Observer-based anti-windup compensator design for saturated control systems using an LMI approach

AbstractIn practical control systems, actuator saturation usually induces a windup phenomenon and potentially results in system instability. Accordingly, this paper develops an observer-based auxiliary anti-windup compensation scheme to mitigate the effects of actuator limitations on the performance and stability of the controlled system. In the proposed approach, the controller output signal passing through the saturation element is treated as an external disturbance imported to the designed controller and an auxiliary controller is designed to minimize the difference between the controller output signal and the system input signal. The conditions required to maintain the system performance in the presence of actuator saturation are formulated as an LMI criterion. The L2-stability criterion of the anti-windup compensator design is also formulated as an LMI condition. It is shown that by integrating the two LMI conditions and solving the resulting optimization problem, the resulting anti-windup controller both minimizes the performance attenuation of the saturated control system and guarantees its L2-stability

Digital repetitive control under varying frequency conditions

Premi extraordinari doctorat curs 2011-2012, àmbit d’Enginyeria IndustrialThe tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area and Repetitive Control has proven to be an efficient way to face this topic; however, in some applications the period of the signal to be tracked/rejected changes in time or is uncertain, which causes and important performance degradation in the standard repetitive controller. This thesis presents some contributions to the open topic of repetitive control working under varying frequency conditions. These contributions can be organized as follows: One approach that overcomes the problem of working under time varying frequency conditions is the adaptation of the controller sampling period, nevertheless, the system framework changes from Linear Time Invariant to Linear Time-Varying and the closed-loop stability can be compromised. This work presents two different methodologies aimed at analysing the system stability under these conditions. The first one uses a Linear Matrix Inequality (LMI) gridding approach which provides necessary conditions to accomplish a sufficient condition for the closed-loop Bounded Input Bounded Output stability of the system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability conditions. Both methodologies yield a frequency variation interval for which the system stability can be assured. Although several approaches exist for the stability analysis of general time-varying sampling period controllers few of them allow an integrated controller design which assures closed-loop stability under such conditions. In this thesis two design methodologies are presented, which assure stability of the repetitive control system working under varying sampling period for a given frequency variation interval: a mu-synthesis technique and a pre-compensation strategy. On a second branch, High Order Repetitive Control (HORC) is mainly used to improve the repetitive control performance robustness under disturbance/reference signals with varying or uncertain frequency. Unlike standard repetitive control, the HORC involves a weighted sum of several signal periods. With a proper selection of the associated weights, this high order function offers a characteristic frequency response in which the high gain peaks located at harmonic frequencies are extended to a wider region around the harmonics. Furthermore, the use of an odd-harmonic internal model will make the system more appropriate for applications where signals have only odd-harmonic components, as in power electronics systems. Thus an Odd-harmonic High Order Repetitive Controller suitable for applications involving odd-harmonic type signals with varying/uncertain frequency is presented. The open loop stability of internal models used in HORC and the one presented here is analysed. Additionally, as a consequence of this analysis, an Anti-Windup (AW) scheme for repetitive control is proposed. This AW proposal is based on the idea of having a small steady state tracking error and fast recovery once the system goes out of saturation. The experimental validation of these proposals has been performed in two different applications: the Roto-magnet plant and the active power filter application. The Roto-magnet plant is an experimental didactic plant used as a tool for analysing and understanding the nature of the periodic disturbances, as well as to study the different control techniques used to tackle this problem. This plant has been adopted as experimental test bench for rotational machines. On the other hand, shunt active power filters have been widely used as a way to overcome power quality problems caused by nonlinear and reactive loads. These power electronics devices are designed with the goal of obtaining a power factor close to 1 and achieving current harmonics and reactive power compensation.Award-winningPostprint (published version

Advanced Anti-Windup Techniques for the Limitation of the Effects of the Actuator Saturation

In this thesis an industrial issue is analysed. The issue consist on the undesirable effect of actuator sturation. Two approaches are given to solve the issue: an accurate inertia identification algorithm based on the DFT coefficient; and advanced anti-windup compensators. The principle of the modern anti-windup (DLAW and MRAW, LMI-based design approach), and a systematic design design procedure for the observer-based anti-windup are given. Simulation and test results are also given.ope

Nonlinear constrained and saturated control of power electronics and electromechanical systems

