A stable system can be classified as a system type, which is defined as the degree of the polynomial for which the steady-state error is a non-zero finite constant. For instance, if the error to a step input, which is a polynomial of zero degree, is a non-zero finite constant, then such a system is called type 0 , and so on. Consider the system in Figure 10.28.

a. Compute the following steady-state errors for: (1) a unit-step reference input, (2) a unit-ramp reference input \(u=t\), and (3) a parabolic reference input \(u=0.5 t^{2}\).

b. Determine the system type.

FIGURE 10.28 Problem 4. R(s) 10s+2 s(s + 8s +25) Y(s)