Environmental Engineering Reference
In-Depth Information
Expert systems (ES) integrate the knowledge of one or more process specialists
into a set of rules or a knowledge base that defines the actions of an expert controller
who acts similarly to a proportional (P), proportional-integral (PI) or proportional-
integral-derivative (PID) automatic control algorithm.
The forms of expert control are numerous, and may:
be based exclusively on the controller's own knowledge of the specific process
being controlled;
use rules to reproduce conventional control algorithms for P, PI, PID or other
control methods;
incorporate estimates of non-measured variables based, for example, on time-
series models;
include certainty factors in the ES control rules or take into account errors in the
measurements.
One of the most frequently adopted alternatives for improving the robustness of
expert control systems in handling uncertainties and errors is fuzzy logic. In this
approach, a membership function μ is assigned to each linguistic variable or fuzzy
set x such that 0
1. The most commonly used membership functions are
triangular, trapezoidal or Gaussian [28, 29].
Expert systems that incorporate fuzzy logic into processing the rules are known
as fuzzy ES. Since the first practical use of fuzzy logic in a control application by
Mamdani [30], many advances have been made at the theoretical level as well as in
applications. The wide array of variants now existing that use fuzzy logic for control
include:
μ
(
x
) ≤
those that only incorporate fuzzy sets in the rule consequents, as proposed by
Mamdani [31];
those that include mathematical expressions in the rule consequents, as suggested
by Sugeno [32].
In both cases the basic concepts of automatic control can be extended through the
introduction of notions such as fuzzy controller [33], fuzzy model [34, 35], fuzzy
system stability [36] or fuzzy model identification [37]. By way of example, Figure
7.2 shows the modular structure of a fuzzy controller that processes signals coming
from sensors (crisp inputs) to generate the signals that will be sent to the actuators
(crisp outputs).
7.3.2 Model Predictive Control
Model predictive control (MPC) embraces a complete family of controllers [38]
whose basic concepts are: (1) the use of an explicit dynamic model to predict pro-
cess outputs at discrete future time instants over a prediction horizon; (2) computa-
tion of a sequence of future control actions through the optimization of an objective
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