Q6 only Common data for Q5 and Q6:For a unity feedback system, with the forward pathtransfer function given by:K(s² + 9)(s +1)(s2 + 16)G(s) =The gain K is varied in the range 0, 00)5) The angle of departure from the openloop complex poles would be:-14°, 14°194°, 166°118°, 242-62°,62°6) The maximum range of K for which thesystem is strictly stable is:[1, 4)[1, 00)(0, 0)O (0, 1

From given open loop transfer function we will find characteristic equation of the closed loop…

Answered: 6) The maximum range of K for which the…

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6) The maximum range of K for which the system is strictly stable is: O [1, 1 [1, 0) (0, 0) O (0, ) 16 9.

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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For a negative unity feedback system with the given forward transfer function:1. Evaluate the system type, Kp, Kv, and Ka.2. What is the value of the position constant?3. What is the value of the velocity constant?4. What is the value of the acceleration constant?5. What is the amount of steady-state error if the system received a parabolic function signal?
Consider the feedback system given the open loop transfer function below G(s)H(s) = K / ( S (s+3) (s+2)) a) Using the Routh-Hurwitz criterion, for which value of K, the poles of the closed-loop system take the pure imaginary value.b) What will be the maximum value of K for the system to be stable?c) Calculate the value of K, where the real value of the complex root of the system is Re{s}=-1. Tip 1: Closed loop transfer function T(s) = G(s) / ( 1+ G(s)H(s)) .Routh HurwitzIn order to perform the criterion analysis, the denominator of the closed-loop function will be examined. Tip 2: The real value of the system complex root Re{s}=-1 is expressed by the following formula f^2(s) = p(s-1) p(s) is the payoff of the closed-loop function.
3. Consider the system a) Use state feedback ? = ?? to assign the eigenvalues of ? + ?? at −0.5 ± ?0.5. Plot TT x(t) = [x1(t), x2(t)] for the open- and closed-loop system with x(0) = [−0.6, 0.4] . b) Design an identity observer with eigenvalues at −? ± ?, where ? > 0. What is the observer gain ? in this case? c) Use the state estimate ?̂ from (b) in the linear feedback control law ? = ? ?̂, where ? was found in (a). Derive the state-space description of the closed-loop system. If ? = ? ?̂ + ?, what is the transfer function between ? and ?? TT d) For ?(0) = [−0.6, 0.4] and ?̂(0)= [0, 0] , plot ?(?), ?̂ (?), ?(?), and ?(?) of the closed- loop system obtained in (c) and comment on your results. Use ? = 1, 2, 5, and 10, and comment on the effects on the system response. Remark: This exercise illustrates the deterioration of system response when state observers are used to generate the state estimate that is used in the feedback control law.
Ex. 1780. A closed-loop system has sustained oscillations (i.e. constant amplitude) with a period of 85 seconds when the gains are: proportional=96, integral=0, and derivative=0. Determine the ideal- PID gains Kp, Ki (minutes^-1), Kd (minutes) using the Ziegler-Nichols method. Also determine the standard-PID values which are commonly used in industry, such as LabVIEW: Kc, Ti (min), Td (min). ans:6
Q1: Without using Routh's criterion, determine if the following systems are a asymptotically stable, marginally stable, or unstable. In each case the closed loop transfer function for each system is given؟
From the closed loop poles shown in the S plane, positioned at -1 and -40, determine:a) The 3rd order transfer function in closed loop, considering that it has a gain equal to 40; b) The 2nd order closed loop transfer function; c) The DC gain of the 3rd order transfer function and also of the 2nd order; d) The damped natural frequency, the values of tp, ts (2% criterion) and Mp, calculated from the 2nd order transfer function.
For the system defined by the first-order differential equation: Draw the log magnitude (dB)-log frequency graph of H(jw). (The phase graph is not required. The frequency axis is expected to be logarithmic when drawing the log magnitude graph.) The input is assumed to be suppressed when the magnitude of H(jw) is -40dB. It is given that the x(t)=coswat signal is suppressed by this system. What is the smallest value of wa in this case?
Ignoring the “zero” in the numerator, and based only on the denominator of the closed-looptransfer-function, determine the range of constants Kp and Ki such that the rise-time of theclosed-loop system is equal (or less than) ?r =0.18 s and so that the relative damping factor ζ isequal to (or greater than) 0.8. Use the textbook approximation for the rise-time.
1. Consider the state space system with the given picture. Is this a valid state-space system? 2. (sperate problame0 Write down a transfer function of a stable system for which pure proportional feedback could drive the system unstable.
In the feedback system given below; G1(s) = 5*K, G2 (s)= 1/s(s+4*4), H(s)= 1 given as time to settle down Ts ≤ 4 s and if the percent overshoot is Y*5 ≤ 5%, then what is the K value and damping ratio? For the K value you found above, the input signal r(t) is a unit step Calculate the steady state error.
Consider unity negative feedback applied to the system: G(s) = k/s(s^2+4s+5) (a) Give a complete sketch of the root locus (0 ≤ k ≤ ∞) for this system assuming a unity feedback configuration. Make sure you show all the significant features on your sketch. Give particular attention to the angle of departure from the complex poles. (b) Indicate on your root locus diagram the point at which the damping ratio of the dominant poles is 0.5.
Generally, why are capacitors used in filters more than inductors? What is the gain/loss in dB of a transmission line fed with 150 Watts but outputs 120 Watts? What is the gain/loss in dB of a circuit fed with 20 Volts and outputs 30 Volts? What is the input impedance of an Ideal Operation Amplifier?