Question 5 The root locus of a system is provided in the following figure. C(s) R(s) + (s-2%s -I)...
A system having an open loop transfer function of G(S) = K10/(S+2)(3+1) has a root locus plot as shown below. The location of the roots for a system gain of K= 0.248 is show on the plot. At this location the system has a damping factor of 0.708 and a settling time of 4/1.5 = 2.67 seconds. A lead compensator is to be used to improve the transient response. (Note that nothing is plotted on the graph except for that...
steps R(s) E(s) C(s) G(s) FIGURE P9.1 FIGURE P9.2 9. Consider the unity feedback system shown in Figure P9.1 with [Section: 9.3] K G(s) (s+4)3 a. Find the location of the dominant poles to yield a 1.6 second settling time and an overshoot of 25%. b. If a compensator with a zero at -1 is used to achieve the conditions of Part a, what must the angular contribution of the compensator pole be? c. Find the location of the compensator...
C(s) G(s) Figure 1: A block diagram for Problems 1-4 For the given unity feedback system with G(s) - s 5)3' (a) Find the location of the dominant poles to yield a 1.2 second settling time and overshoot of 15% (b) If a compensator with a zero at-1 is used to achieve the conditions of Part a, what must be the angular contribution of the compensator pole be? (c) Find the location of the compensator pole. (d) Find the gain...
Q1. Show analytically that the Root Locus for the unity feedback system with open loop transfer function: (a) [10 marks] K(s 4) (s + 2) is a circle, and find the centre and the radius. Determine the minimum value of the damping ratio and the corresponding value of K (b) The root locus of the open loop transfer function: [10 marks] s(s26s +15) is depicted in Figure Q1(b). Find the minimum value of gain K that will render the system...
Lag Compensator Design Using Root-Locus 2. Consider the unity feedback system in Figure 1 for G(s)- s(s+3(s6) Design a lag compensation to meet the following specifications The step response settling time is to be less than 5 sec. . The step response overshoot is to be less than 17% . The steady-state error to a unit ramp input must not exceed 10%. Dynamic specifications (overshoot and settling time) can be met using proportional feedback, but a lag compensator is needed...
3 .0.2) 0(z) ℉.20-1011,. +20s+101)(s+20) 20), the damping ratio for the dominant Problem 2: For a unity feedback system with closed loop poles is to be 0.4, and the settling time is to be 0.5 second for the compensated system. a. b. c. d. Find the coordinates of the dominant poles. Find the location of the compensator zero if the compensator pole is at -15 (lead compensator) Find the required system gain. Compare the performance of the uncompensated and compensated...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifications require a closed-loop pole at (-3+j1). Design a lead compensator to make sure the root locus goes through this point. For the design, pick the pole of the compensator at-23 and analytically find its zero. (Hint: Lead compensator transfer function will be Ge (s)$+23 First plot the poles and zeros...
7. a) Sketch the root-locus Ris) C(s) diagram for the system S(5+) shown in figure when Ge=1. 6) Design phare- lead be compensator such that the system time constant is 0,25 see and != 0,45. Assume compensator at s=-4. Sketch the root-locus diagram of compensated system. c) Find the unit step responses of COMPENSATED and WN COMPENSATED systems and plot these responses. zero
Question 1 (60 points) Consider the following block diagram where G (s) Froarss RMs) GIs) Gls) (a) Sketch the root locus assuming a proportional controller is used. (b) Assume design spocifications require a closed-loop pole at (-3+ j1). Design a lead compensator sure the root locus goes through this point. For the design, pick the pole of the compensator at -23 and analytically find its zero location. (c) Sketch the root locus with the lead compensator in place. Question 1...
For the unity feedback system, where G(s) =-s-2)(s-1) make an accurate plot of the root locus and find the following: (a) The breakaway and break-in points (b) The range of K to keep the system stable (c) The value of K that yields a stable system with critically damped second-order poles (d) The value of K that yields a stable system with a pair of second-order poles that have a damping ratio of 0.707