PROBLEM-4): Consider the following unity feedback closed loop system. For the time domaintransient analysis of this system;R(s)a.b.Ks(Tx+1)C(s)0.Obtain the closed loop transfer function TFC(s).From this TF(s), identify the natural frequency @n and damping ratio in terms of K and T? Re-write this TEC(s) in standard form of 2nd order system in terms of w, and ?G. Response c(t) of this system to a unit step input u(t) is given above. Find the value of formaximum overshoot M,-0.1 (10 % OS)? Find the damped natural frequency @a, undampednatural frequency , the values of K and T? (2d. Find or calculate the time delay ta, rise time t, and 2% settling time ts.Arthave that this evetamadified an

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PROBLEM-4 transient analysis of this system; R(s) a. b. G₁ ): Consider the following unity feedback closed loop system. For the time domain K s(7x + 1) C(s) T 0. Obtain the closed loop transfer function TFC(s). From this TF(s), identify the natural frequency w, and damping ratio in terms of K and T? Re- write this TEC(s) in standard form of 2nd order system in terms of w, and ? Response c(t) of this system to a unit step input u(t) is given above. Find the value of for maximum overshoot M, 0.1 (10 % OS) ? Find the damped natural frequency wa undamped natural frequency , the values of K and T? (Z Findergalculate the tima dalaut 204

PROBLEM-4 transient analysis of this system; R(s) a. b. G₁ ): Consider the following unity feedback closed loop system. For the time domain K s(7x + 1) C(s) T 0. Obtain the closed loop transfer function TFC(s). From this TF(s), identify the natural frequency w, and damping ratio in terms of K and T? Re- write this TEC(s) in standard form of 2nd order system in terms of w, and ? Response c(t) of this system to a unit step input u(t) is given above. Find the value of for maximum overshoot M, 0.1 (10 % OS) ? Find the damped natural frequency wa undamped natural frequency , the values of K and T? (Z Findergalculate the tima dalaut 204

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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how to find the closed loop poles and zeros on a tf like this by hand. With unity feedback.
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(A): Convert the Block Diagram showing in figure (2) to a Signal-Flow Graph (SFG). (B): Reduce the block diagram shown in figure (2) to a single transfer function Y(s)/R(s). (C): For the close loop system, find the values of damping ratio (), natural frequency (wn), percent overshoot (%OS), Peak time (Tp), Rise time (Tr), and settling time (Ts) Y(s) 2500 %3D R(s) s2 + 50 s + 2500 R(s) Y(s) 1 1 K s+0.4 2+1.7s+0.25 G1(s) G2(s) G3(s) Figure (1) 0.1 s+0.1 H(s) R(s) V1(s) V2(s) G1(s) V4(s) V5(s) Y(s) G3(s) G4(s) V3(s) Figure (2) G2(s) V6(s) H(s)
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Explain how the Nyquist stability criterion can be used to determine the stability of a closed-loop feedback system. Formulate the criterion for a system with no right-half plane open-loop poles. (a) (b) Consider the Nyquist plot of the frequency response of the system G(jw) = 500 shown in Figure Q4 below. (jw+1)(jw+10)² i. Explain how the gain margin can be obtained from the Nyquist plot and determine its approximate value from Figure Q4. What is the maximum value of an additional gain K for which the closed loop would still be stable? 0.5 -0.5 -0.5 0.5 Real Axis Figure Q4 i. Explain how the phase margin can be obtained from the Nyquist plot and determine its approximate value from Figure Q4. Assuming that the corresponding point on the plot occurs at 4rad/s, what is the maximum delay which can be added to the system before the closed loop would become unstable? Sketch the approximate Bode diagram for the system in part (b) of the question, clearly showing the asymptotes and corner…
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Explain how the Nyquist stability criterion can be used to determine the stability of a closed-loop feedback system. Formulate the criterion for a system with no right-half plane open-loop poles. Q4 (a) Continued overleaf Page 4 of 10 (b) Consider the Nyquist plot of the frequency response of the system G(jw) = 500 - shown in Figure Q4 below. (jw+1)(jw+10)2 i. Explain how the gain margin can be obtained from the Nyquist plot and determine its approximate value from Figure Q4. What is the maximum value of an additional gain K for which the closed loop would still be stable? 0.5 -1 -1 -0.5 0.5 1 Real Axis Figure Q4 i. Explain how the phase margin can be obtained from the Nyquist plot and determine its approximate value from Figure Q4. Assuming that the corresponding point on the plot occurs at 4rad/s, what is the maximum delay which can be added to the system before the closed loop would become unstable? Sketch the approximate Bode diagram for the system in part (b) of the question,…
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)) The Nyquist Plot of a system G(s) = in a unity feedback loop (Figure 3) is shown in Figure (s+1)² 4 for K = 1: a). Is the closed-loop system stable for K = 1? Justify your conclusion with Nyquist Stability Criterion ? b). Discuss the impact of the value of K, increasing or decreasing, on the closed-loop system stability and find the critical value of K in Nyquist Plot. Applying Routh-Hurwitz Criterion to validate your conclusions. R(s) + Y(s) G(s) Figure 3: Nyquist Diagram 15- 05 Real Asis
A feedback system root locus graph shown in figure below. For damped frequency 8.04 Hz, the gain K = 10 Imaginary Axis (seconds) ÖAN÷O-NWAGALBE -10 -20 -18 -16 Root Locus -14 -12 -10 -8 -6 -4 Real Axis (seconds) Ņ 0