Problem 2: The following is the open-loop transfer function for a unity- feedback discrete system with a sample period of T = 0.01s. Sketch the root-locus for this system. Be sure to also find the closed-loop transfer function and the range of K for stability using the Routh-Hurwitz criterion. Hint: The root locus will be sketched in the z-domain, but the system must be converted into the w-domain to use the Routh-Hurwitz criterion. K(z+0.8) (z – 1)(z – 0.6) G(2) =

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.