Yau-Tarng Juang

Design of fuzzy PID controllers using modified triangular membership functions

A design method for fuzzy proportional-integral-derivative (PID) controllers is investigated in this study. Based on conventional triangular membership functions used in fuzzy inference systems, the modified triangular membership functions are proposed to improve a systems performance according to knowledge-based reasonings. The parameters of the considered controllers are tuned by means of genetic algorithms (GAs) using a fitness function associated with the systems performance indices. The merits of the proposed controllers are illustrated by considering a model of the induction motor control system and a higher-order numerical model.

Adaptive fuzzy particle swarm optimization for global optimization of multimodal functions

This paper proposes an adaptive fuzzy PSO (AFPSO) algorithm, based on the standard particle swarm optimization (SPSO) algorithm. The proposed AFPSO utilizes fuzzy set theory to adjust PSO acceleration coefficients adaptively, and is thereby able to improve the accuracy and efficiency of searches. Incorporating this algorithm with quadratic interpolation and crossover operator further enhances the global searching capability to form a new variant, called AFPSO-QI. We compared the proposed AFPSO and its variant AFPSO-QI with SPSO, quadratic interpolation PSO (QIPSO), unified PSO (UPSO), fully informed particle swarm (FIPS), dynamic multi-swarm PSO (DMSPSO), and comprehensive learning PSO (CLPSO) across sixteen benchmark functions. The proposed algorithms performed well when applied to minimization problems for most of the multimodal functions considered.

Stability analysis of dynamic interval systems

Abstract The stability analysis of interval matrices with certain stability margins is considered. By means of similarity transformation and Gershgorins theorem, new criteria are developed and illustrated by examples. We also demonstrate a counter-example to a recent result by Argoun (1986).

New methods to design an integral variable structure controller

This paper presents two methods to design a single-input/single-output integral variable structure system. Once an overall transfer function is selected, two simple ways are presented to determine the required switching surface and the control function. The proposed methods not only avoid transforming the original plant into a companion form, but also enable the resulting control system to achieve the asymptotic tracking for a step reference signal and disturbance rejection for a bounded disturbance signal simultaneously. Two examples are given to illustrate the effectiveness of the proposed methods.

Robustness of pole-assignment in a specified region

An analysis of pole-assignment is given for systems under linear time-invariant perturbations. Based upon the Lyapunov approach, new techniques to calculate allowable element bounds for highly structured perturbations are presented. Under these allowable perturbations both stability robustness and a certain performance robustness are thus ensured. Examples are given to illustrate the proposed methods. >

Root-locus approach to the stability analysis of interval matrices

A new approach, called the root-locus approach, is developed for the stability analysis of perturbed matrices. The basic idea of this approach is to ensure that the root loci of a continuously perturbed matrix remain in the open-left-half complex s-plane. Based on this approach, new techniques are presented to analyse the stability of interval matrices. Examples are given to demonstrate the merit of the proposed theorems.

New approach to time-domain analysis for stability robustness of dynamic systems

This paper presents a new approach to the analysis of the stability robustness of dynamic systems in state-space models. By continuously perturbing the state matrix, instead of solving the Lyapunov equation, an elegant stability robustness fundamental is derived. Subsequently, the allowable norm bound of the error matrix can be obtained under weakly structured perturbations, and the magnitude bound on individual elements of the error matrix can be obtained under highly structured perturbations. The merits of the theorems and corollary developed are demonstrated by two examples where the results achieved are much better than those already published in the literature. The concept that the perturbed state matrix would depend on the operating frequencies is also introduced.

Stability robustness analysis of digital control systems in state-space models

The stability robustness of discrete linear time-invariant systems in state-space models is analysed. Based on a root-locus approach and from the stable-eigenvalue viewpoint, fundamental criteria for testing the stability robustness of autonomous systems are derived and applied to the robustness analysis of multivariable feedback systems. Both the norm bound and the element bounds for the allowed perturbations are obtained. A stability robustness index is denned which is useful both for the analysis and synthesis of control systems.

Robust stability and robust pole assignment of linear systems with structured uncertainty

Sufficient conditions for the robust stability of linear time-varying systems are presented. The stability criteria are extended to the problem of the robust pole assignment of linear time-invariant systems to a specified region. These criteria, both for robust stability and robust pole assignment, improve some results in the literature. Examples are given to demonstrate the new criteria. >

Dynamic interval systems analysis and design

In this paper, new sufficient conditions for the stability of interval matrices are presented. Subsequently, design procedures are provided to synthesize robust static feedback controllers for dynamic interval systems. Both optimal control and pole region assignment design techniques are applied to make the closed-loop system achieve the requirements in system performance and stability robustness. Examples given confirm the availability of the proposed design approaches.