A Two-Level Fuzzy System for Control of Dynamic Objects

Abstract

The article discusses a two-level fuzzy system for control of dynamic objects, which is a kind of adaptive control systems. The need of adaptation is stemming from variability of controlled plant parameters with time. The system comprises an executive loop and a supervisory loop. The executive loop produces a command directly applied to the plant in accordance with the signal generated at the regulator output. The supervisory loop monitors the system performance quality indicators and periodically adjusts the regulator tuning parameters when the quality indicators go beyond the permissible limits. Solutions for implementing both the executive and supervisory loops on the basis of fuzzy logic inference algorithms are proposed. Fuzzy logic controllers (FLC) have received fairly wide use for control of intricate plants. However, the method of selecting their tuning parameters still remains heuristic in nature. The article describes an approach to tuning a fuzzy-logic controller based on comprehensive studies of its static and dynamic characteristics. The applied approach opened the possibility (i) to assess the influence of various factors on the controller's dynamic properties, (ii) to choose the tunings that can be most effectively used in setting up the supervisory loop, and (iii) to make the search for control solutions ensuring the required control system performance quality indicators more goal-seeking in nature. An algorithm based on fuzzy relational models, which is not an alternative to the well-known algorithms proposed by Mamdani, Larsen, Tsukamoto, is proposed. This algorithm is essentially a modified version of the mechanism of fuzzy logic inference at the rules activation stage and can be used in conjunction with the above mentioned algorithms. In using this algorithm, a fuzzy correspondence between the input and output fuzzy variables is established. In this case, there is no need of linking to any of fuzzy implication operations, and it becomes possible to modify the fuzzy inference result by changing not only the term membership functions of input and output linguistic variables, but also the elements of fuzzy correspondence The main factors influencing the dynamic properties of a fuzzy logic controller are formulated, and recommendations on using each of these factors in adjusting the controller are worked out. The conditions under which it is advisable to adapt a fuzzy controller to the changing parameters of a controlled plant are determined. The membership functions and the rule bases for the fuzzy inference algorithms that ensure high-quality performance of the system for controlling a plant with varying parameters in a sufficiently wide input signal frequency band are drawn up. The system simulation results are presented, which demonstrate that addition of a supplementary supervisory loop opens the possibility to maintain the system operability and to ensure acceptable control quality indicators of an unsteady dynamic object.