In the unity-feedback closed-loop system shown, G(z) K Sketch the root locus plot for the system. →G(z) = Z-0.6 z(z2-1.5z+0.81)
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- Given the following characteristic equation: 1+K/S(S2+2S2+8S+5)=0 (a) Using Routh method determine the range of K for which this closed loop system is stable. (b) Find the value of K for which the system has purely imaginary roots and determine the corresponding frequency of oscillations.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.By plotting the locus-root curve of the open-loop transfer function G(s)= K / s (s+2); a) When K=4, show the locations of the closed loop poles on the root locus. Determine the damping ratio ζ and the natural frequency (wn) values at this gain value. b) Calculate and scale the unit step response of this closed-loop system by calculating the %overshoot, tp and ts (percent overshoot, peak and settling times, respectively). c) In order for this supervised system to work at least in the performance criteria (computed (greater than ζ and wn)) in question (a), scan the region where the pairs of conjugate poles should be located on the root-locus curve.
- Hello, please solve this question , Greetings Q1. Choose the correct answer 1. Which among the following is not an advantage of an open loop system? a. Simplicity in construction & design b. Easy maintenance c. Rare problems of stability d. Requirement of system recalibration from time to time 2. Which notation represents the feedback path in closed loop system representation? a. b(t) b. c(t) c. e(t) d. r(t) 3. Which among the following represents an illustration of closed loop system? a. Automatic washing machine b. Automatic electric iron c. Bread toaster d. Electric hand drier 4. Transfer function of the system is defined as the ratio of Laplace output to Laplace input considering initial conditions________ a) 1 b) 2 c) 0 d) infinite Feedback can always reduce the effects of noise and disturbance on system performance? a) True b) False 6. Which among the following is not an advantage of an open loop system? a. Simplicity in construction & design b. Easy…Control system! (a) For what ranges of α and β is the closed-loop system stable and (b) Given that β is fixed at some positive value, for what value of α is the closed-loop systemmarginally stable and what are the associated locations in the s-plane of those marginally stable poles?A unity feedback system has the open loop function G(s)=1/3s3+2s2+0.6s+11 Using RH criterion, Write whether the system is stable or unstable. The system is : Answer
- What is the effect on %VR value if taken at half-load lagging pf? Justify and explain briefly your answer on one(1) sentence.Control System , Given transfer function, T (s) = αs + β / s^2 + (α + 2)s + β (i) Pick a pair of values for parameters α and β such that the closed-loop system is stable (ii) Pick a pair of values for parameters α and β such that the closed-loop step response exhibitszero steady-state error. (iii) Pick a pair of values for parameters α and β such that the closed-loop step response isunderdamped, exhibiting a settling time of 4/5 seconds and a peak time of π/7 seconds.Draw the Root-Locus graph of the closed loop system whose block diagram is given below. (number of branches, asymptotes Calculate the values of the angle and intersection point, the point where it intersects the imaginary axis, the split point)
- In order for the closed loop system, whose block diagram is given below, to be stable, the parameters K1 and K2 must be determined. Calculate the values it will take. Draw the graph of the stable region in the K1-K2 plane. (Hint: Routh-Hurwitz use the method)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 = 4Consider 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.