On designing observers for time-delay systems with nonlinear disturbances

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2002 Taylor & Francis LtdIn this paper, the observer design problem is studied for a class of time-delay nonlinear systems. The system under consideration is subject to delayed state and non-linear disturbances. The time-delay is allowed to be time-varying, and the non-linearities are assumed to satisfy global Lipschitz conditions. The problem addressed is the design of state observers such that, for the admissible time-delay as well as non-linear disturbances, the dynamics of the observation error is globally exponentially stable. An effective algebraic matrix inequality approach is developed to solve the non-linear observer design problem. Specifically, some conditions for the existence of the desired observers are derived, and an explicit expression of desired observers is given in terms of some free parameters. A simulation example is included to illustrate the practical applicability of the proposed theory.The work of Z. Wang was supported in part by the University of Kaiserslautern of Germany and the Alexander von Humboldt Foundation of Germany

A low-order linear functional observer for time delay systems

This paper presents an efficient technique to design low order state function observers for linear time-delay systems. Assuming the existence of a linear state feedback controller to achieve stability or some control performance criteria of the time-delay system, a design procedure is proposed forreconstruction of the state feedback control action. The procedure involves solving an optimisation problem with the objective to generate a matrix that is as close as possible to the given feedback gain of the required feedback controller. A condition for robust stability of the time-delay system using the observer-based control scheme is given. The attractive features of the proposed design procedure are that the resulted linear functional state observer is of a very low order and it requires information of a small number of outputs. Numerical examples are given to demonstrate the design procedure and its merits.<br /

Time-delay systems : stability, sliding mode control and state estimation

University of Technology, Sydney. Faculty of Engineering and Information Technology.Time delays and external disturbances are unavoidable in many practical control systems such as robotic manipulators, aircraft, manufacturing and process control systems and it is often a source of instability or oscillation. This thesis is concerned with the stability, sliding mode control and state estimation problems of time-delay systems. Throughout the thesis, the Lyapunov-Krasovskii (L-K) method, in conjunction with the Linear Matrix Inequality (LMI) techniques is mainly used for analysis and design. Firstly, a brief survey on recent developments of the L-K method for stability analysis, discrete-time sliding mode control design and linear functional observer design of time-delay systems, is presented. Then, the problem of exponential stability is addressed for a class of linear discrete-time systems with interval time-varying delay. Some improved delay-dependent stability conditions of linear discrete-time systems with interval time-varying delay are derived in terms of linear matrix inequalities. Secondly, the problem of reachable set bounding, essential information for the control design, is tackled for linear systems with time-varying delay and bounded disturbances. Indeed, minimisation of the reachable set bound can generally result in a controller with a larger gain to achieve better performance for the uncertain dynamical system under control. Based on the L-K method, combined with the delay decomposition approach, sufficient conditions for the existence of ellipsoid-based bounds of reachable sets of a class of linear systems with interval time-varying delay and bounded disturbances, are derived in terms of matrix inequalities. To obtain a smaller bound, a new idea is proposed to minimise the projection distances of the ellipsoids on axes, with respect to various convergence rates, instead of minimising its radius with a single exponential rate. Therefore, the smallest possible bound can be obtained from the intersection of these ellipsoids. This study also addresses the problem of robust sliding mode control for a class of linear discrete-time systems with time-varying delay and unmatched external disturbances. By using the L-K method, in combination with the delay decomposition technique and the reciprocally convex approach, new LMI-based conditions for the existence of a stable sliding surface are derived. These conditions can deal with the effects of time-varying delay and unmatched external disturbances while guaranteeing that all the state trajectories of the reduced-order system are exponentially convergent to a ball with a minimised radius. Robust discrete-time quasi-sliding mode control scheme is then proposed to drive the state trajectories of the closed-loop system towards the prescribed sliding surface in a finite time and maintain it there after subsequent time. Finally, the state estimation problem is studied for the challenging case when both the system’s output and input are subject to time delays. By using the information of the multiple delayed output and delayed input, a new minimal order observer is first proposed to estimate a linear state functional of the system. The existence conditions for such an observer are given to guarantee that the estimated state converges exponentially within an Є-bound of the original state. Based on the L-K method, sufficient conditions for Є-convergence of the observer error, are derived in terms of matrix inequalities. Design algorithms are introduced to illustrate the merit of the proposed approach. From theoretical as well as practical perspectives, the obtained results in this thesis are beneficial to a broad range of applications in robotic manipulators, airport navigation, manufacturing, process control and in networked systems

Robust control tools for traffic monitoring in TCP/AQM networks

Several studies have considered control theory tools for traffic control in communication networks, as for example the congestion control issue in IP (Internet Protocol) routers. In this paper, we propose to design a linear observer for time-delay systems to address the traffic monitoring issue in TCP/AQM (Transmission Control Protocol/Active Queue Management) networks. Due to several propagation delays and the queueing delay, the set TCP/AQM is modeled as a multiple delayed system of a particular form. Hence, appropriate robust control tools as quadratic separation are adopted to construct a delay dependent observer for TCP flows estimation. Note that, the developed mechanism enables also the anomaly detection issue for a class of DoS (Denial of Service) attacks. At last, simulations via the network simulator NS-2 and an emulation experiment validate the proposed methodology

