Analysis and design of multiresolutional fuzzy variable structure controller

The dependence between accuracy and control complexity of control systems is discussed. Multiresolutional control systems are introduced as a tool of reducing control complexity. A multiresolutional feedback controller is introduced which uses different levels of granularity of the information to attain the prescribed accuracy. The results are presented to determine the number of levels and the number of granules in each of the levels of multiresolutional controller. An approach for engineering design of a fuzzy controller which uses multiresolutional representation is presented. The prescribed accuracy is different at different levels of granularity. When the prescribed accuracy is low, a fuzzy controller based on lower resolution information can be used. As the process moves from level to level, the prescribed accuracy becomes higher and approaches the highest accuracy, the resolution of information to fuzzy controller becomes high. The high accuracy of control means that the controlled variables will have to be represented at high resolution which increases the complexity of the controller which for a fuzzy controller is proportional to the number of rules to be evaluated and the granularity of its inputs.; It was demonstrated how multiresolutional fuzzy controller can be merged with variable structure controllers (VSC) to develop a controller which guarantees the prescribed accuracy in the case of certain class of uncertain systems. The ability of fuzzy controller to handle measurement uncertainty can be used to make the VSC robust with respect to these uncertainties.