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There are two types of feedback, negative and positive. In this problem we explore their differ- ence. (a) Consider negative feedback. Suppose you have a system with transfer function H(s) = Y (s)/E(s) where E(s)= C(s) – Y (s), and C(s) and Y (s) are the transforms of the feed- back system's reference c(t) and output y(t). Find the transfer function of the overall system G(s) =Y(s)/C(s). (b) In positive feedback, the only equation that changes is E(s)= C(s)+Y(s), the other equations remain the same. Find the overall feedback system transfer function G(s) = Y (s)/C(s). (c) Suppose that C(s) =1/s, H(s)=1/(s+1) determine G(s) for both negative and positive feedback. Find y(t) = L='[Y(s)] for both types of feedback and comment on the differ- ence in these signals.

There are two types of feedback, negative and positive. In this problem we explore their differ- ence. (a) Consider negative feedback. Suppose you have a system with transfer function H(s) = Y (s)/E(s) where E(s)= C(s) – Y (s), and C(s) and Y (s) are the transforms of the feed- back system's reference c(t) and output y(t). Find the transfer function of the overall system G(s) =Y(s)/C(s). (b) In positive feedback, the only equation that changes is E(s)= C(s)+Y(s), the other equations remain the same. Find the overall feedback system transfer function G(s) = Y (s)/C(s). (c) Suppose that C(s) =1/s, H(s)=1/(s+1) determine G(s) for both negative and positive feedback. Find y(t) = L='[Y(s)] for both types of feedback and comment on the differ- ence in these signals.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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.20 There are two types of feedback, negative and positive. In this problem we explore their differ- ence. (a) Consider negative feedback. Suppose you have a system with transfer function H(s)= Y (s)/E(s) where E(s) = C(s) – Y (s), and C(s) and Y (s) are the transforms of the feed- back system's reference c(t) and output y(t). Find the transfer function of the overall system G(s) =Y(s)/C(s). (b) In positive feedback, the only equation that changes is E(s)= C (s) + Y (s), the other equations remain the same. Find the overall feedback system transfer function G(s) = Y (s)/C(s). (c) Suppose that C(s) = 1/s, H (s) = 1/(s+1) determine G(s) for both negative and positive feedback. Find y(t) = L¯'[Y (s)] for both types of feedback and comment on the differ- ence in these signals. Answers: Positive feedback: G(s) = H(s)/(1 – H(s)).
Transcribed Image Text:.20 There are two types of feedback, negative and positive. In this problem we explore their differ- ence. (a) Consider negative feedback. Suppose you have a system with transfer function H(s)= Y (s)/E(s) where E(s) = C(s) – Y (s), and C(s) and Y (s) are the transforms of the feed- back system's reference c(t) and output y(t). Find the transfer function of the overall system G(s) =Y(s)/C(s). (b) In positive feedback, the only equation that changes is E(s)= C (s) + Y (s), the other equations remain the same. Find the overall feedback system transfer function G(s) = Y (s)/C(s). (c) Suppose that C(s) = 1/s, H (s) = 1/(s+1) determine G(s) for both negative and positive feedback. Find y(t) = L¯'[Y (s)] for both types of feedback and comment on the differ- ence in these signals. Answers: Positive feedback: G(s) = H(s)/(1 – H(s)).
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