C.W. Tao

Design of sliding mode controllers for bilinear systems with time varying uncertainties

Sliding mode controllers for the bilinear systems with time varying uncertainties are developed in this paper. The bilinear coefficient matching condition which is similar to the traditional matching condition for linear system is defined for the homogeneous bilinear systems. It can be seen that the bilinear coefficient matching condition is very limited and is not generally applicable to the nonhomogeneous bilinear system. Thus, the sliding coefficient matching condition is also considered for the bilinear systems with time varying uncertainties. Then, the sufficient conditions are provided for the reaching mode of the time varying uncertain bilinear systems to be guaranteed by the designed sliding mode controllers. Moreover, the stability of the uncertain bilinear systems with the sliding mode controller is discussed. Simulation results are included to illustrate the effectiveness of the proposed sliding mode controllers.

Temperature control of a plastic extrusion barrel using PID fuzzy controllers

In this paper, a new PID fuzzy scheme is proposed to control the temperature of a plastic extrusion barrel. This fuzzy controller is based on the proportional-integral derivative fuzzy control scheme with if-then rules and triangular membership functions. For a traditional PID controller, the output is a linear combination of the error of the system, the derivative of the error, and the integral of the error. On the other hand, a conventional fuzzy controller has a nonlinear function of the error of the system and the derivative of the error as output. Since a nonlinear controller can usually control a nonlinear system more efficiently, thus fuzzy controllers often provide better performances than PID controllers in terms of shorter rise time and smaller overshoot. However, the traditional fuzzy controller cannot improve its steady-state performance for time-varying systems. To avoid this drawback, the PID fuzzy controller is developed. The design of this controller is briefly described. Then the experiment results are demonstrated. It is shown that the PID fuzzy control algorithm can meet the requirement of this temperature control project.

A Novel Fuzzy Ant Colony System for Parameter Determination of Fuzzy Controllers

In this paper, a novel fuzzy ant colony system (FACS) with a fuzzy mechanism and a fuzzy probable mechanism is presented for parameter determinations. Based on the fuzzy rules, the transition behavior of ants is simulated. The fuzzy probable mechanism is introduced with fuzzy probable rules to implement the diverse searching. The fuzzy probable rules are proposed to have the fuzziness in the antecedent parts and the probability in the consequent parts. To indicate the effectiveness, the fuzzy ant colony system is applied to find the proper parameters of the fuzzy sliding controllers for swinging and balancing the inverted pendulum and cart system. Also, the comparisons between the proposed fuzzy ant colony system and other ant colony optimization algorithms are provided in the simulations.

Stable anti-lock braking system using output-feedback direct adaptive fuzzy neural control

In this paper, an output feedback direct adaptive fuzzy neural controller for an anti-lock braking system (ABS) is developed. It is assumed that only the system output and the wheel slip ratio, is available for measurement. The main control strategy is to force the wheel slip ratio tracking variant optimal slip ratios, which may vary with the environment and assumed to be known during the vehicle-stopping period. By using the strictly-positive-real (SPR) Lyapunov theory, the stability of the closed-loop system can be verified. To demonstrate the effectiveness of the proposed method, simulation results are illustrated.

Design of fuzzy-learning fuzzy controllers

In this paper, the nested design approach with partial fuzzy if-then rule base is proposed to reduce the complexity of the fuzzy controllers. In the design procedure, the fuzzy controllers are first constructed with basic fuzzy if-then rules. When the performance requirements of the fuzzy control system are not satisfied the fuzzy controller will be adjusted accordingly. Based on the nested structure of the partial fuzzy rule base, the fuzzy rule base of a fuzzy controller is modified by replacing the unsatisfactory fuzzy rules with additional efficient fuzzy rules. Each fuzzy region of the input space can be partitioned all by itself into fuzzy subregions to avoid generating the redundant rules. And the nested structure of the partial fuzzy rule base can be further simplified into the nonnested one. Finally, simulations are carried out to show the effectiveness of the fuzzy controllers with nested fuzzy if-then rules.

A robust fuzzy control of a nonlinear magnetic ball suspension system

A methodology for the position control of a nonlinear magnetic ball suspension system based on fuzzy if-then rules is presented in this paper. With the experience of stabilizing the magnetic ball at a desired position using a PD controller, a robust complexity-reduced fuzzy controller is designed. Simulations with different initial position conditions of the ball suspension system are provided. Simulation results illustrate that the fuzzy controller is more robust than a classical PD controller in the sense of being able to stabilize a steel ball with a larger range of initial position conditions. Also, the performances of the fuzzy controller is shown to be better than a PD controller.

A Robust Fuzzy Support Vector Machine for Two-class Pattern Classification

This paper proposes a systematic method to classify data with outliers. The essential techniques consist of the outlier detection and the fuzzy support vector machine (FSVM). In this approach, the main body set for each class is first determined by the outlier detection algorithm (ODA) that estimates the outliers based on the total similarity objective function. Then, incorporated with the total similarity measure of the ODA, a fuzzy membership degree is assigned to each training sample. Experiments show that the proposed method can greatly reduce the effects of outliers in the training process and the final decision surface of the FSVM is insensitive to outliers.

Robust control of the mismatched systems with the fuzzy integral sliding controller

An adaptive fuzzy integral sliding mode controller for mismatched time-varying linear systems is presented in this paper. The proposed fuzzy integral sliding mode controller is designed to have zero steady state system error under step inputs and alleviate the undesired chattering around the sliding surface. The parameters in the fuzzy mechanism are adapted on-line to improve the performance of the fuzzy integral sliding mode control system. Thus, the bounds of the uncertainties are not required to be known in advance. The designed fuzzy integral sliding mode control system is shown to be invariant on the sliding surface. Moreover, the reaching mode of the sliding surface is guaranteed and the close-loop system is stable. Simulation results are included to illustrate the effectiveness of the presented fuzzy integral sliding mode controller.

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deadline: January 22, 2016

Sliding control for linear uncertain systems

A new design approach to enhance a terminal sliding mode controller for linear systems with mismatched time-varying uncertainties is presented in this paper. The nonlinear sliding surface is used to have the system states arrive at the equilibrium point in the finite time period. The sliding coefficient matching condition is extended for the terminal sliding mode control. The uncertain system with the proposed terminal sliding mode controller is shown to be invariant on the sliding surface. The reaching mode of the sliding surface is guaranteed and the close-loop system is stable. Moreover, the undesired chattering is alleviated with the designed terminal sliding mode controller. Simulation results are included to illustrate the effectiveness of the presented terminal sliding mode controller.