Q1 (a) The characteristic equation of a general nth order system is given by q(s) = s" + a,s"-1 + a2s"-2 + ... + an-2s² + an-1s + an Using the Routh-Hurwitz criterion, derive conditions for stability of a general i) first-order system, ii) second-order system iii) third-order system in terms of the coefficients a1, a2, ... An.
Q1 (a) The characteristic equation of a general nth order system is given by q(s) = s" + a,s"-1 + a2s"-2 + ... + an-2s² + an-1s + an Using the Routh-Hurwitz criterion, derive conditions for stability of a general i) first-order system, ii) second-order system iii) third-order system in terms of the coefficients a1, a2, ... An.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).
Question
Transcribed Image Text:Q1
(a)
The characteristic equation of a general nth order system is given by
q(s) = s" + a1s"-1 + a2s"-2 + .. + an-2s² + an-1s + an
Using the Routh-Hurwitz criterion, derive conditions for stability of a general
i) first-order system,
ii) second-order system
iii) third-order system
in terms of the coefficients a1, a2, ... an.
(b)
The transfer function of a system is given by
G(s) =
s2 + 10s + 30
Calculate the response of this system to a unit impulse input.
(c)
Consider an open loop transfer function of the form K G(s). Briefly describe
three different methods which can be used to determine the values of K for
which the closed loop system remains stable.
(d)
Consider the open-loop transfer function G(s) = What is meant by the
s+1
frequency response of G(s)? Sketch a Nyquist plot and a Bode plot of the
frequency response of this function.
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