MIT6_003S10_lec11

MIT6_003S10_lec11 - .003: Signals and Systems Feedback and...

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Unformatted text preview: .003: Signals and Systems Feedback and Control arch 11, 2010 Feedback and Control Feedback is pervasive in natural and artificial systems. p V Turn steering wheel to stay centered in the lane. desired position driver car actual position Feedback and Control Concentration of glucose in blood is highly regulated and remains nearly constant despite episodic ingestion and use. tissues food digestive system glucose circulatory system glucose insulin cells & glucose insulin pancreas ( cells) glucose in stored glucose circulatory system insulin pancreas ( cells) glucose + concentration cells & tissues odays goal Use systems theory to gain insight into how to control a system. xample: wallFinder System Approach a wall, stopping a desired distance d i in front of it. d i = desiredFront d o = distanceFront d o d o K = . 5 K = 1 t t d o t K = 8 t d o K = 2 hat causes these different types of responses? Structure of a Control Problem (Simple) Control systems have three parts. + X Y E S C controller plant sensor The plant is the system to be controlled. The sensor measures the output of the plant. The controller specifies a command C to the plant based on the difference between the input X and sensor output S . nalysis of wallFinder System Cast wallFinder problem into control structure. + X Y E S C controller plant sensor d i = desiredFront d o = distanceFront proportional controller: v [ n ] = Ke [ n ] = K d i [ n ] d s [ n ] locomotion: d o [ n ] = d o [ n 1] Tv [ n 1] sensor with no delay: d s [ n ] = d o [ n ] nalysis of wallFinder System: Block Diagram Visualize as block diagram. d i = desiredFront d o = distanceFront proportional controller: v [ n ] = Ke [ n ] = K d i [ n ] d s [ n ] locomotion: d o [ n ] = d o [ n 1] Tv [ n 1] sensor with no delay: d s [ n ] = d o [ n ] + K T + R D i D o V nalysis of wallFinder System: System Function Solve. d i = desiredFront d o = distanceFront + K T + R D i D o V KT R D o = 1 R = KT R = KT R D i 1 + KT R 1 R KT R 1 (1 + KT ) R 1 R nalysis of wallFinder System: Poles The system function contains a single pole at z = 1 + KT . D o = KT R D i 1 (1 + KT ) R Unit-sample response for KT = . 2 : h [ n ] n . 2 Unit-step response s [ n ] for KT = . 2 : 1 n hat determines the speed of the response? Could it be faster? heck Yourself Find KT for fastest convergence of unit-sample response....
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MIT6_003S10_lec11 - .003: Signals and Systems Feedback and...

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