##### 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

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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##### Topics of Interest

9.2.3   PI Control Design Using Root Locus In pole placement design, the desired closed-loop poles are determined based on an a priori specification of desired properties of the closed-loop...

9.6.2   Designing a PI Controller for the Apache HTTP Server Using Pole Placement Design This example applies the analytic techniques developed in Section 9.2.4 to the Apache HTTP Server of...

9.4   PID CONTROL Proportional–integral–differential control (PID control) combines the three control actions that we have studied thus far. Figure 9.24 contains a block diagram of...

9.6   EXTENDED EXAMPLES 9.6.1   PI Control of the Apache HTTP Server Using Empirical Methods This example extends Section 8.7.2 in which proportional control is used to manage the Apache...

*9.7   DESIGNING PI CONTROLLERS IN MATLAB In this section we describe ways to use MATLAB in controller design. In Section 8.8 we introduce the MATLAB functions feedback, pole, zero, dcgain, and...

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