A unity feedback system has the open loop transfer function shown below. Find the imaginary axis crossing of the root locus s= ±jw Enter the value of a to two decimal places. Do not enter ±j K s(s²+4s+8) HG (s) =
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Linear Feedback Systems
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- 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.A unity-feedback system has forward transfer function (see attached). a) Sketch the root locus for this system as K varies from 0 to ∞; b) Use the Routh-Hurwitz test to determine the range of K for the system to be stable; show this value of K on the root locus plot.The margins of stability for K = 12 of the unit feedback system shown in the figure are given below. Phase crossover frequency : Wfc = 2rad/s Gain crossover frequency: wgc = 1.4rad/s Phase Margin = 16.8 degree Amplitude Margin Kg = 6dB (NOTE: Use 3 decimal places in your operations.) a) Calculate the amplitude margin for K 60. b) Calculate the point where the KG(jw) Nyquist Diagram intersects the negative real axis for K 60.
- Consider the unity feedback system with the following root locus for K>0. Find the approximate value of K which leads to the maximum possible overshoot of the closed loop system. Also, find all ranges of K for which the system is overdamped and as well as the steady state error to a unit step input.The forward transfer function G(s) with a H(s) feedback configuration of an uncompensated Basic Satellite Launching System is as shown in figures 1 and 2. A- in the picture B- Compute the percent overshoot, peak time and settling time, using second order approximation through pole zero cancellation and unity feedback configuration shown in figure 2. C- Summarise the results (a) and (b) in tabular form and comment on the stability of both systems based on time response graph for (a) and computed values in (b).Consider unity FBCS (feedback contrpl system) whose open loop transfer function is given by G(s)= 0.4+1/s(s+0.6) , Obtain the response to stop i/p. For the same calculate rise time Tr, peak overshoot Mp, peak time Tp and setting time Ts?
- Consider a unity negative feedback system with loop transfer function shown in Figure where L(s)=GcG(s)=K(s2+6s+1)(s2+5s+1)L(s)=GcG(s)=K(s2+6s+1)(s2+5s+1) Determine the value of K for which the closed-loop system is stable.When a unit ramp input is applied to the unity feedback system having closed loop transfer function, C(s)/R(s)= Ks+b/s2+as+b , (a>0, b>0, K>0), the steady state error will be ?The unity feedback system with loop transfer function is given as . Gc(s)G(s)=50/s(s+40) the bandwidth of the closed-loop system. 6.4 rad/sec3.2 rad/sec12.8 rad/sec1.29 rad/sec
- The circuit as shown is a shunt-shunt feedback amplifier. Use feedback analysis to find the midband input resistance, output resistance, and transresistance of the amplifier if RI = 500 Ω, RE = 2 kΩ, β0 = 100, VA = 50 V, RL = 5.6 kΩ, and RF = 47 kΩ, when vi and RI are replaced by a Norton equivalent circuit. What is the voltage gain for the circuit as drawn?A unity feedback system has loop transfer function: L(s) = Gc(s)G(s) = 4(s+z)/s(s+1)(s+3) a) Draw root locus as z varries from 0 to100 b) using root locus, estimate the percentage overshoot and settling time (within 2%) of system at z =4 c) determine actual overshoot and settling time at z = 4A unity feedback system has the following open loop transfer function G(s) = 1(s+2)(s+4)(s+10) Determine the following for system operating at 52% overshoot Damping ratio Natural frequency Setting time Peak time