From Feedback Control of Computing Systems

9.2.2   PI Control Design by Pole Placement

Consider the closed-loop system with PI control in Figure 9.9. We have four
design goals for the PI controller: (1) the closed-loop system is stable; (2) steady-
state error is minimized; (3) settling time does not exceed; and (4) maximum

Fig. 9.9 Block diagram of a computing system G(z) with proportional–integral control.

overshoot does not exceed . The first design goal is achieved by ensuring that
all poles lie within the unit circle. The second goal is achieved by using a PI
controller, at least for a step change in the reference and/or disturbance inputs.
Thus, the design problem is reduced to goals 3 and 4. These control goals can
be achieved by properly selecting the parameters KP and KI of the PI controller.

Our approach assumes that G(z) is a first-order system. If G(z) is a higher-order
system, we can use Equation (3.30) to construct a first-order approximation
of G(z). The case of G(z) having order 0 is considered in the problems at the end
of the chapter. Note that if G(z) is first order, the closed-loop system is second
order since the PI controller...

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