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Egor Koshelev
Egor Koshelev

Robust Control And Filtering For Time-Delay Sys... _VERIFIED_



A discussion of robust control and filtering for time-delay systems. It provides information on approaches to stability, stabilization, control design, and filtering aspects of electronic and computer systems - explicating the developments in time-delay systems and uncertain time-delay systems. There are appendices detailing important facets of matrix theory, standard lemmas and mathematical results, and applications of industry-tested software.




Robust Control and Filtering for Time-Delay Sys...



In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some (typically compact) set. Robust methods aim to achieve robust performance and/or stability in the presence of bounded modelling errors.


The early methods of Bode and others were fairly robust; the state-space methods invented in the 1960s and 1970s were sometimes found to lack robustness,[1] prompting research to improve them. This was the start of the theory of robust control, which took shape in the 1980s and 1990s and is still active today.


In contrast with an adaptive control policy, a robust control policy is static, rather than adapting to measurements of variations, the controller is designed to work assuming that certain variables will be unknown butbounded.[2][3]


Informally, a controller designed for a particular set of parameters is said to be robust if it also works well under a different set of assumptions. High-gain feedback is a simple example of a robust control method; with sufficiently high gain, the effect of any parameter variations will be negligible. From the closed-loop transfer function perspective, high open-loop gain leads to substantial disturbance rejection in the face of system parameter uncertainty. Other examples of robust control include sliding mode and terminal sliding mode control.


Robust control systems often incorporate advanced topologies which include multiple feedback loops and feed-forward paths. The control laws may be represented by high order transfer functions required to simultaneously accomplish desired disturbance rejection performance with the robust closed-loop operation.


Probably the most important example of a robust control technique is H-infinity loop-shaping, which was developed by Duncan McFarlane and Keith Glover of Cambridge University; this method minimizes the sensitivity of a system over its frequency spectrum, and this guarantees that the system will not greatly deviate from expected trajectories when disturbances enter the system.


An emerging area of robust control from application point of view is sliding mode control (SMC), which is a variation of variable structure control (VSC). The robustness properties of SMC with respect to matched uncertainty as well as the simplicity in design attracted a variety of applications.


While robust control has been traditionally dealt with along deterministic approaches, in the last two decades this approach has been criticized on the basis that it is too rigid to describe real uncertainty, while it often also leads to over conservative solutions. Probabilistic robust control has been introduced as an alternative, see e.g.[6] that interprets robust control within the so-called scenario optimization theory.


When system behavior varies considerably in normal operation, multiple control laws may have to be devised. Each distinct control law addresses a specific system behavior mode. An example is a computer hard disk drive. Separate robust control system modes are designed in order to address the rapid magnetic head traversal operation, known as the seek, a transitional settle operation as the magnetic head approaches its destination, and a track following mode during which the disk drive performs its data access operation.


"Stability Analysis and Robust Control of Time-Delay Systems" focuses on essential aspects of this field, including the stability analysis, stabilization, control design, and filtering of various time-delay systems. Primarily based on the most recent research, this monograph presents all the above areas using a free-weighting matrix approach first developed by the authors. The effectiveness of this method and its advantages over other existing ones are proven theoretically and illustrated by means of various examples. The book will give readers an overview of the latest advances in this active research area and equip them with a pioneering method for studying time-delay systems. It will be of significant interest to researchers and practitioners engaged in automatic control engineering.


Singular systems have been widely studied in the past two decades due to their extensive applications in modelling and control of electrical circuits, power systems, economics and other areas. Interest has grown recently in the stability analysis and control of singular systems with parameter uncertainties due to their frequent presence in dynamic systems, which is much more complicated than that of state-space systems because controllers must be designed so that the closed-loop system is not only robustly stable, but also regular and impulse-free (in the continuous case) or causal (in the discrete case), while the latter two issues do not arise in the state-space case. This monograph aims to present up-to-date research developments and references on robust control and filtering of uncertain singular systems in a unified matrix inequality setting. It provides a coherent approach to studying control and filtering problems as extensions of state-space systems without the commonly used slow-fast decomposition. It contains valuable reference material for researchers wishing to explore the area of singular systems, and its contents are also suitable for a one-semester graduate course.


This paper overviews the research investigations pertaining to stability and stabilization of control systems with time-delays. The prime focus is the fundamental results and recent progress in theory and applications. The overview sheds light on the contemporary development on the linear matrix inequality (LMI) techniques in deriving both delay-independent and delay-dependent stability results for time-delay systems. Particular emphases will be placed on issues concerned with the conservatism and the computational complexity of the results. Key technical bounding lemmas and slack variable introduction approaches will be presented. The results will be compared and connections of certain delay-dependent stability results are also discussed.


The occurrence of time-delay phenomenon appears to present many real-world systems and engineering applications. This takes place in either the state, the control input side, or the measurements side. It turns out that delays are strongly involved in challenging areas of communication and information technologies including stabilization of networked controlled systems and high-speed communication networks. In many cases, time-delay is a source of instability. However, for some systems, the presence of delay can have a stabilizing effect. The stability analysis and robust control of time-delay systems (TDS) are, therefore, of theoretical and practical importance.


The primary objective of this paper is to(i)familiarize wider readers with TDS,(ii)provide a systematic treatment of modern ideas and techniques for researchers.The paper bridges the huge gap from some basic classical results to recent developments on Lyapunov-based analysis and design with applications to the attractive topics of network-based control and interconnected time-delay control systems. Essentially, it provides an overview on the progress of stability and stabilization of time-delay systems (TDS). Particular emphases will be placed on issues concerned with the conservatism and the computational complexity of the results. For simplicity in exposition, the discussions are limited to linear or linearizable systems. Some methods and techniques used to derive stability conditions for time-delay systems are reviewed. Several future research directions on this topic are also discussed.


Linear Parameter Varying (LPV) systems and their control have gained attraction recently as they approximate nonlinear systems with higher order than ordinary linear systems. On the other hand, time delay is an inherent part of various real-life applications. A supervisory control structure is proposed in this paper for LPV systems subject to time delays. In the proposed control structure, a supervisor selects the most suitable controller from a bank of controllers; which desires to enhance the performance of closed-loop system in contrast with using a single robust controller. The analysis is based on the celebrated Smith predictor for time delay compensation and we provide a sufficient condition to assure the stability of the closed-loop switched system in terms of dwell time. Simulations on blood pressure control of hypertension patients in postoperative scenario are used to exemplify the effectiveness of the utilized technique. The operating region of the system is partitioned into five smaller operating regions to construct corresponding robust controllers and perform hysteresis switching amongst them. Simulation results witnessed that the proposed control scheme demonstrated a pressure undershoot less than the desired value of 10 mmHg while the Mean Arterial Pressure (MAP) remains within 5 mmHg of the desired value.


The remaining document is structured in the following order. Section II provides the description of control problem and its preliminaries. Section III focuses on design of switching robust controllers. Section IV presents the stability result for the overall closed-loop switched system while section V illustrates the application of our proposed method on a practical problem of blood pressure regulation. Section VI mentions the algorithm, section VII shows simulations and results, and section VIII provides conclusion and future directions in this area. 041b061a72


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