Control Strategy for Time-Delay Systems: Part II: Engineering Applications

Since delays are present in 99% of industrial processes, Control Strategy for Time-delay Systems covers all the important features of real-world practical applications which will be valuable to practicing engineers and specialists The book presents the views of the editors on promising research directions and future industrial applications in this area.

Although the fundamentals of time-delay systems are discussed, the book focuses on the advanced modelling and control of such systems and will provide the analysis and test (or simulation) results of nearly every technique described in the book For this purpose, highly complex models are introduced to ?describe the mentioned new applications which are characterized by ?time-varying delays with intermittent and stochastic nature, several types of nonlinearities, and the presence ?of different time-scales.

Researchers, practitioners and PhD students will gain insights into the prevailing trends in design and operation of real-time control systems, reviewing the shortcomings and future developments concerning the practical system issues such as standardization, protection and design.

• Language: English
• Publisher: Academic Press
• Release date: Nov 27, 2020
• ISBN: 9780323858045

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Preface

The definition of a time-delay plant implies the property that the future evolution of a specific plant depends on its previous experiences, in addition to its current states. Time delays frequently occur in real-world engineering problems involved in their inputs/outputs, measurements, and states. Except rare cases, the presence of time delays is likely to lead to deteriorated performance, reduced stability, and insufficient robustness, which consequently bring great challenges to the analysis and control of systems subjected to delayed feedback. Since the time delays impose destabilization impact on the performance of a closed-loop system, extra conditions and particular analysis methodologies, assuming that there is a delay in the measured data, are necessitated in the control design stage of such systems. However, the control design of time-delayed systems is faced with more complexity when the system is subjected to a long time delay.

The efforts to control time-delay systems have been intensified during the last ten years, and they have grown steadily in interest and popularity. Given this period of creative work, it seems that the subject has undergone a significant leap in terms of concept and practical action; its scope and characteristics have been remarkably evolved. A brief look at the large number of research works published in these years, in conferences, and archival journals gives a strong idea about the scale and extent of this progress. Despite significant advances in the control of time-delayed systems, the scientific community is faced with various difficulties because of the emergence of new application regions, chiefly in the context of control and analysis of modern interconnected networks (e.g., cyberphysical systems, distributed decision-making, sensor networks, networked control systems, etc.). These new applications are often accompanied by high-sophisticated models described by variable time delays with stochastic feature, various sources of nonlinearities including saturation of actuators, limitations of sensing abilities, and the existence of various time scales. These obstacles necessitate the need to progress, especially in the improvement of theoretical analysis, applicable control structures to satisfy the desired stability, and robustness characteristics from the control engineering point of view.

Despite the rich body of literature on time-delayed systems, almost all available studies concentrated on the theoretical aspects of this area, whereas only a few researchers developed their suggested schemes on practical case-studies. For this reason, this book is provided and conceived as a useful reference for theoretical analysis of time-delay systems, for academic researchers interested in robust control theory in the context of time-delay systems and engineers that work in the field of designing controllers for practical systems with delays. The developed control methodologies try to consider the typical sever conditions of time-delayed systems and address the gap between the theory of robust control and control synthesis of practical plants. We claim that, wisely used, it could be a source for the advanced graduate course. An adequate background in the mathematics of control theory, advanced controllers, and predictive control schemes are required to follow some specialized topics of this book. The essential technical preliminaries have been included in the relative chapters, which make it a self-contained textbook. This book is organized in ten chapters.

Organization

Chapter 1 proposes a wide-area damping controller to alleviate the interarea oscillations in power systems stemming from communication delays. The application outcomes revealed that the suggested control framework is insensitive under variable time delay, thus paving the way to handle arbitrary variations of delay in the communication channel or of delay that may be caused by a denial-of-service type of cyberattack.

Chapter 2 considers two individual test systems corresponding to the distributed and centralized controllers. It was demonstrated that the designed controllers have sufficient resilience against the delay in the communication links.

Chapter 3 proposes the robustness of a nested saturation controller for unmanned aerial vehicles (UAVs) subjected to time delay. To ensure the asymptotic stability of the system, an upper bound of time delay is reached. The experiments on quadrotor platform revealed that the suggested control scheme is simple to implement and needs no any modifications (e.g., predictor-based control) that explicitly compensate time delay.

