Multivariable Fuzzy Sliding Mode Control by Using a Simplex of Control Vectors
Since the basic work by Zadeh in the late sixties xc12, xc13, fuzzy logic has been intensively applied in the area of control system theory and design, in order to set up control environments which do not require the pecise knowledge of the mathematical model of the process to be controlled (see, for instance, xc3, xc8 and the references therein cited).
Indeed, fuzzy logic, enabling the definition of sets and membership functions of a certain elemenst to given sets by using natural language, appears to be suitable to deal with all those practical situations in which a certain level of uncertainty in the description of the system under study has to be taken into account.
The design of a fuzzy controller consists of a fixed number of steps. The aim of the controller is that of relating the relevant variables, such as input or error signals, usually described in a crisp way, to the cotnrol action. The first step is therefore devoted to the convension of the crisp input variables to the fuzzy form by associating with them the corresponding linguistic values.
The core of the controller is represented by a set of linguistic rule. These latter are evaluated according to the compositional rule of inference, producing a fuzzy output which, once transformed into a crisp variables, enables the generation of the suitable control action.
In spite of the wide variety og applications of fuzzy controllers to industrial processes, a certain number of problems, mainly related to the efficient design of the look-up table containing the fuzzy ruels, still remain to be overcome. A noteworthly attempt in this direction is constituted by the possibility of combining a controller design procedure based on fuzzy logic with a less qualitative design approach, such as that inspired to the variable structure systems theory, recently outlined in the literature xc7.
A variable structure controller (VSC) enables the definition of a suitable sliding manifold on which the state trajectories of the controlled system are kept, from a certain time instant onwards, in spite of the uncertainties assumed on the process in questions xc10, xc11. The sliding manifold coincides with the intersection of the discontinuity surfaces associated with the various control signals on the plan- t. As a consequence, the overall control strategy, once the state trajectory of the controlled systems lies on the sliding manifold becomes discontinuous.
KeywordsMembership Function Fuzzy Logic Control Vector Fuzzy Controller State Trajectory
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