b) In another unity feedback system, the root locus is depicted in Figure Q.1 (b). If the system is operated at a damping ratio of 0.5, identify the following: (i) (ii) (iii) The dominant closed-loop poles for this case. The operational gain, K at the dominant closed-loop poles. For a step input response, determine the (approximated) settling time, T, and the peak time, Tp. (iv) Determine the range of K for stability

b) In another unity feedback system, the root locus is depicted in Figure Q.1 (b). If the system is operated at a damping ratio of 0.5, identify the following: (i) (ii) (iii) The dominant closed-loop poles for this case. The operational gain, K at the dominant closed-loop poles. For a step input response, determine the (approximated) settling time, T, and the peak time, Tp. (iv) Determine the range of K for stability

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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(B) The state space representation for a closed loop system is shown in figure (5): 1. What is the poles and zeros for this system 2. Obtain the open loop transfer function G(s) for this system if it has a unity feedback .H(s)-1 -10 U(Q) 10 -12 Figure (5)
Q2) Consider the following feedback system outlined in Figure Q2 Plant R(s) + 10 1 C(s) S+ 1 K, Figure Q2 a) Derive the closed loop transfer function GRC (S). b} Calculate the value of Ky that will result in the closed loop system to have a maximum overshoot of 35% and a peak time of approximately 1 second. c) For the following systems assume zero initial conditions. Determine i) The peak overshoots. ii) Corresponding peak times iii) Decay rate characteristics. Produce a sketch of the unit step response using the above values calculated.
Consider the following feedback amplifier circuit. Assume lambda= 0, VDD RD2 R01 VinM₁ M₂ -Vout Select one: O a. none of these R₂ the open loop input resistance RinoL and the closed loop input resistances RincLare respectively: O b. RinoL = 1/gm and RincL= 1/gm(1+kA1) O C. RinoL = ∞o and Rincl= (1+ KA1) d. RinoLand RinCL = 00
For the feedback control system given in the figure on the right, R(s) + (a) Find the closed-loop transfer function, C(s)/R(s). (b) Determine the system's stability range for gain Kusing Routh-Hurwitz criterion. (c) What is the type of the system? (Hint: you need to convert the system to a simple unity feedback.) K 1 s(s+2)(s+5) C(s) (d) Sketch the root-locus in Matlab (hint: you need to use the open-loop transfer function with K = 1) and validate the stability region you found in (b). (e) Plot the step responses up to 10 seconds for the input of 1.5u(t) when the gain K = 22 and has the value that makes the system marginally stable on the same plane. (f) Calculate the steady-state error for the input step of 1.5u(t) for K = 22. Confirm the result with the related plot you obtained in (e). (g) Calculate the steady-state error now for an input ramp of 1.5tu(t) for K = 22 and plot this response together with the input function up to 10 seconds in order to indicate the steady-state error…
Consider a non-unity feedback system shown in Figure 3. R(S) s² + 4s + 10 s²+s+2 1 s²+2s +1 Figure 3: A non-unity feedback system. Derive the closed-loop transfer function of the system. C(s)
Question 3 The block diagram of a feedback control system is shown in Figure 2. R + Σ GR Gp H Figure 2 (a) Write the closed-loop transfer function of the feedback system in terms of Gp(s), GR(s) and H(s).
)) 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
4. Op-Amp has (a)Single (b) Similar (c)Multiple (d)Differential 5. Write the formula for closed-loop voltage gain of inverting amplifier with feedback using of voltage gain and gain of the feedback circuit. (a)AF= A/(1+AB) (b)AF= -A/(1+AB) (c)AF=-B/(1+AB) (d)None of the m 6. Voltage shunt feedback amplifiers are also called as (a)Non-inverting amplifier with feedback (c)Inverting amplifier with feedback (b)Non-inverting amplifier without (d)Inverting amplifier without feed outputs.
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For the following op-amp circuit (i) (ii) (iii) (iv) R₁ R₂ What is the function of the circuit? Derive the mathematical expression for the closed loop voltage gain What is the high frequency closed loop gain if R₂ = 2.5 k2, R₂ = 50 kN and C = 20 nF? Calculate the cutoff frequency
a) An operational amplifier with non-inverting voltage feedback is given in Figure Q4.a. It has the following properties: Vin + 1 kQ Figure Q4.a Open loop gain: 100,000 Open loop output impedance: 400 Open loop bandwidth: 10 Hz Calculate: 1) The closed-loop voltage gain 2) The closed-loop output impedance 3) The closed-loop bandwidth Vout 99 ΚΩ R₁
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,…