Chapter 4 proposes a novel robust controller based on the Takagi–Sugeno (TS) fuzzy controller for the time-delayed glucose–insulin metabolic system. Sufficient conditions for designing a parallel distributed compensation (PDC) are formulated in the form of linear matrix inequalities by deploying the Lyapunov–Krasovskii theory.

Chapter 5 addresses the application of the delay-product-type Lyapunov–Krasovskii functional with negative definite terms, and its derivative is estimated by the third-order Bessel–Legendre (B-L) based integral inequality together with mixed convex combination approaches.

Chapter 6 presents two different approaches including model predictive control and T-S fuzzy model to tackle linear and nonlinear systems under various classes of delays (constant, time-varying, unknown).

Chapter 7 proposes an ultralocal model (ULM) control based on the Smith predictor (SP) for the pitch angle regulation of a 2-mass WT model. Since the quality of control actions of the suggested controller depends on the coefficients of the ULM controller, a deep deterministic policy gradient (DDPG) was adopted to adaptively adjust these coefficients.

Chapter 8 describes four adaptive nonlinear control methodologies for lag-synchronization of two nonidentical time-delayed chaotic systems with fully unknown parameters in the presence of unknown external disturbances and input nonlinearity.

Chapter 9 presents a systematic control strategy based on the reset observer technique for a class of nonlinear systems, which guarantees the closed-loop system asymptotic stability by appropriately choosing Lyapunov–Krasovskii functionals.

Chapter 10 is focused on developing a combination of approaches to the development of time-delay systems, which combines different tools in the development process of cyberphysical systems (CPSs). This chapter illustrates that it is possible to efficiently use the INTO-CPS application, cosimulation, and design space exploration (DSE) in the estimation of the maximum allowable delay bound of a model of a CPS combined with a model of time delays.

Chapter One: Wide-area damping controller for randomly varying delay: a dynamic output feedback approach

Spandan Roya; Abhilash Patelb    aRobotics Research Center, International Institute of Information Technology Hyderabad (IIIT-H), Hyderabad, India

bDepartment of Electrical Engineering, Indian Institute of Technology Delhi (IITD), New Delhi, India

Abstract

One of the important issues in an interconnected power system is the low damping of inter-area oscillations, and it becomes challenging in the face of communication delay. However, most of the present state-of-the-art damping controllers cannot handle arbitrary variation of delay: such situations may not only originate due to geographical distances, but may also arise from cyberattack scenarios like denial-of-service. Motivated from such potent problems, in this work, we propose a new dynamic output feedback-based damping controller. We analytically show that the proposed scheme is insensitive toward the variations in time delay. We also study the robustness of the proposed controller against parametric uncertainties and exogenous disturbances. Performance of the proposed scheme is validated via extensive simulations under various uncertain scenarios.

Keywords

Dynamic controller; Input delay; Output feedback; Lyapunov–Krasovskii; Wide-area control

Chapter Outline

1.1  Introduction

1.2  System description

1.2.1  Small signal model of power system

1.2.1.1  Synchronous machine

1.2.1.2  Excitation system

1.2.1.3  Power system stabilizer

1.2.1.4  Load and network interface

1.2.2  Modal analysis

1.2.3  Selection of wide-area loop

1.2.3.1  Model order reduction

1.3  Controller design and analysis

1.3.1  Controller design

1.3.2  Stability analysis

1.4  Robustness analysis of the proposed controller

1.4.1  Stability analysis

1.5  Application: four-machine eleven-bus system

1.5.1  System description

1.5.2  Performance verification for inter-area mode

1.5.3  Performance verification for local mode

1.6  Conclusion

Appendix 1.A  LMI solution of Ψ

References

1.1 Introduction

As the power demand is rising with modernization, installing new transmission lines are also meeting various constraints. Consequently, the modern power systems are facing several challenges to transfer large amount of power over long transmission lines. To improve transient stability, systems are generally equipped with fast acting automatic voltage regulator, which enhances the synchronizing torque component. However, such a success comes at the cost of damping torque component [1], which eventually leads to low-frequency electromechanical oscillations, known in the literature as swing modes. Such oscillations are introduced across weak tie-lines when heavy power transfer occurs. According to their participations, these swing modes can be classified as local and inter-area modes [1]. In the case of inter-area mode, the oscillation occurs between a group of machines from an area against a group of machines from a different area, connected over a weak tie-line. On the other hand, when swing modes take place between an individual or a group of machines against another individual or a group of machines from the same area, it is termed as a local mode.

