ON THE STABILITY OF LARGE-SCALE POWER SYSTEMS

Abstract

This paper deals with the problem of transient stability of large-scale power systems by visting decomposition-aggregation techniques. In this approach based on a priori criteria, the system is decomposed to N-subsystems, the first (N— 1) subsystems described by linear model and the Nthdescribed by nonlinear model. Then each linear subsystem is reduced by aggregation techniques to an equivalent machine. Using this approach the problem of transient stability of large power systems is investigated. An algorithm for calculating the critical switching time based on this technique is proposed. The validity of this method is examined by studying large power systems of 11 machines, and the results obtained using IBM 370/165 digital computer of L.A-A.S. are reported.     

Robust H ∞ fuzzy control of nonlinear systems with multiple time delays

A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and R_k of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H ^∞ control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach.     

Exponential stability and robust H∞ control of a class of discrete-time switched non-linear systems with time-varying delays via T-S fuzzy model

This paper deals with stability and robust H_∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H_∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.     

Relaxed stability condition and state feedback H ∞ controller design for T-S fuzzy systems

In this paper, a fuzzy Lyapunov approach is presented for stability analysis and state feedback H _∞ controller design for T-S fuzzy systems. A new stability condition is obtained by relaxing the ones derived in previous papers. Then, a set of LMI-based sufficient conditions which can guarantee the existence of state feedback H _∞ controller for T-S fuzzy systems is proposed. In comparison with the existing literature, the proposed approach not only provides more relaxed stability conditions but also ensures better H _∞ performance. The effectiveness of the proposed approach is shown through two numerical examples. Recommended by Editor Young-Hoon Joo. Xiao-Heng Chang received the B.E. and M.S. degrees from Liaoning Technical University, China, in 1998 and 2004, respectively, and the Ph.D. degree from Northeastern University, China, in 2007. He is currently a Lecturer in the School of Information Science and Engineering, Bohai University, China. His research interests include fuzzy control and robust control as well as their applications. Guang-Hong Yang received the B.S. and M.S. degrees in Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, nonfragile control systems design, and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), and an Associate Editor of the Conference Editorial Board of the IEEE Control Systems Society.     

Fuzzy Sets and Neural Networks

Abstract

It is possible that a better model for the behavior of a nerve cell may be provided by what might be called a fuzzy neuron, which is a generalization of the McCulloch-Pitts model. The concept of a fuzzy neuron employs some of the concepts and techniques of the theory of fuzzy sets which was introduced by Zadeh [2, 3] and applied to the theory of automaton by Wee and Fu [6], Tanaka et al. [7], Santo [8] and others. In effect, the introduction of fuzziness into the model of a neuron makes it better adapted to the study of the behavior of systems which are imprecisely defined by virtue of their high degree of complexity. Many of the biological systems, economic systems, urban systems and more generally, large-scale systems fall into this category.

In the nearly three decades since its publication, the pioneering work of McCulloch and Pitts [1], has had a profound influence on the development of the theory of neural nets, in addition to stimulating much of the early work in automata theory and regular events.

Although the McCulloch-Pitts model of a neuron has contributed a great deal to the understanding of the behavior of neural-like systems, it fails to reflect the fact that the behavior of even the simplest type of nerve cell exhibits not only randomness but, more importantly, a type of imprecision which is associated with the lack of sharp transition from the occurrence of an event to its non-occurrence.

In this paper, some basic properties of fuzzy neural networks as well as their applications to the synthesis of fuzzy automata are investigated. It is shown that any n-state minimal fuzzy automaton can be realized by a network of m fuzzy neurons, where ┌log₂ n┐ ? m ? 2n. Examples are given to illustrate the procedure. As an example of application, a realization of λ-fuzzy language recognizer using a fuzzy neural network is presented. The techniques described in this paper may be of use in the study of neural networks as well as in formal languages, pattern recognition, and learning.     

Reconstruction analysis-based algorithm to decompose a complex system into subsystems

Two previous papers [Mirats et al. (2002a) “On the selection of variables for Qualitative Modelling of Dynamical Systems”, International Journal of General Systems 31(5) pp. 435–467; Mirats et al. (2002b) “Variable selection procedures and efficient suboptimal mask search algorithms in Fuzzy Inductive Reasoning”, International Journal of General Systems 31(5), pp. 469–498] were devoted to the selection of a set of variables that can best be used to model (reconstruct) a given output variable, whereby only static relations were analysed. Yet even after reducing the set of variables in this fashion, the number of remaining variables may still be formidable for large-scale systems. The present paper aims at tackling this problem by discovering substructures within the whole set of the system variables. Hence whereas previous research dealt with the problem of model reduction by means of reducing the set of variables to be considered for modelling, the present paper focuses on model structuring as a means to subdivide the overall modelling task into subtasks that are hopefully easier to handle. The second and third sections analyse this problem from a system-theoretic perspective, presenting the reconstruction analysis (RA) methodology, an informational approach to the problem of decomposing a large-scale system into subsystems. The fourth section uses the fuzzy inductive reasoning (FIR) methodology to find a possible structure of a system. The study performed in this paper only considers static relations.     

