 4 10 5 1 10 10 2 10 3 10 4 10 5 10 6 [log scale] | K ( j ) | [logscale] 2 1 10 10 2 10 3 10 4 10 5 10 6 [log scale] K ( j ) | Frequency dependence of LM741 op-amp. Check Yourself What system function has this frequency response? 10 2 10 3 10 4 10 5 | K ( j ) | [logscale] 2 1 10 10 2 10 3 10 4 10 5 10 6 [log scale] K ( j ) | 1. K s + 2. K s s + 3. K ( s + ) s 4. K ( s + ) 5. none Check Yourself What system function has this frequency response? 1 10 2 10 3 10 4 10 5 | K ( j ) | [logscale] 2 1 10 10 2 10 3 10 4 10 5 10 6 [log scale] K ( j ) | 1. K s + 2. K s s + 3. K ( s + ) s 4. K ( s + ) 5. none Op-Amp Low-gain at high frequencies limits applications. 10 2 10 3 10 4 10 5 1 10 10 2 10 3 10 4 10 5 10 6 [log scale] | K ( j ) | [logscale] audio frequencies 2 1 10 10 2 10 3 10 4 10 5 10 6 [log scale] K ( j ) | Unacceptable frequency response for an audio amplifier. Op-Amp An ideal op-amp has fast time response....
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lec13 - 6.003: Signals and Systems CT Feedback and Control...

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