Power electronic converters are extensively adopted for the solution of timely issues, such as power quality improvement in industrial plants, energy management in hybrid electrical systems, and control of electrical generators for renewables. Beside nonlinearity, this systems are typically characterized by hard constraints on the control inputs, and sometimes the state variables. In this respect, control laws able to handle input saturation are crucial to formally characterize the systems stability and performance properties. From a practical viewpoint, a proper saturation management allows to extend the systems transient and steady-state operating ranges, improving their reliability and availability. The main topic of this thesis concern saturated control methodologies, based on modern approaches, applied to power electronics and electromechanical systems. The pursued objective is to provide formal results under any saturation scenario, overcoming the drawbacks of the classic solution commonly applied to cope with saturation of power converters, and enhancing performance. For this purpose two main approaches are exploited and extended to deal with power electronic applications: modern anti-windup strategies, providing formal results and systematic design rules for the anti-windup compensator, devoted to handle control saturation, and “one step” saturated feedback design techniques, relying on a suitable characterization of the saturation nonlinearity and less conservative extensions of standard absolute stability theory results. The first part of the thesis is devoted to present and develop a novel general anti-windup scheme, which is then specifically applied to a class of power converters adopted for power quality enhancement in industrial plants. In the second part a polytopic differential inclusion representation of saturation nonlinearity is presented and extended to deal with a class of multiple input power converters, used to manage hybrid electrical energy sources. The third part regards adaptive observers design for robust estimation of the parameters required for high performance control of power systems

congestion control of data network by using anti-windup approach

Producción CientíficaAn Active Queue Management (AQM) scheme is design to control congestion in data networks, which includes anti-windup to deal with control signal saturation. More precisely, a methodology is proposed to design advanced AQM systems capable of regulating queue size even in the presence of significant disturbances. Hence, we first provide sufficient conditions for stabilization for the equivalent class of systems, which are derived in terms of LMI: this makes possible to derive optimization solutions that ensure performance and stability for a large domain of initial conditions. This approach is validated with a numerical example that illustrates the methodology, and the improvements with respect to previous congestion control solutions

Incorporation of Robustness Properties into the Observer Based Anti-Windup Scheme in the Case of Actuator Uncertainties

Abstract-Saturation is a very common nonlinearity in control systems and may produce serious performance deterioration or even loss of stability. To cope with saturation, several anti-windup (AW) schemes have been developed over a long time. Unfortunately, they are based on the assumption that there is a static nonlinearity between the output of the controller and the plant input, which, in many situations, is not the case, because of an actuator dynamics. Against this background we provide a design procedure for the design of the AW-compensator that guarantee stability of the observer based anti-windup to face unmodeled actuator dynamics and guarantee a certain level of performance. This mixed performance method is later extended for systems with unmeasurable actuator outputs by the use of an unknown input observer (UIO). The effectiveness of the presented algorithm is demonstrated on an engine test-bench simulator. I. INTRODUCTION S result of physical limitations, the output of actuators is always limited in amplitude and rate, such as maximum or minimum torque in an engine or the maximum safe pitch rate in an aircraft. Such limits must be taken in account in the control design, otherwise the controller output will be different from the plant input, leading to wrong update of the controller states and to consequences ranging from performance deterioration over large overshoots and sometimes even to limit cycles or stability loss. Therefore, this phenomenon -usually called "controller windup" -has a paramount practical relevance and therefore many existing techniques address this problem of actuator constraints, e.g. the "Model Predictive Control" (MPC) Among the many contributions to handle input constraints for this class of problems, we recall the recent surveys of Galeani [3], Tarbouriech and Turner [4] about early and recent anti-windup research. The observer-based antiwindup design goes back to the publications of Åström and Hägglund Martin Bruckner and Luigi del Re are with the Institute for Design and Control of Mechatronical Systems (e-mail: [email protected]; [email protected]). In the case of actuator or plant uncertainties there are only a few contributions, such as the approach of Teel In this paper based on the Integral-Quadratic-Constraints (IQCs) framework we extend the observer-based antiwindup design procedure to handle actuator uncertainties and present a design procedure that allows tuning the AW for performance requirements. To this end two weighting matrices are introduced in the performance criteria. In addition some nicely interpretable rules are provided for choosing the weighting matrices. In the case, where the true plant input can't be measured the closed-loop system is extended with an unknown input observer (UIO). To the best of our knowledge, we are not aware of any work in the literature dealing with a mixed performance AW-design, jointly tackling both, unmeasurable actuator outputs and dynamic actuator uncertainty. All these algorithms are tested on an engine test-bench simulation example. The paper is structured as follows: first we introduce the observer based anti-windup compensator and present some robust stability considerations in the case of actuator uncertainties based on the IQC-framework. Afterwards an UIO is introduced to keep the performance in the case, when the output of the actuator isn't available for measurement. Finally the method is tested on a test-bench simulator. II. OBSERVER BASED ANTI-WINDUP DESIGN For reasons of global stability, throughout the paper the plant P of order n is assumed to be stable, and that the controller ( , , , ) c c c c A B C D stabilizes the system when the saturation is not active. The plant is described by the standard equations: is the state-space realization of the controller and L is the desired feedback matrix of the antiwindup compensator (se