Disturbance-observer-based robust control for time delay uncertain systems

A robust control scheme is proposed for a class of systems with uncertainty and time delay based on disturbance observer technique. A disturbance observer is developed to estimate the disturbance generated by an exogenous system, and the design parameters of the disturbance observer are determined by solving linear matrix inequalities (LMIs). Based on the output of the disturbance observer, a robust control scheme is proposed for the time delay uncertain system. The disturbance-observer-based robust controller is combined of two parts: one is a linear feedback controller designed using LMIs and the other is a compensatory controller designed with the output of the disturbance observer. By choosing an appropriate Lyapunov function candidate, the stability of the closed-loop system is proved. Finally, simulation example is presented to illustrate the effectiveness of the proposed control scheme

Meromorphic observer-based pole assignment in time delay systems

summary:The paper deals with a novel method of control system design which applies meromorphic transfer functions as models for retarded linear time delay systems. After introducing an auxiliary state model a finite-spectrum observer is designed to close a stabilizing state feedback. The observer finite spectrum is the key to implement a state feedback stabilization scheme and to apply the affine parametrization in controller design. On the basis of the so- called RQ-meromorphic functions an algebraic solution to the problem of time- delay system stabilization and control is presented that practically provides a finite spectrum assignment of the control loop

H ∞ sliding mode observer design for a class of nonlinear discrete time-delay systems: A delay-fractioning approach

Copyright @ 2012 John Wiley & SonsIn this paper, the H ∞  sliding mode observer (SMO) design problem is investigated for a class of nonlinear discrete time-delay systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. Attention is focused on the design of a discrete-time SMO such that the asymptotic stability as well as the H ∞  performance requirement of the error dynamics can be guaranteed in the presence of nonlinearities, time delay and external disturbances. Firstly, a discrete-time discontinuous switched term is proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of ‘delay fractioning’ and by introducing some appropriate free-weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. Finally, an illustrative example is given to show the effectiveness of the designed SMO design scheme

Multi-Rate Observers for Model-Based Process Monitoring

Very often, critical quantities related to safety, product quality and economic performance of a chemical process cannot be measured on line. In an attempt to overcome the challenges caused by inadequate on-line measurements, state estimation provides an alternative approach to reconstruct the unmeasured state variables by utilizing available on-line measurements and a process model. Chemical processes usually possess strong nonlinearities, and involve different types of measurements. It remains a challenging task to incorporate multiple measurements with different sampling rates and different measurement delays into a unified estimation algorithmic framework. This dissertation seeks to present developments in the field of state estimation by providing the theoretical advances in multi-rate multi-delay observer design. A delay-free multi-rate observer is first designed in linear systems under asynchronous sampling. Sufficient and explicit conditions in terms of maximum sampling period are derived to guarantee exponential stability of the observer, using Lyapunov’s second method. A dead time compensation approach is developed to compensate for the effect of measurement delay. Based on the multi-rate formulation, optimal multi-rate observer design is studied in two classes of linear systems where optimal gain selection is performed by formulating and solving an optimization problem. Then a multi-rate observer is developed in nonlinear systems with asynchronous sampling. The input-to-output stability is established for the estimation errors with respect to measurement errors using the Karafyllis-Jiang vector small-gain theorem. Measurement delay is also accounted for in the observer design using dead time compensation. Both the multi-rate designs in linear and nonlinear systems provide robustness with respect to perturbations in the sampling schedule. Multi-rate multi-delay observer is shown to be effective for process monitoring in polymerization reactors. A series of three polycondensation reactors and an industrial gas-phase polyethylene reactor are used to evaluate the observer performance. Reliable on-line estimates are obtained from the multi-rate multi-delay observer through simulation

State and input simultaneous estimation for a class of time-delay systems with uncertainties

This brief addresses the problem of estimation of both the states and the unknown inputs of a class of systems that are subject to a time-varying delay in their state variables, to an unknown input, and also to an additive uncertain, nonlinear disturbance. Conditions are derived for the solvability of the design matrices of a reduced-order observer for state and input estimation, and for the stability of its dynamics. To improve computational efficiency, a delay-dependent asymptotic stability condition is then developed using the linear matrix inequality formulation. A design procedure is proposed and illustrated by a numerical example.<br /

Estimation and control of some classes of dynamical systems with application to biological wastewater treatment

It is well-known that there are no general approaches for observer and controller design for nonlinear systems. Instead, focus is placed upon design for classes of systems. On the other hand, a wide variety of dynamical systems belong to the class of state-affine systems. Amongst these are biological wastewater treatment processes, which are essential in order to prevent pollution in the environment and prevent disease in the consumption of recycled water. An interesting aspect found in biological wastewater treatment systems, and many typical industrial processes, are time-delays. In almost all systems there are time-delays and nonlinearities and it is not surprising that time-delay and nonlinear systems have received a great deal of attention in mathematics and control engineering. This project introduces new methodologies for the design of controllers and observers for a class of state-affine systems and a class of linear time-delay systems. Firstly, new observable and controllable canonical forms are introduced. These are then used to establish new controller and observer design methodologies for a class of state¬affine systems. In particular, an adaptive observer design is established. The methodologies are simple since they are based upon linear techniques. Secondly, a full-state controller and a separation principle are established for a class of single-input single-output linear time-delay systems. The designs are based on a new stability criterion and are derived from first principles. Finally, the new observer design methodology for the class of state-affine systems is used to produce observers for the estimation of biomass concentration in a biological wastewater treatment bioreactor. The observers are applied in theory and in simulation, where a full and a partial knowledge of the kinetic rate of reaction of biomass are considered. In addition, the performances are shown both in the absence and in the presence of measurement noise for a variety of influent flow characteristics.EThOS - Electronic Theses Online ServiceGBUnited Kingdo