Question

Problem 30 (15 points) Consider the closed-loop sampled-data system in Figure 6 that uses a sample period of 600 ms. The pulse transfer function of the continuous-time plant is Ge)- 0.04147 z-0.7408 while Ge(2) is the transfer function of a discrete-time compensator. E(Z)G.(2) Figure 6: Closed-loop sampled-data system with compensator Ge() I. (5 points) Is it possible to achieve a steady-sate error ess- 0.05 for a unit-step input r(k) = uo(k) using proportional feedback Ga(z) = K? If yes, derive the desired numeric value of K. If not, explain why and support your reasoning with an appropriate analytical analysis. 2. (10 points) Design a phase-lag compensator Ge(2) that yields the desired steady-state error of 0.05 fora unit-step input and a phase margin of 45°.

Answer 1

1- → steady stakes rox be achieved ess-o.05 そ D.740? e.$s → Hene ess exists an, value of K. so we can achieve patopert K value 0.05 今|K: 118 .82y , t K(o 1579) 2- そー! Given GC2)-K Z-07102