Manuel de la Sen

ROBUST STABILIZATION OF A CLASS OF UNCERTAIN TIME DELAY SYSTEMS IN SLIDING MODE

This paper addresses the problem of robust stabilization of a class of uncertain systems subject to internal (i.e., in the state) point delays, external (i.e., in the input) point delays and nonlinear disturbances by using sliding mode control. Methods for the design of sliding mode controllers based on state feedback, static output feedback and dynamic output feedback, respectively, are proposed. Sufficient conditions for the asymptotic stability and robustnesss of the closed–loop systems are given under a wide class of admissible nonlinear disturbances.

Second-order counterexamples to the discrete-time Kalman conjecture

The Kalman conjecture is known to be true for third-order continuous-time systems. We show that it is false in general for second-order discrete-time systems by construction of counterexamples with stable periodic solutions. We discuss a class of second-order discrete-time systems for which it is true provided the nonlinearity is odd, but false in general. This has strong implications for the analysis of saturated systems.

Exponential stability of simultaneously triangularizable switched systems with explicit calculation of a common Lyapunov function

In this note, a common quadratic Lyapunov function is explicitly calculated for a linear hybrid system described by a family of simultaneously triangularizable matrices. The explicit construction of such a function allows not only obtaining an estimate of the convergence rate of the exponential stability of the switched system under arbitrary switching but also calculating an upper bound for the output during its transient response. Furthermore, the presented result is then extended to the case where the system is affected by parametric uncertainty, providing the corresponding results in terms of the nominal matrices and uncertainty bounds.

Discretization and FIR filtering of continuous linear systems with internal and external point delays

A discrete quasi-autoregressive moving average (QARMA) model and an equivalent impulse response (IR) description are established for linear continuous systems with internal and external point delays which are discretized through a sampler and zero-order-hold device. The QARMA-model is proved to differ from the standard autoregressive moving average (ARMA) models because of its infinite input memory caused by the delays. Based on the IR-model, a finite impulse response (FIR)-filter is proposed to approximate the input-output description under exponential stability of the unforced system. Its implementation is discussed by using fast filtering design tools.

On vaccination control tools for a general SEIR-epidemic model

This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The control objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously that the remaining populations tend asymptotically to zero.

Wind turbine output power maximization based on sliding mode control strategy

The efficiency of the wind power conversions systems can be greatly improved using an appropriate control algorithm. In this work, a robust control for variable speed wind power generation that incorporates a doubly feed induction generator is described. In the presented design it is applied the so called vector control theory. The proposed control scheme uses stator flux-oriented control for the rotor side converter bridge control and grid voltage vector control for the grid side converter bridge control. The proposed robust control law is based on a sliding mode control theory, that, as it is well known, presents a good performance under system uncertainties. The stability analysis of the proposed controller under disturbances and parameter uncertainties is provided using the Lyapunov stability theory. Finally simulated results show, on the one hand that the proposed controller provides high-performance dynamic characteristics, and on the other hand that this scheme is robust with respect to the uncertainties that usually appear in the real systems.

Decentralized stabilization of networked complex composite systems with nonlinear perturbations

The objective of this paper is to propose an approach to decentralized stabilization with sampled-data delayed feedback for a class od networked continuous-time complex systems. Such a class is composed of identical nominal subsystems, symmetric nominal interconnections, and nonlinear perturbations. The proposed method employs the structural properties of the system to construct a low order control design model and the convex optimization approach. The effect of data-packet dropout and communication delays between the plant and the controller is included in the controller design. It is shown how this methodology can lead to a reduced-order control design with time-varying delay in the input. For such a purpose, a delay-dependent approach is considered in order to obtain a robustly delay-dependent stable overall closed-loop system with a decentralized controller.

Decentralized active control of a class of uncertain cable-stayed flexible structures

This paper addresses the problem of designing robust stabilizing controllers for a class of cable-stayed flexible structures. The dynamic behaviour of the structure is characterized by a beam decomposed into a finite number of concentrated masses. The mathematical model exhibits uncertainties in parameters, stay cable geometry and couplings, as well as in the unknown environmental excitation. The controller design is made based on the principle of sliding mode to reduce the magnitude of the transverse vibrations of the structure induced by the environmental excitation. A numerical simulation example is presented to illustrate the effectiveness of the proposed control scheme.

Model-based expert system to automatically adapt milling forces in Pareto optimal multi-objective working points

Highlights? Open and modular model-based expert system is proposed based on rules. ? The design of a novel cost function allows interface easily with the operator. ? The expert system incorporates main characteristics of intelligent systems. ? Integrate decision support or intelligent system working in parallel is allowed. The objective of this paper is to present an open and modular expert rule-based system in order to automatically select cutting parameters in milling operations. The knowledge base of the system presents considerations of stability, machine drives efficiency and restrictions while adaptively controlling milling forces in suitable working points. Moreover, a novel classical cost function has been conceived and constructed to Pareto-optimise cutting parameters subjected to multi-objective purposes, namely: tool-life, surface roughness, material remove rate and stability rate parameter. Different Pareto optimal front solutions can be obtained modulating the weighting factors of the cost function. Additional rules have been added in order to manually and/or automatically modulate this cost function. Furthermore, a database which relates weighting factors, cutting conditions and cost function variables is produced for learning purposes. Chatter detection and suppression system automatically feedback to the system to take into account non-modelled disturbances. Finally, since the knowledge of the system is basically obtained from mathematical models, the possibility of combining experience and knowledge from expert engineers and operators is included. In this way, best practice from mathematical modelling and expert engineers and operators is joined in one system obtaining a full, automated system combining the best of each world.As a result, the expert rule-based system selects Pareto optimal cutting conditions for a broad range of milling processes, sorting out automatically different problems such as chatter vibrations, incorporating model reference adaptive control (MRAC) of forces. This procedure is intuitive, being executed in the same way as a human expert would do and it provides the possibility to interact with expert engineers and operators in order to take into account their experience and knowledge. Finally, the expert system is designed in modular form allowing incorporating new functionalities in rule based forms to them or just adding new modules to improve the performance of the milling system.

Non-periodic and adaptive sampling. A tutorial review

The paper describes the use of adaptive and non-periodic sampling in different fields of System Theory and Control. The review is organized in a very comprehensive way and it presents results of the last thirty years about the problem of signal applications using as main tool adaptive sampling schemes including results is the improvement of the transient behaviors. Also, related results are presented about the use of non-periodic sampling in compensation as an alternative design to the wellknown frequency domain methods and about the choice of the sampling points in order to improve the transmission of measuring and/or rounding errors towards the results when studying the properties of dynamic systems such as controllability, observability and identifiability.