Analysis and design of a stable fuzzy control system

This paper addresses the analysis and design of fuzzy control systems for a class of complex uncertain single input single output nonlinear systems. In the design procedure, we represent the nonlinear system using a Takagi-Sugeno fuzzy model and construct a global fuzzy logic controller by blending all local state feedback controllers with a sliding mode controller. Unlike the commonly used parallel distributed compensation technique, we can design a global stable fuzzy controller without finding a common Lyapunov function for all local control systems, and can obtain a good tracking performance. Furthermore, a stability analysis is carried out not for the fuzzy model but for a real nonlinear system with uncertainties. One simulation example is given to show the effectiveness and feasibility of the proposed fuzzy controller design method.

In this second part of the paper on the analysis and design of uncertain fuzzy control systems, we present a controller design method for a class of uncertain fuzzy control systems. This class of systems can be represented by the discrete-time uncertain fuzzy models discussed in Part I. Since this model representation considers system uncertainties and system disturbance, the controller design problem for this kind of model becomes a H/sub /spl infin// control problem for a nonlinear uncertain system. A new stability analysis and control system design approach are then developed for this kind of uncertain fuzzy model. Furthermore, a constructive algorithm is developed to obtain the H/sub /spl infin// feedback control law.

In this paper, a class of fuzzy stochastic control systems with random delays is examined. The fuzzy rule base used consists of a collection of r fuzzy IF-THEN rules defined as a function of the conditional variable. The method of theory of invariant cones is used to design a class of local fuzzy control law. A verifiable sufficient condition for stochastic stability of the fuzzy stochastic delay differential equation is given.

Over the past two decades, there has been a rapidly growing interest in approximating a nonlinear system by a Takagi-Sugeno (T-S) fuzzy model (Takagi & Sugeno, 1985). In general, this model is represented by using a set of fuzzy rules to describe a global nonlinear system in terms of a set of local linear models which are smoothly connected by fuzzy membership functions. Based on the T-S fuzzy model, recently, various fuzzy controllers have been developed under the so-called parallel-distributed compensation (PDC) scheme (in which each control rule is distributively designed for the corresponding rule of a T-S fuzzy model) and have been widely and successfully applied in fields ranging from aerospace to process control. The reason is because the fuzzy model-based control method provides a natural, simple and effective design approach to complement other nonlinear control techniques that require special and rather involved knowledge. Below are listed the main features of T-S model-based fuzzy control method: 1. It does not require severe structural assumptions on the plant model. 2. It preserves well-understood linear intuition. 3. It is naturally compatible with decompositions of the overall control problem. The decompositions are typically not hierarchical, and the interactions of sub-problems are captured by physical variables that are typically state variables in a more complete model of the overall system. 4. It enables control systems to respond rapidly to changing operating conditions. For this reason, it is important that the selected physical variables reflect changes in plant dynamics as operating conditions change. In fact, the T-S model-based fuzzy control method (of divide and conquer type) constructs a nonlinear controller, with certain required dynamic properties, by combining, in some sense, the members of appropriate family of linear time-invariant controllers. Here, nonlinear control design task is broken into a number of linear sub-problems, which enable linear design methods to be applied to nonlinear problems. Within the general framework of the T-S fuzzy model-based control method, a flurry of research activities have quickly yielded many important results on the design of fuzzy control systems by means of the following Lyapunov function approaches: 1. Common quadratic Lyapunov function approach (Tanaka & Sugeno, 1992; Tanaka et al, 1996; Wang et al, 1996; Cao & Frank, 2000; Assawinchaichote, 2004).

Stability is one of the most important concepts of analysis and design of control systems. Stability analysis of fuzzy control systems has been difficult since fuzzy systems are essentially nonlinear systems. Recently, stability analysis techniques [l]-[6] [13]-[16] based on nonlinear stability theory have been reported. Langari and Tomizuka [2, 6] analyzed stability of fuzzy linguistic control systems. Kitamura [3] realized stability analysis of fuzzy control systems by using extended circle criterion. Farinwata [5] and Kato [14] utilized phase plane analysis type of techniques, tanaka and co-authors [1,3,4] applied Lyapunov approach to fuzzy control systems and recently developed LMI-based designs [10, 17, 28-37], where LMI stands for nonlinear matrix inequality.

Gravitational search algorithm-based design of fuzzy control systems with a reduced parametric sensitivity

We show how frequency domain design procedures can be effectively used in nonlinear fuzzy control systems. For this purpose, theoretical justifications of the approach discussed here are provided to show that solid notions from nonlinear system and control theory can be successfully applied in the fuzzy control domain. The methodology proposed is very simple, but powerful, effective and practical. In addition, it supports systematic control system design and stability analysis in the frequency domain for systems described by mathematical, linguistic or experimental models. Several case studies are included to illustrate the usefulness of frequency response in conventional fuzzy control systems analysis and design.

