Evaluation of Robust Performance of Fuzzy Supervisory Control Technique

Abstract

This paper describes the robust performance of fuzzy supervisory control (FSC) approach for the seismic response control of cable-stayed bridges. FSC is a hybrid control method with the hierarchical structure of several sub-controllers and fuzzy supervisor. Each sub-controller is preliminarily designed to reduce the selected response of the structure only, and a fuzzy supervisor is introduced to improve the overall control performance by modulating the predesigned static gains into time-varying dynamic gains. To demonstrate the robust performance of the proposed strategy, the FSC and linear quadratic Gaussian (LQG) controller are optimally designed and their seismic performances are compared according to the variation of the bridge stiffness in the phase I benchmark control problem. The comparative results show that the FSC system can clearly guarantee the robust performance against the uncertainties of the bridge model. FUZZY SUPERVISORY CONTROLFor the active control of the structure, optimal control methods such as LQR, LQG [1], H 2 , and H ∝ are commonly used. These optimal controls specify a cost function characterized as single control gain. However, it is not easy to aggregate all the performance requirements into a single-valued cost function. Since there exist a number of operation conditions which need to be considered for the control system, a satisfactorily performing control system may not be achieved by a single gain controller. One of the effective approaches is FSC technique which can modulate several types of well-developed controllers continuously during controlling a structure. To improve the control performance of active control system, therefore, we adopt fuzzy supervisory control method.Since the fuzzy supervisory control approach takes a form of a hierarchical structure as shown in Figure 1, it involves a two-step design procedure comprising design of subcontrollers and fuzzy-tuning of the pre-designed sub-controllers [2]. In this paper, LQG control method is used for the design of the sub-controllers, and then a fuzzy tuner is introduced to modulate the pre-designed static gains into time-varying dynamic gains. The fuzzy tuner is composed of four elements, i.e., a fuzzification interface, an inference mechanism, a rule-base and a defuzzification interface, which are characterized as an input membership function, a fuzzy rule table and an output membership function. Fuzzy rule table can be illustrated graphically as a fuzzy rule surface in Figure 2. It identifies the current behavior of the structural system and reasonably determines the contribution factors of the sub-controllers in accordance with the structural response information. As a result, the fuzzy tuning process for various earthquake excitations differently modulates the sub-controllers.