From Feedback Control of Computing Systems


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 the PID controller. There is one parameter for each control action: KP, KI,
and KD. Since PID controllers have more parameters, there is more flexibility in
design. However, there is more complexity as well.

Before continuing, we want to underscore the generality provided by the PID
controller. In Figure 9.24 the three control actions correspond to the three rows
of boxes in the PID controller. Observe that a proportional controller is a special
case of a PID controller in which KI = KD = 0. This is equivalent to deleting the
first and third rows of boxes inside the PID controller. Similarly, the PI controller
is constructed by having KD = 0, which corresponds to deleting the third row in
the PID controller, and the PD controller is constructed by having KI = 0, which
is obtained by deleting the first row of boxes in the PID controller.

The difference equation for a PID controller is


Figure 9.23

Figure 9.24

To find the transfer function...

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Topics of Interest

9.5   SUMMARY Integral controllers adjust the control input based on KI times the sum of the control errors. Integral control can eliminate steady-state error but can also increase settling...

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;...

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...

9.2.3   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   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...