The paper discusses the controller design for a class of fuzzy systems. A new method is developed for the design of fuzzy control systems. The basic idea of this new method is to represent the fuzzy system in a family of local state space models, and then to construct a global controller by considering each local state feedback controller. It is shown that this controller guarantees global stability of the closed loop fuzzy system. The issue of a state observer for the fuzzy system is also addressed. A numerical example is given for demonstration of the performance of the method. >

This paper presents a rigorous mathematical development for the design of robust intelligent type-2 fuzzy control systems with regards to the disturbance rejection problem. The majority of the papers in the literature uses only type-1 fuzzy systems for the modeling of both plant ant controller. In the control structure presented in this paper, we use type-2 fuzzy systems, which are more generalized than their type-1 counterparts and particularly known for handling uncertainties. This work extends and generalizes the previous results for the design of robust intelligent control systems. The final robust criteria are given based on linear matrix inequalities (LMIs), and two examples are provided to demonstrate the developed methodologies. The simulation results also show the potential of type-2 fuzzy controllers in improving robustness compared to type-1. The mathematically-sound general framework proposed in this paper provides a systematic tool for the design of robust intelligent controllers, and hence it is expected to widen their applications.

This paper presents the design and application of fuzzy neural network control system for the rotary cement kiln system. Due to the dynamic characteristics and reaction process parameters are with features of large inertia, pure hysteresis, nonlinearity and strong coupling, the fuzzy neural network controller combining both the advantages of neural network and fuzzy control was applied. The fuzzy neural network is an adaptive control process whose parameters can be adjusted by learning algorithms automatically which is aimed to eliminate the shortcomings of conventional control methods. The main control system structure includes mainly the pressure control loop, the burning zone control loop and the back-end of kiln temperature control loop. Simulation results show the effectiveness of the control scheme with satisfied dynamic performances on response time and overshoot.

In the past several years, research results on type- 2 fuzzy control have started to emerge in the literature. None of them, however, are concerned with mathematical input-output relationship of a type-2 fuzzy controller. Establishing such relationship is important as it will deepen our understanding of type- 2 fuzzy controller structures, how they function, and their advantages and drawbacks as compared to type-1 fuzzy controllers and conventional controllers (e.g., the PID controller). The availability of such structure will also lay a foundation for more rigorous theoretical analysis and design of type-2 fuzzy control systems. In this paper, we derive the mathematical input-output relation of a type-2 fuzzy PD (or PI) controller that has one of the simplest possible configurations - only two interval type-2 fuzzy sets for each input variables, four fuzzy rules with Zadeh AND operator, and four interval type-2 output fuzzy sets. We relate the resulting structure to conventional control theory and show that it actually is a PD (or PI) controller with the proportional and derivative (or integral) gains changing as the input variable values vary.

A systematic methodology for the design of a learning fuzzy logic control system is presented. The basic design idea is an indirect control approach where selection of control parameters relies on the estimates of process parameters. The control law consists of three components: an online fuzzy identifier, a desired transition model, and a fuzzy controller. The fuzzy version of the signal Hebbian learning law is introduced for adaptively identifying the process relation of the unknown plant. The desired transition model is constructed so that the control designer's goal can be achieved. A computationally efficient way to construct the transition model is provided via a forward-in-time method based on the concept of truncated policy space. Clear trade-offs between control performance and computational complexity are obtained. >

Based on the properties analysis of Takagi-Sugeno (T-S) fuzzy systems with two-overlapped fuzzy partition (TFP) inputs, an analytical design approach of T-S fuzzy control systems is proposed in this paper. This approach includes two parts: (1) a new method to check the stability of a T-S fuzzy control system which only requires to find a common positive-definite matrix in each maximal overlapped-rules group (MORG). This method can reduce the conservatism and difficulty of the former stability analysis methods. (2) The systematic design of T-S fuzzy controllers by means of the parallel distributed compensation (PDC) and linear matrix inequalities (LMI). The simulation results of a nonlinear mass-spring-damper system show that this approach is effective.

A new DNA-based immune genetic algorithm (DNA-IGA) is proposed to design a class of Takagi-Sugeno fuzzy control systems. The DNA-IGA is developed from the structures of biological immune system and DNA. The genetic operators of the method are based on the DNA genetic operations and evaluation of immune system. It uses DNA encoding method stemmed from the biological DNA to encode the design parameters of the fuzzy controllers. The DNA encoding method can significantly shorten the code length of antibodies and is suitable for complex knowledge representation. The proposed method has the local search ability and prevents the premature convergence. As a demonstration, we show how to implement the new method to optimize the design parameters of the TS fuzzy controller in control of a nonlinear system. Computer simulation indicates that the designed fuzzy controller is satisfactory.

The paper proposes the design of the supervisory heuristic fuzzy control system applied to a Sequencing Batch Reactor (SBR) in the Wastewater Treatment Plant (WWTP). Based on real data records and the biological process and aeration system models, a control system for biological processes has been designed. The supervisory control system performs management of the reactor work cycle, determines the phase length, controls the sludge age, calculates the setpoint of dissolved oxygen, and adapts parameters of the lower control layer. The results of simulation tests for the case study wastewater treatment plant are presented.