A language-independent approach to the extraction of dependencies between source code entities

ContextSoftware networks are directed graphs of static dependencies between source code entities (functions, classes, modules, etc.). These structures can be used to investigate the complexity and evolution of large-scale software systems and to compute metrics associated with software design. The extraction of software networks is also the first step in reverse engineering activities.ObjectiveThe aim of this paper is to present SNEIPL, a novel approach to the extraction of software networks that is based on a language-independent, enriched concrete syntax tree representation of the source code.MethodThe applicability of the approach is demonstrated by the extraction of software networks representing real-world, medium to large software systems written in different languages which belong to different programming paradigms. To investigate the completeness and correctness of the approach, class collaboration networks (CCNs) extracted from real-world Java software systems are compared to CCNs obtained by other tools. Namely, we used Dependency Finder which extracts entity-level dependencies from Java bytecode, and Doxygen which realizes language-independent fuzzy parsing approach to dependency extraction. We also compared SNEIPL to fact extractors present in language-independent reverse engineering tools.ResultsOur approach to dependency extraction is validated on six real-world medium to large-scale software systems written in Java, Modula-2, and Delphi. The results of the comparative analysis involving ten Java software systems show that the networks formed by SNEIPL are highly similar to those formed by Dependency Finder and more precise than the comparable networks formed with the help of Doxygen. Regarding the comparison with language-independent reverse engineering tools, SNEIPL provides both language-independent extraction and representation of fact bases.ConclusionSNEIPL is a language-independent extractor of software networks and consequently enables language-independent network-based analysis of software systems, computation of design software metrics, and extraction of fact bases for reverse engineering activities.     

DECENTRALIZED STABILIZATION OF H FUZZY CONTROL FOR NONLINEAR MULTIPLE TIME‐DELAY INTERCONNECTED SYSTEMS

A robustness design of fuzzy control is proposed in this paper to overcome the effect of modeling errors between nonlinear multiple time‐delay systems and fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the UUB (uniformly ultimately bounded) stability of nonlinear multiple time‐delay interconnected systems with disturbances. Based on this criterion and the decentralized control scheme, a set of fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time‐delay interconnected systems and the Hcontrol performance is achieved in the mean time.     

Decentralised direct adaptive output feedback fuzzy controller for a class of large-scale nonaffine nonlinear systems and its applications

A novel cooperation-based decentralised direct adaptive fuzzy control via output feedback is developed for a class of large-scale nonaffine uncertain nonlinear systems using a direct adaptive fuzzy approach in this article. Under assumption that all the controllers share their prior information about the subsystem reference models, the interconnections between subsystems are relaxed to arbitrarily strong nonlinearities without matching conditions. The assumption on input gains is extended from typical positive constants to highly nonlinear functions. The feedback and adaptation mechanisms require neither the typical observation error filtering nor the famous strictly positive-real condition. Based on Lyapunov's direct method, the tracking errors of the closed-loop large-scale system are guaranteed to converge to tunable neighbourhoods of the origin. The proposed algorithm is applied to controlling two mechanical large-scale systems and simulation results substantiate its effectiveness.     

Supervisor localisation for large-scale discrete-event systems under partial observation

ABSTRACT

Recently we developed partial-observation supervisor localisation, a top-down approach to distributed control of discrete-event systems (DES) under partial observation. Its essence is the decomposition of the partial-observation monolithic supervisor into partial-observation local controllers for individual controllable events. In this paper, we extend the partial-observation supervisor localisation to large-scale DES, for which the monolithic supervisor may be incomputable. Specifically, we first employ an efficient heterarchical supervisor synthesis procedure to compute a heterarchical array of partial-observation decentralised supervisors and partial-observation coordinators. Then, we localise each of these supervisors/coordinators into partial-observation local controllers. This procedure suggests a systematic approach to the distributed control of large-scale DES under partial observation. The results are illustrated by a system of automatic guided vehicles serving a manufacturing workcell.     

GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

Generalized H2 （GH2） stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.     

Optimal fuzzy control of exponential synchronisation via genetic algorithm

In this study, a novel approach via GA-based fuzzy control is proposed to realize the exponential optimal H^∞ synchronisation of MTDC systems. A robustness design of model-based fuzzy control is first presented to overcome the effect of modelling errors between the MTDC systems and T-S fuzzy models. Next, a delay-dependent exponential stability criterion is derived in terms of Lyapunov's direct method to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability conditions of this criterion are reformulated into LMIs. According to the LMIs, a fuzzy controller is then synthesised to exponentially stabilise the error systems. Moreover, the capability of GA in random search for near-optimal solutions, the lower and upper bounds of the search space based on the feedback gains via LMI approach can be set so that the GA will seek better feedback gains of fuzzy controllers to speed up the synchronisation. Additionally, an IGA was proposed to overcome both the shortcomings of premature convergence of GA and local search. According to the IGA, a fuzzy controller is synthesised not only to realise the exponential synchronisation but also to achieve the optimal H^∞ performance by minimising the disturbance attenuation level.     

