A Data-driven Approach to Robust Control of Multivariable Systems by Convex Optimization

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like $H_2$, $H_\infty$ and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex-concave optimization problem and then convexified by linearization of the concave part around an initial controller. The performance criterion converges monotonically to a local optimal solution in an iterative algorithm. The effectiveness of the method is compared with fixed-structure controllers using non-smooth optimization and with full-order optimal controllers via simulation examples. Finally, the experimental data of a gyroscope is used to design a data-driven controller that is successfully applied on the real system

Process operating mode monitoring : switching online the right controller

This paper presents a structure which deals with process operating mode monitoring and allows the control law reconfiguration by switching online the right controller. After a short review of the advances in switching based control systems during the last decade, we introduce our approach based on the definition of operating modes of a plant. The control reconfiguration strategy is achieved by online selection of an adequate controller, in a case of active accommodation. The main contribution lies in settling up the design steps of the multicontroller structure and its accurate integration in the operating mode detection and accommodation loop. Simulation results show the effectiveness of the operating mode detection and accommodation (OMDA) structure for which the design steps propose a method to study the asymptotic stability, switching performances improvement, and the tuning of the multimodel based detector

A comparative study of three validities computation methods for multimodel approach

The multimodel approach offers a very satisfactory results in modelling, diagnose and control of complex systems. In the modelling case, this approach passes by three steps: the determination of the model’s library, the validities computation and the establishment of the final model. In this context, this paper focuses on the elaboration of a comparative study between three recent methods of validities computation. Thus, it highlight the method that offers the best performances in term of precision. To achieve this goal, we apply, these three methods on two simulation examples in order to compare their performances

Enhanced LFR-toolbox for MATLAB and LFT-based gain scheduling

We describe recent developments and enhancements of the LFR-Toolbox for MATLAB for building LFT-based uncertainty models and for LFT-based gain scheduling. A major development is the new LFT-object definition supporting a large class of uncertainty descriptions: continuous- and discrete-time uncertain models, regular and singular parametric expressions, more general uncertainty blocks (nonlinear, time-varying, etc.). By associating names to uncertainty blocks the reusability of generated LFT-models and the user friendliness of manipulation of LFR-descriptions have been highly increased. Significant enhancements of the computational efficiency and of numerical accuracy have been achieved by employing efficient and numerically robust Fortran implementations of order reduction tools via mex-function interfaces. The new enhancements in conjunction with improved symbolical preprocessing lead generally to a faster generation of LFT-models with significantly lower orders. Scheduled gains can be viewed as LFT-objects. Two techniques for designing such gains are presented. Analysis tools are also considered

Design of a Fractional Order CRONE and PID Controllers for Nonlinear Systems using Multimodel Approach

This paper deals with the output regulation of nonlinear control systems in order to guarantee desired performances in the presence of plant parameters variations. The proposed control law structures are based on the fractional order PI (FOPI) and the CRONE control schemes. By introducing the multimodel approach in the closed-loop system, the presented design methodology of fractional PID control and the CRONE control guarantees desired transients. Then, the multimodel approach is used to analyze the closed-loop system properties and to get explicit expressions for evaluation of the controller parameters. The tuning of the controller parameters is based on a constrained optimization algorithm. Simulation examples are presented to show the effectiveness of the proposed method

The Middeck Active Control Experiment (MACE)

The Middeck Active Control Experiment (MACE) is a NASA In-Step and Control Structure Interaction (CSI) Office funded Shuttle middeck experiment. The objective is to investigate the extent to which closed-loop behavior of flexible spacecraft in zero-gravity (0-g) can be predicted. This prediction becomes particularly difficult when dynamic behavior during ground testing exhibits extensive suspension and direct gravity coupling. On-orbit system identification and control reconfiguration is investigated to improve performance which would otherwise be limited due to errors in prediction. The program is presently in its preliminary design phase with launch expected in the summer of 1994. The MACE test article consists of three attitude control torque wheels, a two axis gimballing payload, inertial sensors and a flexible support structure. With the acquisition of a second payload, this will represent a multiple payload platform with significant structural flexibility. This paper presents on-going work in the areas of modelling and control of the MACE test article in the zero and one-gravity environments. Finite element models, which include suspension and gravity effects, and measurement models, derived from experimental data, are used as the basis for Linear Quadratic Gaussian controller designs. Finite element based controllers are analytically used to study the differences in closed-loop performance as the test article transitions between the 0-g and 1-g environments. Measurement based controllers are experimentally applied to the MACE test article in the 1-g environment and achieve over an order of magnitude improvement in payload pointing accuracy when disturbed by a broadband torque disturbance. The various aspects of the flight portion of the experiment are also discussed

On the Characterization of Hankel and Toeplitz Operators Describing Switched Linear Dynamic Systems with Point Delays

This paper investigates the causality properties of a class of linear time-delay systems under constant point delays which possess a finite set of distinct linear time-invariant parameterizations (or configurations) which, together with some switching function, conform a linear time-varying switched dynamic system. Explicit expressions are given to define pointwisely the causal and anticausal Toeplitz and Hankel operators from the set of switching time instants generated from the switching function. The case of the auxiliary unforced system defined by the matrix of undelayed dynamics being dichotomic (i.e., it has no eigenvalue on the complex imaginary axis) is considered in detail. Stability conditions as well as dual instability ones are discussed for this case which guarantee that the whole system is either stable, or unstable but no configuration of the switched system has eigenvalues within some vertical strip including the imaginary axis. It is proved that if the system is causal and uniformly controllable and observable, then it is globally asymptotically Lyapunov stable independent of the delays, that is, for any possibly values of such delays, provided that a minimum residence time in-between consecutive switches is kept or if all the set of matrices describing the auxiliary unforced delay—free system parameterizations commute pairwise.Ministerio de Educación (DPI2006-00714

A Novel Discrete Internal Model Control Method for Underactuated System

This article provides a comparative analysis of two common control configurations used to control the side-stream distillation used to separate benzene, toluene and xylene as suggested by Doukas and Lyben. Their under-actuated model has been considered as the model of distillation column and the internal model controller is designed considering a Singular Value Decomposition (SVD) and Virtual Inputs (VI) techniques. An internal controller design based on VI is proposed in this article for this kind of underactuated systems. This design is used to control in parallel the distillation process and its model in real time. The proposed controller design is simple and systematic in relation with the desired closed loop specifications of the internal model control structure. Furthermore, the controller obtained ensure robustness to process variations. The SVD technique can realize the decoupling of under-actuated processes and wipe out unrealizable factors by introducing compensation terms, affecting the dynamic of the system. The aim of this article is to make a comparison between our proposed VI controller and the SVD approach. The results we obtained confirmed the potentials of the proposed controller based on VI considering the set point tracking and its robustness

Dissipativity analysis of stochastic fuzzy neural networks with randomly occurring uncertainties using delay dividing approach

This paper focuses on the problem of delay-dependent robust dissipativity analysis for a class of stochastic fuzzy neural networks with time-varying delay. The randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated Bernoulli-distributed white noise sequences. Based on the Itô's differential formula, Lyapunov stability theory, and linear matrix inequalities techniques, several novel sufficient conditions are derived using delay partitioning approach to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties. It is shown, by comparing with existing approaches, that the delay-partitioning projection approach can largely reduce the conservatism of the stability results. Numerical examples are constructed to show the effectiveness of the theoretical results