L. K. Wong

A fuzzy sliding controller for nonlinear systems

It is well known that sliding-mode control can give good transient performance and system robustness. However, the presence of chattering may introduce problems to the actuators. Many chattering elimination methods use a finite DC gain controller which leads to a finite steady-state error. One method to ensure zero steady-state error is using a proportional plus integral (PI) controller. This paper proposes a fuzzy logic controller which combines a sliding-mode controller (SMC) and a PI controller. The advantages of the SMC and the PI controller can be combined and their disadvantages can be removed. The system stability is proved, although there is one more state variable to be considered in the PI subsystem. An illustrative example shows that good transient and steady-state responses can be obtained by applying the proposed controller.

Lyapunov-function-based design of fuzzy logic controllers and its application on combining controllers

This paper presents the design of fuzzy logic controllers (FLCs) for nonlinear systems with guaranteed closed-loop stability and its application on combining controllers. The design is based on heuristic fuzzy rules. Although each rule in the FLC refers to a stable closed-loop subsystem, the overall system stability cannot be guaranteed when all these rules are applied together. In this paper, it is proved that if each subsystem is stable in the sense of Lyapunov (ISL) under a common Lyapunov function, the overall system is also stable ISL. Since no fuzzy plant model is involved, the number of subsystems generated is relatively small, and the common Lyapunov function can be found more easily. To probe further, an application of this design approach to an inverted pendulum system that combines a sliding-mode controller (SMC) and a state feedback controller (SFC) is reported. Each rule in this FLC has an SMC or an SFC in the consequent part. The role of the FLC is to schedule the final control under different antecedents. The stability of the whole system is guaranteed by the proposed design approach. More importantly, the controller thus designed can keep the advantages and remove the disadvantages of the two conventional controllers.

Stability design of TS model based fuzzy systems

An approach for designing Takagi-Sugeno (TS) model based fuzzy systems (1985) using output feedback with guaranteed closed-loop stability is proposed in this paper. The complex process on finding a common Lyapunov function to guarantee the system stability can be omitted. This can significantly simplify the design procedure. Moreover the overall closed-loop system behaves like a linear system and the system responses can be designed by properly choosing the coefficients of the closed-loop transfer function. An illustrative example will be given to demonstrate the ability of the proposed approach.

Lyapunov function based design of heuristic fuzzy logic controllers

A stability design of fuzzy logic controllers (FLCs) for nonlinear systems is proposed in this paper. In heuristic design of FLCs, we often have a lot of rules. Although each rule governing the control of the plant refers to a stable closed-loop subsystem, the overall system stability cannot be guaranteed when all of these rules are put together into a rule base for the FLC. This limitation is tackled in this paper. It is shown that on adding arbitrary rules to the FLC without any restriction on the form of membership functions, the system stability can be ensured if each individual rule applying to the plant results in a stable subsystem in the sense of Lyapunov subject to a common Lyapunov function for all rules. Analytical proof of the result is given and its application on designing a heuristic of FLC is illustrated through an example.

A chattering elimination algorithm for sliding mode control of uncertain non-linear systems

It is well-known that sliding mode control is capable of tackling non-linear systems with parameter uncertainties. However, the discontinuous control signal causes a significant problem of chattering. An algorithm is proposed in this paper to eliminate chattering by removing the discontinuous control when the system is operating near the sliding plane. The transient performance as well as the robustness property will not be affected and zero steady-state error is ensured. Mathematical derivation of the algorithm is detailed. This algorithm is applied to a non-linear system with parameter uncertainties and a car-pole inverted pendulum to show its ability and merits.

An improved Lyapunov function based stability analysis method for fuzzy logic control systems

Many existing stability analysis methods for fuzzy logic control systems like TS fuzzy model based methods usually tackle plants that are linear with respect to control. The paper proposes a method which does not have such restriction. The proposed method employs a Lyapunov function to prove the stability of the non-linear fuzzy logic control system. An illustrative example is given to demonstrate the ability of the method. The plant in this example has a control signal function composed of piecewise linear functions, saturation functions and a deadband.

A simple large-signal nonlinear modeling approach for fast simulation of zero-current-switch quasi-resonant converters

A nonlinear modeling approach for zero-current-switch (ZCS) quasi-resonant converters (QRC) is proposed which can be derived easily using simple analytical techniques. The converter model obtained is readily absorbed by MATLAB for analysis and design of both the open- and closed-loop configurations in fast speed. Simulations have shown its accuracy, even for large-signal transient responses. Applications of this modeling approach to the three basic topologies of buck, boost, and buck-boost converters are given as illustrative examples. The condition for zero-current switching is identified from the model. The feasibility of applying this proposed modeling approach to the extended period QRC topologies is to be discussed. Simulation results for the three basic topologies are given to show the merits of the proposed modeling approach.

Control of PWM inverter using a discrete-time sliding mode controller

PWM inverters are widely used in UPS systems and driving induction motors. They give AC sinusoidal voltage under linear or nonlinear loads which is a basic tracking control problem. Since the duty cycle of a PWM inverter is unchanged within one switching period, inverters are very suitable to be represented by discrete-time state equations. A discrete-time sliding-mode controller based on an improved reaching condition has been proposed by Gao et. al. This paper applies this controller to control PWM inverters with linear and nonlinear loads. It is shown that good output responses are obtained in both cases.

The design of stable fuzzy logic controllers with combination of conventional controllers

This paper shows the design of a fuzzy logic controller (FLC) which combines a sliding mode controller (SMC) and a state feedback controller (SFC). Each rule in this FLC has an SMC or an SFC as the consequent part. The role of the FLC is to schedule the two conventional controllers and obtain the final control under different antecedents. Although each sub-system defined by the antecedent part of each rule is readily stabilized by the associated SMC or SFC in the consequent part, the overall system stability on combining the rules cannot be guaranteed immediately. The system stability can be ensured by using a proposed Lyapunov function based design approach. This FLC is applied to balance a car-pole inverted pendulum system as an illustrative example. It is shown that the FLC can keep the advantages and remove the disadvantages of the two conventional controllers.

Design of an analog fuzzy logic controller for a PWM boost converter

Fuzzy logic controllers (FLCs) have been widely used in many applications, However, they are usually implemented digitally by expensive digital signal processors (DSPs), and the performance is restricted by the sampling period. In this paper, an analog FLC implemented by a low-cost device is proposed. Through analog circuitry, the features of an FLC such as membership function shaping, rule inference and defuzzification are realized. The controller is successfully applied to regulate a PWM boost power converter with satisfactory performance.