For the system of Figure 18.14, consider Gz(z) of the form of Equation 18.76 with m = 1 (a Type 1 system). Determine the value of e*(∞) for each of the three standard inputs (step, ramp, and parabolic), assuming that the system is stable.

For the definitions of Equations 18.68, 18.70, and 18.73 and from Table 18.2, the following results are obtained:

Thus, a Type 1 S-D stable system (1) can follow a step input with zero steady-state error, (2) can follow a ramp input with a constant error E0, and (3) cannot follow a parabolic input. Equation 18.87 indicates that the value of E0, for a given value of R1 (for the ramp input), may be made smaller by making K1 larger. This assumes that the desired degree of stability and the desired transient performance are maintained while K1 is increasing in value. A similar analysis can be made for Types 0 and 2 systems (see problems).