##### From Feedback Control of Computing Systems

**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 HTTP Server. As before, KeepAlive (the time that idle HTTP

connections are held) is manipulated so as to regulate CPU (CPU utilizations).

This example describes the use of a PI controller instead of the proportional

controller of Example 8.7.2.

Figure 9.26 displays a block diagram of the Apache HTTP Server with

noise that is modeled as an additive effect on CPU. The operating point is

= (0.58, 11). The input and output offsets are

*u*(

*k*) = KA(

*k*) −

and

*y*(

*k*) = CPU(

*k*) − , respectively. The controller has the transfer function

*K*+

_{P}*zK*/(

_{I}*z*− 1), and the transfer function of the target system is

*G*(

*z*) =

−0.014/(z − 0.59). Our focus is on noise rejection. The transfer function from

the noise to the output is

Note that *F _{N}*(1) = 0, so this system should have no steady-state error in response

to a step noise as...

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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...

9.2.2 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;...

*9.7 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...

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...

9.2 PROPORTIONAL–INTEGRAL CONTROL Proportional–integral (PI) control combines the advantages of integral control (zero steady-state error) with those of proportional control...