The Research Of T-S Fuzzy Control Systems Via Delta Operator Opproach

In the actual industrial production, many real-world physical processes are generally characterized by the presence of nonlinearity. It has been shown that T-S fuzzy technology gives an effective way to represent complex nonlinear systems by some simple local linear dynamic systems with their linguistic description. Then, we can analyze control and stability of the nonlinear system based on the traditional theory. In recent years, many researchers have studied T-S fuzzy control system. Meanwhile, a lot of achievements have been got. However, there have been few papers on nonlinear systems via delta operator approach, which motivates us to make an effort in this paper.Delta operator which is a new discretization method has been combined continuous and discrete systems. Now delta operator systems are the method of a unified description between continuous-time and discrete-time systems. Delta operator systems have not only avoided the numerical instability caused by the conversion issue, but also have made it reality that the method of the traditional design for continuous system can be directly applied to discrete time systems. The shorter the sampling period is, the better the system performances are for discrete time control systems. Delta operator solves a series of problems caused by the shift operator rapid sampling method, which has got successes such as high-speed signal processing, broadband communications and digital sampling control, and made a series of new progress and new achievements in the area of optimal filtering, sliding mode control, signal processing, networked control. In this paper, there some issues are discussed about fuzzy system based on the delta operator approach: fault detection for uncertain, fault-tolerant control, robust fuzzy contol subject to actuator saturation.Firstly, the uncertain T-S fuzzy systems for fault detection based on delta operator approach have been studied. We have constructed a fuzzy fault detection filter system and dynamics of filtering error generator by means of the T-S fuzzy model. The proposed fault-detection filter is sensitive to faults and simultaneously insensitive to disturbances and model uncertainties, which can quickly detect the fault. Some simulation results are provided to demonstrate the effectiveness of the obtained results.Secondly, fault-tolerant control for a class of T-S fuzzy systems via delta operator approach has been discussed. A fuzzy fault detection observer is constructed by means of T-S fuzzy delta operator systems. Moreover, a new approach is established for the estimation of faults in a class of nonlinear systems. Then, an active fault-tolerant controller is designed to compensate for the effect of the faults and makes the closed-loop fuzzy delta operator system stable. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.Finally, we focus on robust fuzzy-scheduling control for nonlinear systems with actuation saturation via delta operator approach. A set invariance condition is established in the T-S fuzzy delta operator system. Based on the set invariance condition, an optimization approach is proposed to estimate the domain of attraction for the fuzzy delta operator systems. Both PDC and non-PDC control laws are designed; such that the domain of attraction of the closed-loop T-S fuzzy delta operator system is arbitrarily close to a null controllable region. We use the balancing and swing-up of an inverted pendulum on a cart to demonstrate the effectiveness of the proposed methods in this paper.