Problem 4 Consider a unity (negative) feedback system whose open-loop transfer function is given by K(s+1)(s+2) G(s): s(s +10) Assume K = 1. (a) What is the type of the system? (b) Find static position error constant Kp, static velocity error constant Ky and static acceleration error constant Ka (c) Find the steady state-error of the system for following each of the following inputs. (i) (!!) t³ 1(t) (t+2) 1(t) (d) Find the range of K, for which steady-state error of the system for ramp input will be less than 0.05?

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The unity feedback system with open loop transfer function G(s) K S² is to be designed to have closed loop poles at -2.4 + j4.16. If the compensator's zero is placed at -1, do the following: a) Find the compensator pole b) Find the system gain c) Find the location of the third pole. d) Evaluate the steady-state error characteristic. e) Plot the step response of the compensated system

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Copy the control system shown in Figure Q2 into your answer book, labelling the actual output, control signal, desired output, plant, feedback and error signal. Q2 (a) 2 Σ K+ K, (s+1)(s+2) Figure Q2 (b) Determine the closed-loop transfer function for the system shown in Figure Q2 and hence obtain the characteristic equation for the system. Using Routh 's stability criterion, find the range of the controller gains (K, Ki) for which this system is stable. (c) For the system shown in Figure Q2, find the frequency, jo, and gain, Kı, for which the root locus crosses the imaginary axis (assume K = 1). (d) (e) What would you expect to see for the frequency, calculated in part (d), when you decrease K below 1.

QUESTION4 Consider the feedback system in the figure with G(s) Using the Ziegler-Nichols Oscillation Method. %3D (s+1)(s+3)(s+10) for an ideal PID controller C(s) - K, ++ Kps determine the gains K K, and K. Choose the closest set of gains. C(s) G(s) OK, - 18, K, = 12.81, K, = 6.32 O Kp = 4.80, K, = 2.65, Kp = 2.18 O Kp - 47.52, K, = 85.57, K, - 12.60 %3D O K, - 68.64, K, = 143.27, Kp = 8.22

CALCULATE Q 4 PART A B i, ii

HG(s) = QUESTION 6 s²+4s+5 Consider the root locus of a unity feedback system that has the open loop transfer function shown below. Find the break point. K(s+1) ² $3 HG(s) = AKI a... bmit. Click Save All Answers to save all answers.