As damping controllers, power system stabilizers (PSSs) are usually employed in a system to tackle such oscillations stemming from swing modes [2]. This has been a standard solution over decades, and they are typically installed at a generating station. However, such configuration has limited inter-area information and solely relies on local feedback signals: as a result, with inadequate control over the inter-area mode, their effectiveness is restricted to only handling the local mode [3,4]. As an alternate solution, researchers have also employed very high gain local PSSs to damp an inter-area mode. Such a measure, on the other hand, may lead to voltage instability owing to large control action [5]. To remove the bottleneck of inadequate inter-area signals, wide-area measurement systems (WAMSs) are deployed over wide geographical areas: now remote signals being available for feedback, employing wide-area damping controller (WADC) has become feasible via fusing both local and remote signals as feedback [6,7].

One of the earliest attempts to damp oscillations in a system was via proportional-plus-derivative (PD) compensation, where damping was achieved by the derivative action involved in the controller. However, it is well known that derivative actions are susceptible to noise in the signals, especially in power systems where the measurement noise often contaminates feedback signals. Therefore practical implementation of PD compensator becomes infeasible. Nevertheless, some of the recent research works have made it possible to imitate the performance of a derivative action to a certain extent: via introducing delay into the system artificially (or intentionally), an approximate performance of a PD compensator was achieved in wide-area controller [17] and being less computationally expensive over methods like model predictive control [18] and controller allocation-based design [19]. However, Razumikhin-theorem-based static gain selections as in [8] rely on an empirical method.

One crucial aspect in wide-area control is the inevitable effect of delay in the communication channel due to geographical distances between the areas, which in turn may deteriorate a WADC performance [20,21]. A few notable works that attempted to compensate the pervasive effects of time delay include the predictor approach [22,23], addition of phase lead [24,25], approach based on stochastic time-delay expectation model [26], discrete-time-based system modeling approach [27], and Pade approximation-based methods [28–30]. In a different line of work, a control gain tuning method was proposed in [31] by exploiting the trade-off between damping and delay margin. Unfortunately, most of the existing methods either require knowledge of the delay [24,25,27–30] or impose a restriction on the rate of change in delay [22,23,31–34]. On the other hand, under practical circumstances, it is not always possible to have exact knowledge of the delay or its variation a priori: one such situation is the denial-of-service type cyberattack, where attacker may block the flow of data arbitrarily, causing random variation in delay.

In view of the above discussion, a systematic WADC framework that can handle arbitrary/random variations in communication delay while damping inter-area modes is to a large extent missing. The major contributions of this work are as follows:

•  The envisaged control framework neither requires precise knowledge of the communication delay nor asserts any a priori constraints on the rate of variations in communication delay. Such a feature, prudent under the circumstances like denial-of-service attack, is achieved via a stability notion that allows the system to tackle any arbitrary variations in channel delay.

•  In contrast to the Razumikhin-theorem-based empirical gain selection approaches as in [8,9,11,12], a more systematic and less conservative LMI-based approach is proposed via Lyapunov–Krasovskii-based analysis. The delay-dependent closed-loop stability result establishes a relation between the controller gains and the maximum allowable delay. Such analysis is also extended for the cases where parametric perturbations and external disturbances appear.

The effectiveness of the proposed design is validated via extensive simulations under various uncertain scenarios using the IEEE benchmark model of 2-area 4-machine system.

The remainder of this chapter is organized as follows. Section 1.2 presents a detailed overview of the modeling aspects involved in a wide-area system. Section 1.3 presents the control problem and the proposed solution along with its detailed closed-loop stability analysis. The robustness issue of the proposed design under the effects of parametric uncertainties and exogenous disturbances are analyzed in Section 1.4. Simulation results are provided in Section 1.5, and Section 1.6 presents concluding