H AA Signals and systems Fall 2003 Lecture#20 0Noⅴ ember2003 Feedback Systems 2. Applications of Feedback Systems
Signals and Systems Fall 2003 Lecture #20 20 November 2003 1. Feedback Systems 2. Applications of Feedback Systems
A Typical feedback system To Be Designed Reference or-- Command Input ? Plant To Be Designed Why use Feedback? Reducing effects of nonidealities Reducing Sensitivity to Uncertainties and variability Stabilizing Unstable Systems Reducing effects of Disturbances Tracking Shaping system response Characteristics(bandwidth/speed)
Why use Feedback? • Reducing Effects of Nonidealities • Reducing Sensitivity to Uncertainties and Variability • Stabilizing Unstable Systems • Reducing Effects of Disturbances • Tracking • Shaping System Response Characteristics (bandwidth/speed) A Typical Feedback System
One motivating example 0 k ki[0D-8(t) Potentia meter Comparator Amplifie gain a(t) e(t) Potentia v(t) Motor e(t k Motor e(t) Platform voltage angular Open-Loop System Closed-Loop Feedback System
One Motivating Example Open-Loop System Closed-Loop Feedback System
Analysis of( Causal!LTI Feedback Systems: Black's Formula CT System (t)- e H(s) Loop r G(s) Y H X()1+G(s)H( Blacks formula(1920s) orward gain Closed-loop system function loop gain Forward gain-total gain along the forward path from the input to the output Loop gain-total gain around the closed loop
Analysis of (Causal!) LTI Feedback Systems: Black’s Formula CT Syste m Black’s formula (1920’s) Closed -loop system function = forward gain 1 - loop gain Forward gain — total gain along the forward path from the input to the output Loop gain — total gain around the closed loop
Applications of Blacks Formula Example: A(s) d(t A(s) C(s) Y(s Forward gain A B X(s 1-loop gain 1+ A' BC AB 1+A X() 1+A+ABC Forward gain B B(1+ -loop gain 1+A'BC 1+A+ABC
Applications of Black’s Formula Example: 1) 2)