A novel robust disturbance rejection anti-windup framework

This is an Author's Original Manuscript of an article submitted for consideration in the International Journal of Control [copyright Taylor & Francis] and is available online at http://www.tandfonline.com/10.1080/00207179.2010.542774In this article, we propose a novel anti-windup (AW) framework for coping with input saturation in the disturbance rejection problem of stable plant systems. This framework is based on the one developed by Weston and Postlethwaite (W&P) (Weston, P.F., and Postlethwaite, I. (2000), ‘Linear Conditioning for Systems Containing Saturating Actuators’, Automatica, 36, 1347–1354). The new AW-design improves the disturbance rejection performance over the design framework usually suggested for the coprime-factorisation based W&P-approach. Performance improvement is achieved by explicitly incorporating a transfer function, which represents the effect of the disturbance on the nonlinear loop, into the AW compensator synthesis. An extra degree of freedom is exploited for the coprime factorisation, resulting in an implicitly computed multivariable algebraic loop for the AW-implementation. Suggestions are made to overcome the algebraic loop problem via explicit computation. Furthermore, paralleling the results of former work (Turner, M.C., Herrmann, G., and Postlethwaite, I. (2007), ‘Incorporating Robustness Requirements into Antiwindup Design’, IEEE Transactions on Automatic Control, 52, 1842–1855), the additive plant uncertainty is incorporated into the AW compensator synthesis, by using a novel augmentation for the disturbance rejection problem. In this new framework, it is shown that the internal model control (IMC) scheme is optimally robust, as was the case in Turner, Herrmann, and Postlethwaite (2007) and Zheng and Morari (Zheng, A., and Morari, M. (1994), ‘Anti-windup using Internal Model Control’, International Journal of Control, 60, 1015–1024). The new AW approach is applied to the control of dynamically substructured systems (DSS) subject to external excitation signals and actuator limits. The benefit of this approach is demonstrated in the simulations for a small-scale building mass damper DSS and a quasi-motorcycle DSS

Control of systems subject to uncertainty and constraints

All practical control systems are subject to constraints, namely constraints aris¬ing from the actuator’s limited range and rate capacity (input constraints) or from imposed operational limits on plant variables (output constraints). A linear control system typically yields the desirable small signal performance. However, the presence of input constraints often causes undesirable large signal behavior and potential insta¬bility. An anti-windup control consists of a remedial solution that mitigates the effect of input constraints on the closed-loop without affecting the small signal behavior. Conversely, an override control addresses the control problem involving output con¬straints and also follows the idea that large signal control objectives do not alter small signal performance. Importantly, these two remedial control methodologies must in¬corporate model uncertainty into their design to be considered reliable in practice. In this dissertation, shared principles of design for the remedial compensation problem are identified which simplify the picture when analyzing, comparing and synthesiz¬ing for the variety of existing remedial schemes. Two performance objectives, each one related to a different type of remedial compensation, and a general structural representation associated with both remedial compensation problems will be consid¬ered. The effect of remedial control on the closed-loop will be evaluated in terms of two general frameworks which permit the unification and comparison of all known remedial compensation schemes. The difference systems describing the performance objectives will be further employed for comparison of remedial compensation schemes under uncertainty considerations and also for synthesis of compensators. On the ba¬sis of the difference systems and the general structure for remedial compensation, systematic remedial compensation synthesis algorithms for anti-windup and override compensation will be given and compared. Successful application of the proposed robust remedial control synthesis algorithms will be demonstrated via simulation