A First Course in FUZZY and NEURAL CONTROL

2.5. CONTROLLER DESIGN 43

Figure 2.14. Set-point control

The most commonly used configuration is shown in Figure 2.14 (a) in which
the controller is placed in series with the plant to be controlled. This type
of control is referred to asseriesorcascade compensation.ThePIDcon-
troller has a configuration illustrated in Figure 2.14 (a). In Figure 2.14 (b) the
compensator is placed in the minor feedback path and is usually referred to
as feedback compensation. State-variable and output-feedback controllers have
the configuration shown in Figure 2.14 (b).
Standard control is based on knowledge of a mathematical model of the
system. The mathematical model can take on basically two forms:

1. Theactual modelof the system.


2. Anestimated modelof the system.

For the classical design of controllers, we need to know something numerical
about the system. The so-called numerical approach requires that we know
something about the dynamics of the system. As briefly discussed earlier, the
model of the plant can be described by a set of equations. Typically, what we
have is a set of nonlinear differential equations for which a transfer function
does not exist. Designing a controller for a nonlinear system requires that
the systemfirst be linearized about some nominal operating point. From this
linearized model, atransfer functionof the plant, that is, the ratio of the
output function to the input function, can be derived.
These computations are normally donein the ìfrequency domainî obtained
by taking Laplace transforms of the state equations. TheLaplace transform
of a functionx(t)is defined as

àx(s)=

Z∞

0

x(t)e−stdt