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Unformatted text preview: 6.01: Introduction to EECS 1 Week 4 September 29, 2009 1 6.01: Introduction to EECS I Feedback and Control Week 4 September 29, 2009 Feedback and Control Feedback is pervasive in natural and artificial systems. p V Turn steering wheel to stay centered in the lane. car driver desired position actual position Feedback and Control Feedback is useful for regulating a system’s behavior, as when a thermostat regulates the temperature of a house. thermostat desired temperature actual temperature heating system Feedback and Control Concentration of glucose in blood is highly regulated and remains nearly constant despite episodic ingestion and use. food digestive system glucose circulatory system glucose insulin cells & tissues glucose insulin pancreas ( β cells) + body − food glucose concentration pancreas ( β cells) insulin concentration Feedback and Control Motor control relies on feedback from pressure sensors in the skin as well as proprioceptors in muscles, tendons, and joints. Try building a robotic hand to unscrew a lightbulb! Shadow Dexterous Robot Hand (Wikipedia) Feedback and Control Today’s goal: use system theory to gain insight into how to control a system. Courtesy of the Shadow Robot Company. Used with permission. 6.01: Introduction to EECS 1 Week 4 September 29, 2009 2 wallFinder Example: control the robot to move to desired distance from a wall. d i [ n ] = desired distance (input) d o [ n ] = current distance (output) Think about this system as having 3 parts: + controller plant sensor d i [ n ] d o [ n ] − wallFinder Example: control the robot to move to desired distance from a wall. + controller plant sensor d i [ n ] d o [ n ] e [ n ] v [ n ] d s [ n ] − Controller (brain) – sets velocity ∝ error v [ n ] = Ke [ n ] = K ( d i [ n ] − d s [ n ] ) Plant (robot locomotion) – integrates velocity to get position: d o [ n ] = d o [ n − 1] − T v [ n − 1] Sensor (robot inputs) – introduces a delay d s [ n ] = d o [ n − 1] Check Yourself v [ n ] = K ( d i [ n ] − d s [ n ] ) d o [ n ] = d o [ n − 1] − T v [ n − 1] d s [ n ] = d o [ n − 1] Find the system functional H = D o D i . 1. KT R 1 − R 2. − KT R 1 + R + KT R 2 3. − KT R 1 − R − KT R 2 4. − KT R 1 − R + KT 5. none of above wallFinder The behavior of the system depends critically on KT . n KT = − . 3 d o [ n ] n KT = − . 6 n KT = − . 9 Today’s goals: relate behavior to system functional H ( R ) , and learn to design well-behaved control systems Feedback Consider a simpler system with feedback . + R p x [ n ] y [ n ] − 1 0 1 2 3 4 n x [ n ] = δ [ n ] − 1 0 1 2 3 4 n y [ n ] Find y [ n ] given x [ n ] = δ [ n ] : y [ n ] = x [ n ] + p y [ n − 1] y  = x  + p y [ − 1]= 1 + 0 = 1 y  = x  + p y  = 0 + p = p y  = x  + p y  = 0 + p 2 = p 2 . . ....
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- Spring '09
- Complex number, Geometric progression, DI, cyclic signal ﬂow