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Unformatted text preview: 6.003: Signals and Systems CT Feedback and Control October 27, 2009 Midterm Examination #2 Tomorrow, October 28, 7:309:30pm, Walker Memorial. No recitations tomorrow. Coverage: cumulative with more emphasis on recent material lectures 1–12 homeworks 1–7 Homework 7 includes practice problems for midterm 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 1hour 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 continuoustime 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 OpAmp Much of the utility of opamps depends on their having high gain. Ideal opamp: lim K → ∞ V + V − V o = K ( V + − V − ) K OpAmp The gain of an opamp depends on frequency. 10 2 10 3 10 4 10 5 1 10 10 2 10 3 10 4 10 5 10 6 ω [log scale]  K ( jω )  [logscale] − π 2 1 10 10 2 10 3 10 4 10 5 10 6 ω [log scale] ⚢ K ( jω )  Frequency dependence of LM741 opamp. Check Yourself What system function has this frequency response? 10 2 10 3 10 4 10 5  K ( jω )  [logscale] − π 2 1 10 10 2 10 3 10 4 10 5 10 6 ω [log scale] ⚢ K ( jω )  1. αK s + α 2. K s s + α 3. K ( s + α ) s 4. K ( s + α ) α 5. none Check Yourself What system function has this frequency response? 1 10 2 10 3 10 4 10 5  K ( jω )  [logscale] − π 2 1 10 10 2 10 3 10 4 10 5 10 6 ω [log scale] ⚢ K ( jω )  1. αK s + α 2. K s s + α 3. K ( s + α ) s 4. K ( s + α ) α 5. none OpAmp Lowgain 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 ω [log scale]  K ( jω )  [logscale] audio frequencies − π 2 1 10 10 2 10 3 10 4 10 5 10 6 ω [log scale] ⚢ K ( jω )  Unacceptable frequency response for an audio amplifier. OpAmp An ideal opamp has fast time response....
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 Spring '11
 DennisM.Freeman
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