Consider the system of Fig. P8.2-2 with a gain factor K K added to the plant. (a)

Consider the system of Fig. P8.2-2 with a gain factor $K$ added to the plant.
(a) Show that the pulse transfer function is given by(b) Sketch the root locus for this system, and find the value of $K$ that results in critical damping, that is, in two real and equal roots of the system characteristic equation.
(c) Find the time constants of the two poles in part (b).
(d) It is desired that the gain in part (b) be multiplied by 1.8, while the characteristic-equation roots remain approximately the same. Design a phase-lag controller that meets these specifications. Use $z_p={0.999}^{\circ }$
(e) By computer, verify the characteristic-equation roots in part (d).

Fig. P8.2-2

Transcribed Image Text:

z - 1 1 0.368(z+0.717) N s(s + 1)] - (z 1)(z 0.368) -