### Open-Loop Transfer Function Analysis#### Problem StatementThe open-loop transfer function of a system is given by:\[ G(S)H(S) = \frac{K(S - 1)}{(S + 2)} \]where \( K = 1 \).Figure 2 displays the general Nyquist plot for this transfer function. Utilizing the Nyquist criterion, please determine the following:a) How many poles are on the right half of the plane for the closed-loop function? Is the system stable or unstable? Justify your answer.b) What is the gain margin expressed in dB?c) How much does the gain \( K \) have to be changed, expressed in dB, to obtain a marginally stable system?#### Nyquist Diagram DescriptionThe Nyquist plot shows a curve on the complex plane with the real axis ranging from -1 to 0.1 and the imaginary axis ranging from -1 to 1. The curve starts and ends near the point (0.1, 0) with the real part ranging from approximately -0.9 to near 0. The plot includes arrows indicating the direction of the curve.The plot has the following characteristics:- The curve makes a loop, crossing the real axis around -0.3 and extending to approximately -0.5.- The plot does not encircle the critical point (-1,0), a crucial factor in determining system stability using the Nyquist criterion.These visual features will aid in assessing the stability and gain margin as per the questions above.

We have given the transfer function G(s)H(s)=K/(S-1)(S+2) where K=1 Given figure shows the general…

1.- The open-loop transfer function of a system is: G(S)H(S) = K/(S – 1)(S + 2), where K = 1. Figure 2 shows the general Nyquist plot for this transfer function. Using the Nyquist criterion determine: a) How many poles are on the right half of the plane for the closed-loop function? Is the system stable or unstable? Justify your answer b) What is the gain margin expressed in dB? c) How much the gain K has to be changed expressed in dB in order to obtain a marginally stable system

1.- The open-loop transfer function of a system is: G(S)H(S) = K/(S – 1)(S + 2), where K = 1. Figure 2 shows the general Nyquist plot for this transfer function. Using the Nyquist criterion determine: a) How many poles are on the right half of the plane for the closed-loop function? Is the system stable or unstable? Justify your answer b) What is the gain margin expressed in dB? c) How much the gain K has to be changed expressed in dB in order to obtain a marginally stable system

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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