EE210_Lec14_Applications

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Feedback Systems & Applications Examples from MIT 6.003 Signals & Systems Spring 2011 (Prof. Q. Hsu) & Spring 2010 (Prof. D. Freeman) 2 Why use Feedback? Reducing Nonlinearities Reducing Sensitivity to Uncertainties and Variability Stabilizing Unstable Systems Reducing Effects of Disturbances Tracking Shaping System Response Characteristics (bandwidth/speed) A Typical Feedback System feed forward feed backward http://ocw.mit.edu/courses/ , EE 6.003 S11 Controller 3 One Motivating Example –– pointing a telescope Open-loop System Aim –– shoot Closed-loop Feedback System Not done until it is pointed http://ocw.mit.edu/courses/ , EE 6.003 S11 4 Another example –– A robot car http://ocw.mit.edu/courses/ , EE 6.003 S11

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5 System Function of a Closed-loop System Example: A basic Feedback System — By its nature, we are dealing with real physical systems. They are all causal . E ( s ) = X ( s ) " R ( s ) = X ( s ) " G ( s ) Y ( s ) " Q ( s ) = Y ( s ) X ( s ) = H ( s ) 1 + G ( s ) H ( s ) Y ( s ) = H ( s ) E ( S ) = H ( s )[ X ( s ) " G ( s ) Y ( s )] G ( s ) Y ( s ) –– System function of the close-loop http://ocw.mit.edu/courses/ , EE 6.003 S11 6 Can show for any closed-loop systems, the system function is given by Black ± s formula (H. S. Black in the 1920 ± s, along with Nyquist and Bode): Forward gain — total gain along the forward path from the input to the output the gain of an adder is 1 Loop gain — total gain along the closed loop — shared by all the system functions General formula for a closed-loop system: Black ± s Formula Closed - loop system function = forward gain 1 - loop gain Q ( s ) = Y ( s ) X ( s ) = H ( s ) 1 + G ( s ) H ( s ) http://ocw.mit.edu/courses/ , EE 6.003 S11 Feedback and Control Using feedback to enhance performance. 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 http://ocw.mit.edu/courses/ , EE 6.003 S10 13 P ( s ) — unstable Design C ( s ), G ( s ) so that the closed-loop system is stable poles of Q ( s ) = roots of 1+ C ( s ) P ( s ) G ( s ) on LHP (Do not use pole/zero cancellation.) ) ( ) ( ) ( 1 ) ( ) ( ) ( s G s P s C s P s C s Q + = Stabilization of Unstable Systems http://ocw.mit.edu/courses/ , EE 6.003 S11