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

Sliding mode adaptive state observation for time-delay uncertain nonlinear systems

In this paper a method to design robust adaptive sliding mode observers (ASMO) for a class of nonlinear time- delay systems with uncertainties, is proposed. The objective is to achieve insensitivity and robustness of the proposed sliding mode observer to matched disturbances. A novel systematic design method is synthesized to solve matching conditions and compute observer stabilizing gains. The Lyapunov-Krasovskii theorem is employed to prove the ultimate stability with arbitrary boundedness radius of the estimation error of the proposed filter. Finally, the ability of ASMO for fault reconstruction is studied

A new strategy for integration of fault estimation within fault-tolerant control

© 2016 Elsevier Ltd. All rights reserved. The problem of active fault tolerant control (FTC) of dynamical systems involves the process of fault detection and isolation/fault estimation (FDI/FE) used to either make a decision as to when and how to change the control, based on FDI or to compensate the fault in the control system via FE. The combination of the decision-making/estimation and control gives rise to a bi-directional uncertainty in which the modelling and fault uncertainties and disturbances all affect the quality and robustness of the FTC system. This leads to the FTC requirement for an integrated design of the FDI/FE and control system reconfiguration. This paper focuses on the FTC approach using FE and fault compensation within the control system in which the design is achieved by integrating together the FE and FTC controller modules. The FE is based on a modified reduced-/full-order unknown input observer and the FTC system is constructed by sliding mode control using state/output feedback. The integrated design is converted into an observer-based robust control problem solved via H ∞ optimization with a single-step LMI formulation. The performance effectiveness of the proposed integrated design approach is illustrated through studying the control of an uncertain model of a DC motor

Discrete-time sliding mode control of high precision linear drive using frictional model

The paper deals with high precision motion control of linear drive system. The accuracy and behavior of the linear drive system are highly affected by the non-linear frictional component compromising of stiction, viscous and stribeck effect present in the system especially in the vicinity of zero velocity. In order to achieve the high accuracy and motion it is mandatory to drive our system with low velocity resulting in many non linear phenomena like tracking error, limit cycles and undesired stick-slip motion etc. This paper discuss the design and implementation of discrete time sliding mode control along with the implementation of dynamic frictional model in order to estimate and compensate the disturbance arising due to frictional component. Experimental results are presented to illustrate the effectiveness and achievable control performance of the proposed scheme

Sliding mode based piezoelectric actuator control

In this paper a control of method for a piezoelectric stack actuator control is proposed. In addition briefly the usage of the same methods for estimation of external force acting to the actuator in contact with environment is discussed. The method uses sliding mode framework to design both the observer and the controller based on an electromechanical lumped model of the piezoelectric actuator. Furthermore, using a nonlinear differential equation the internal hysteresis disturbance is removed from the total disturbance in an attempt to estimate the external force acting on the actuator. It is then possible to use this external force estimate as a means of force control of the actuator. Simulation and experiments are compared for validating the disturbance and external force estimation technique. Some experiments that incorporate disturbance compensation in a closed-loop SMC control algorithm are also presented to prove the effectiveness of this method in producing high precision motion

Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Algebraic observer design for PEM fuel cell system

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, the concept of the algebraic observer is applied to Proton Exchange Membrane Fuel Cell (PEMFC) system. The aim of the proposed observer is to reconstruct the oxygen excess ratio through estimation of their relevant states in real time from the measurement of the supply manifold air pressure. A robust differentiation method is adopted to estimate in finite-time the time derivative of the supply manifold air pressure. Then, the relevant states are reconstructed based on the output-state inversion model. The objective is to minimize the use of extra sensors in order to reduce the costs and enhance the system accuracy. The performance of the proposed observer is analyzed through simulations considering measurement noise and different stack-current variations. The results show that the algebraic observer estimates in finite time and robustly the oxygen-excess ratio.Peer ReviewedPostprint (author's final draft

An observer design for active suspension system

The purpose of this paper is to construct an active suspension for a quarter car model with observer design. The proportional-integral sliding mode is chosen as a control strategy, and the road profile is estimated by using an observer design. The performance of the proposed controller will be compared with the linear quadratic regulator by performing extensive computer simulation