Vilma A. Oliveira

Digital implementation of a magnetic suspension control system for laboratory experiments

In this paper, a digital control experiment using a magnetic suspension system is described. Although the results presented are for a quadratic optimal controller, the control system configuration used can cope with more advanced real-time control algorithms. Practical issues concerning parameter identification, computer simulation, discrete-time implementation, use of a digital signal processor based controller and filter design are addressed. Simulated and experimental responses are presented and analyzed. Finally, a detailed plan on reproducing the control experiment is included.

Technical communique: Synthesis of PID controllers for a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results on the design of proportional plus integral plus derivative (PID) controllers for a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. As far as we know, previous results on the synthesis of PID controllers rely on the solution of transcendental equations. This paper also extends previous results on the synthesis of proportional controllers for a class of delay systems of retarded type to a larger class of delay systems.

Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions

In this article, the fuzzy Lyapunov function approach is considered for stabilising continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing slack LMI variables into the problem formulation. The relaxation conditions given can also be used with a class of fuzzy Lyapunov functions which also depends on the membership function first-order time-derivative. The stability results are thus extended to systems with large number of rules under membership function order relations and used to design parallel-distributed compensation (PDC) fuzzy controllers which are also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilising conditions presented.

On the design of guaranteed cost controllers for a class of uncertain linear systems

In this paper, we consider the guaranteed cost control problem (GCCP) for a class of uncertain linear systems with structured parametric uncertainty. We present an approach to the GCCP for systems with arbitrary rank uncertainty matrices based on a rank-one description of the uncertain linear system. A search for an adequate rank-one overbounding of the uncertainty matrices is included in an optimisation problem thus reducing the conservatism of previous methods based on rank-one description of the uncertain system. The paper extends previous results on the GCCP for a rank-one description of the uncertain system, an important description of uncertain systems. A feature of the proposed approach is that an upper bound on the guaranteed cost is minimized by solving an optimization problem with linear matrix inequalities. A numerical example is presented to illustrate the computational efficiency of the proposed approach. For comparison, we also include results for a polytopic description of the uncertain linear system.

Fuzzy Stabilization of Power Systems in a Co-Generation Scheme Subject to Random Abrupt Variations of Operating Conditions

In this brief, a new stabilizing controller for the power system of an industrial plant operating in a co-generation scheme is proposed. The main source of perturbations considered in the operating conditions are random abrupt fluctuations in the local load, corresponding to the industrial processes being turned on and/or off. These fluctuations are described as Markovian jumps in the parameters of the power system. The proposed controller follows a standard structure which combines an automatic voltage regulator with a supplementary stabilizing term. This term is obtained with a fuzzy-model-based control technique formulated in the context of linear matrix inequalities under damping and control input constraints. Simulations performed on both a single-machine infinite-bus model and on a multimachine model show the effectiveness of the proposed fuzzy control strategy in reducing the oscillations as well as in maintaining a desired operating condition

Using Bayesian networks with rule extraction to infer the risk of weed infestation in a corn-crop

This paper describes the modeling of a weed infestation risk inference system that implements a collaborative inference scheme based on rules extracted from two Bayesian network classifiers. The first Bayesian classifier infers a categorical variable value for the weed-crop competitiveness using as input categorical variables for the total density of weeds and corresponding proportions of narrow and broad-leaved weeds. The inferred categorical variable values for the weed-crop competitiveness along with three other categorical variables extracted from estimated maps for the weed seed production and weed coverage are then used as input for a second Bayesian network classifier to infer categorical variables values for the risk of infestation. Weed biomass and yield loss data samples are used to learn the probability relationship among the nodes of the first and second Bayesian classifiers in a supervised fashion, respectively. For comparison purposes, two types of Bayesian network structures are considered, namely an expert-based Bayesian classifier and a naive Bayes classifier. The inference system focused on the knowledge interpretation by translating a Bayesian classifier into a set of classification rules. The results obtained for the risk inference in a corn-crop field are presented and discussed.

Stabilizing a class of time delay systems using the Hermite–Biehler theorem

Abstract In this paper we use the Hermite–Biehler theorem to establish results for the design of fixed order controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered.

Technical Communique: Gain scheduled controllers for dynamic systems using sector nonlinearities

In this work we explore the use of gain scheduling for the control of nonlinear systems. The nonlinear system is represented locally by uncertain linear models using sector nonlinearities representation. The uncertain linear models are then used to design a family of robust controllers. We propose a gain scheduling procedure for the problem of guaranteed transition from an actual operating condition to a desired one by constructing a pre-specified path in the state space for the system operating points. As far as we know this problem has not been addressed before. The gain scheduling control procedure given is illustrated in the context of the regulator problem with state feedback.

Synthesis of an LMI-based fuzzy control system with guaranteed cost performance: a piecewise Lyapunov approach

A new stability analysis and design of a fuzzy switching control based on uncertain Takagi-Sugeno fuzzy systems are proposed. The fuzzy system adopted is composed by a family of local linear uncertain systems with aggregation. The control design proposed uses local state feedback gains obtained from an optimization problem with guaranteed cost performance formulated in the context of linear matrix inequalities and a fuzzy switching scheme built from local Lyapunov functions. The global stability is guaranteed by considering a class of piecewise quadratic Lyapunov functions. Examples are given to illustrate the applicability of the proposed approach.

An extension of the invariance principle for dwell-time switched nonlinear systems

Abstract In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V , also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems.