It is shown in Example 6.6 that the system of Fig. 6.2-2 has the parameters =

Question:

It is shown in Example 6.6 that the system of Fig. 6.2-2 has the parameters ζ = 0.250 , ωn = 0.9191 , and τ = 4.36 s . (a) Find , , and for the sample period 7 = 0.5. (b) Repeat part (a) for T = 0.1. (c) Repeat part (a) for the

Example 6.6

For this example we will consider the system of Example 6.4. For this system the closed-loop transfer function was calculated to be G(z) 1 + G(z) Thus the system characteristic equation is The poles are then complex and occur at then Since,

Example 6.4

The system for this example is shown in Fig. 6-2. As in the first example, we will calculate the unit-step response. This system will also appear in many of the following examples. As was demonstrated in Chapter 5, the system output can be expressed as R(s) = T=1 1-8-7's S G(s) 1 s(s+1) C(s) where, from the tables in Appendix VI, 1 Z = ( = ) - = [ 5 (5! S(S + 1)]T=1 G(z) Then Since then = 0.368z +