Decentralised direct adaptive fuzzy control for a class of large-scale nonaffine nonlinear systems and application to AHS

A novel decentralised direct adaptive fuzzy controller design is presented for a class of large-scale nonaffine uncertain nonlinear systems in this article. By integrating a fuzzy logic system and H _∞ tracking technique, the designed controller is able to adaptively compensate for interconnections and disturbances with unknown bounds, but none of the control and adaptation laws contains a sign function so that control chattering can be shunned. The closed-loop large-scale system is guaranteed to be asymptotically stable and obtain good H _∞ tracking performance. The control approach developed is applied to the following control problem of a string of vehicles within an automated highway system (AHS) and simulation results verify its validity.     

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

The stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H_∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive fuzzy controller design with observer for a class of uncertain nonlinear MIMO systems

In this paper, an adaptive fuzzy control approach is proposed to stabilize a class of uncertain nonlinear MIMO systems with the unmeasured states and the external disturbances. The fuzzy logic systems are used to approximate the unknown functions. Because it does not required to assume that the system states are measurable, it needs to design an observer to estimate the system unmeasured states. The considered MIMO systems are more general, i.e. they consist of N subsystems and each subsystem is in the non‐affine form. The stability of the closed‐loop system is verified by using Lyapunov analysis method. Two simulation examples are utilized to verify the effectiveness of the proposed approach. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Decentralised H ∞ filtering of interconnected discrete-time fuzzy systems with time delays

This article considers the decentralised H _∞ filtering of interconnected discrete-time fuzzy systems with time delays based on piecewise Lyapunov–Krasovskii functionals. The fuzzy system consists of J interconnected time-delay discrete-time Takagi–Sugeno fuzzy subsystems and the decentralised H _∞ filter is designed for each subsystem. It is shown that the stability with H _∞ performance of overall filtering error system can be established if a piecewise Lyapunov–Kroasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of the presented approach.     

Computation of parameter stability margins using polynomial programming techniques

In this paper, we consider linear time invariant (LTI) systems with parameter uncertainty. For such systems, we present global optimization techniques to determine permissible perturbations of the parameters of the system that maintain stability (the so-called parameter stability margins), for cases in which the coefficients of the characteristic equation of the system are polynomial functions of the uncertain parameters. The parameter uncertainty domains for maintaining stability are characterized as hypersolids, defined with respect to l_p -norms for various values of p ? (1, ∞). Algorithms are devised based on the reformulation–linearization/convexification technique (RLT) in concert with branch-and-bound methods to solve the underlying parametric non-convex subproblems for computing the stability margins. Several illustrative examples are solved to demonstrate the efficacy of the proposed approach towards producing global optimal solutions. We also present comparative computational experience with the commercial global optimizer BARON.     

H∞ fuzzy static output feedback control of T‐S fuzzy systems based on fuzzy Lyapunov approach

This paper is concerned with the problem of H_∞ fuzzy static output feedback control for discrete‐time Takagi‐Sugeno (T‐S) fuzzy systems, and new design methods are presented. By defining a fuzzy Lyapunov function, a new sufficient condition guaranteeing the H_∞ performance of the T‐S fuzzy systems is derived, and the condition is expressed by a set of linear matrix inequalities. In comparison with the existing literature, the proposed approach may provide more relaxed condition while ensuring better H_∞ performance. The simulation results illustrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

H∞Fuzzy State‐Feedback Control Plus State‐Derivative‐Feedback Control Synthesis for Photovoltaic Systems

This paper addresses the problem of designing an H_∞fuzzy state‐ feedback (SF) plus state‐derivative‐feedback (SDF) control system for photovoltaic (PV) systems based on a linear matrix inequality (LMI) approach. The TS fuzzy controller is designed on the basis of the Takagi‐Sugeno (TS) fuzzy model. The sufficient condition is found such that the system with the fuzzy controller is asymptotically stable and an H_∞performance is satisfied. First, a dc/dc buck converter is considered to regulate the power output by controlling state and state‐derivative variables of PV systems. The dynamic model of PV systems is approximated by the TS fuzzy model in the form of nonlinear systems. Then, based on a well‐known Lyapunov functional approach, the synthetic is formulated of an H_∞fuzzy SF plus SDF control law, which guarantees the L₂‐gain from an exogenous input to the regulated output to be less than or equal to some prescribed value. Finally, to show effectiveness, the simulation of the PV systems with the proposed control is assessed by the computer programme. The proposed control method shows good performance for power output and high stability for the PV system.