A real continuous-time LTI system is given by the block diagram below. R(s) + E(s) Y(s) G(s) The input is denoted by R(s) while the output is denoted by Y(s). The error function, E(s), is equal to the difference between the input and the output signals, E(s) = R(s) – Y(s). G(s : K(s – 5) s² – 4s + 29 where K is a positive scaling factor. 1.1. Determine the pole(s), zero(s), and region of convergence of the forward transfer func- tion G(s). 1.2. Sketch the pole-zero diagram of the forward transfer function G(s). Label all relevant points and the two axes properly. 1.3. Is G(s) stable? Explain. 1.4. Determine the transfer function H(s) = 0 in terms of K. R(s) 1.5. What will happen to the location of the poles of H(s) as K increases? 1.6. Determine the minimum value of K that will make the system (marginally) stable.

A real continuous-time LTI system is given by the block diagram below. R(s) + E(s) Y(s) G(s) The input is denoted by R(s) while the output is denoted by Y(s). The error function, E(s), is equal to the difference between the input and the output signals, E(s) = R(s) – Y(s). G(s : K(s – 5) s² – 4s + 29 where K is a positive scaling factor. 1.1. Determine the pole(s), zero(s), and region of convergence of the forward transfer func- tion G(s). 1.2. Sketch the pole-zero diagram of the forward transfer function G(s). Label all relevant points and the two axes properly. 1.3. Is G(s) stable? Explain. 1.4. Determine the transfer function H(s) = 0 in terms of K. R(s) 1.5. What will happen to the location of the poles of H(s) as K increases? 1.6. Determine the minimum value of K that will make the system (marginally) stable.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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