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Fuzzy Control and Identification by John H. Lilly

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CHAPTER 10

ADAPTIVE FUZZY CONTROL

An adaptive controller is one that adjusts itself to changes in the plant it is controlling. For instance, consider a robotic arm carrying a load in its end manipulator (hand) and being controlled by an adaptive tracking controller. The controller is designed to force the arm to follow a prescribed reference trajectory through space while moving the load from its start point to its destination. If the mass being moved changes mid-trajectory (say the manipulator accidentally drops some of its load), the controller, because it is adaptive, can adapt to this change and still obtain the same tracking performance as before.

Adaptive controllers fall into two categories [27,33,36–39]: indirect and direct. The approach in indirect adaptive control is to identify a model for the plant, then to derive a controller based on this identified model. The controller calculation is done simultaneously with the plant identification, so model and controller evolve together.

This is called the certainty equivalence principle: at each point in the evolution, the controller design is based on the current plant estimate. It is assumed that, as the estimated plant model gets more accurate, the controller also gets more accurate and, in the limit, perfect control is obtained. Furthermore, since the identifier and controller run continuously, if the plant changes in some way (like the robotic arm dropping part of its load in the example above) the estimated model and corresponding ...

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