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Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.

Isolated microgrids, which are crucial for supplying electricity to remote areas using local energy sources, have garnered increased attention due to the escalating integration of renewable energy sources in modern microgrids. This integration poses technical challenges, notably in mitigating frequency deviations caused by non-dispatchable renewables, which threaten overall system stability. Therefore, this paper introduces decentralized fixed structure robust μ-synthesis controllers for continuous-time applications, surpassing the limitations of conventional centralized controllers. Motivated by the increasing importance of microgrids, this work contributes to the vital area of frequency regulation. The research challenge involves developing a controller that not only addresses the identified technical issues but also surpasses the limitations of conventional centralized controllers. In contrast to their centralized counterparts, the proposed decentralized controllers prove more reliable, demonstrating enhanced disturbance rejection capabilities amidst substantial uncertainties, represented through normalized co-prime factorization. The proposed controllers are designed using the D-K iteration technique, incorporating performance weight filters on control actions to maintain low control sensitivity and ensure specific frequency band operation for each sub-system. Importantly, the design considers unstructured uncertainty up to 40%, addressing real-world uncertainties comprehensively. Rigorous robust stability and performance tests underscore the controller's superiority, demonstrating its robustness against elevated uncertainty levels. Robust stability is verified for all controllers, with the proposed controller showing robust stability against up to 171% of the modeled uncertainty. Notably, the controller boasts a fixed structure with lower order compared to other H-infinity controllers, enhancing its practical implementation. Comparative analyses against Coronavirus Herd Immunity Optimizer tuned Proportional-Integral-Derivative (CHIO-PID) controller and CHIO tuned Fractional-Order Proportional-Integral-Derivative (CHIO-FOPID) controller further validate the superior performance of the proposed solution, offering a significant step towards ensuring the stability and reliability of microgrid systems in the face of evolving energy landscapes.

It is highly critical that renewable energy-based power generation units provide continuous and high-quality electricity. This requirement is even more pronounced in standalone wind–diesel systems where the wind power is not always constant or available. Moreover, it is desired that the extracted power be maximized in such a way that less fuel is consumed from the diesel engine. This paper proposes a novel method to design decentralized model-predictive controllers to control the frequency and power of a single standalone generation system, which consists of a wind turbine subsystem mechanically coupled with a diesel engine generator subsystem. Two decentralized model-predictive controllers are designed to regulate the frequency and active power, while the mechanical coupling between the two subsystems is considered, and no communication links exist between the two controllers. Simulation results show that the proposed decentralized controllers outperform the benchmark decentralized linear-quadratic Gaussian (LQG) controllers in terms of eliminating the disturbances from the wind and load power changes. Furthermore, it is demonstrated that the proposed control strategy has an acceptable robust performance against the concurrent variations in all parameters of the system as compared to the LQG controllers.

Dynamometers are used to evaluate the real-world performances of drivetrains in various loading conditions. Due to its superior power density, high bandwidth, and design flexibility, a hydrostatic power-regenerative dynamometer is an ideal candidate for hydrostatic wind turbine transmission testing. A dynamometer can emulate the wind turbine rotor dynamics and allow the investigation of the performance of a unique hydrostatic drivetrain without actually building the physical system. The proposed dynamometer is an energy-efficient system with counter-intuitive control challenges. This paper presents the dynamics, control synthesis, and experimental validation of a power-regenerative hydrostatic dynamometer. A fourth-order non-linear model with three inputs was formulated for the dynamometer. The strength of input–output couplings was identified, and two different decoupling controllers were designed and implemented. During wind turbine testing, the synchronous generator turns at a constant speed and the system model is linear. A steady-state decoupling controller was developed for independent control of the drive and transmission. The implemented decoupling controller demonstrated a negligible change in rotor speed for a 40 bar step increase in pressure, but a 20 bar pressure spike for a 4 rpm step change in rotor speed. However, during starting and stopping, the synchronous generator speed is not constant, and the system model is nonlinear. Therefore, a steady-state decoupling controller will not work. Thus, a decentralized controller with feed-forward control and gain scheduling was designed and implemented. A reference command was designed to avoid cavitation, pressure spikes, and power flow reversal during start-up. The experimental results show precise tracking in steady-state and transient operations. The decentralized controller demonstrated a negligible change in rotor speed for a 40 bar step increase in pressure but a 100 bar pressure spike for a 4 rpm step increase in rotor speed. The pressure spike was reduced by 80 bar with the implementation of feed-forward gain. The proposed electro-hydro-mechanical system requires less power and has the potential to reduce energy expenditure by 50%.

Positive descriptor fractional discrete-time linear systems with fractional different orders are addressed in the paper. The decomposition of the regular pencil is used to extend necessary and sufficient conditions for positivity of the descriptor fractional discrete-time linear system with different fractional orders. A method for finding the decentralized controller for the class of positive systems is proposed and its effectiveness is demonstrated on a numerical example.

This research paper addresses the challenge of designing a decentralized controller for a discrete-time uncertain polytopic system with a linear large-scale (LSS) structure. Specifically, we investigate this problem in cases where the subsystem’s output matrix lacks a decentralized structure. Firstly, the proposed novel procedure of a decentralized controller design transforms the LSS model to have a fully decentralized structure (both input and output matrices are block-diagonal). Then, the robust stability boundary parameter is calculated for the open-loop system. This stability boundary parameter is considered in robust decentralized controller design where an appropriate controller design method is used. The entire process of designing a robust decentralized controller takes place at the subsystem level, and the influence of interaction is considered through the robust stability boundary parameter. Lastly, we present an example of a five-order system comprising two subsystems to show the effectiveness of the new method.

Many interconnected systems in the real world, such as power systems and chemical processes, are often composed of subsystems. A decentralized controller is suitable for an interconnected system because of its more practical and accessible implementation. We use the homotopy method to compute a decentralized controller. Since the centralized controller constitutes the starting point for the method, its existence becomes very important. This paper introduces a non-singular matrix and a design parameter to generate a centralized controller. If the initial centralized controller fails, we can change the value of the design parameter to generate a new centralized controller. A sufficient condition for a decentralized controller is given as a bilinear matrix inequality with three matrix variables: a controller gain matrix and a pair of other matrix variables. Finally, we present numerical examples to validate the proposed decentralized controller design method.

Currently, most control systems of the aero-engines possess a central controller. The core tasks for the control system, such as control law calculations, are executed in this central controller, and its performance and reliability greatly impact the entire control system. This paper introduces a control system design named Software Defined Control Systems (SDCS), which features a controller-decentralized architecture. In SDCS, a network composed of a set of nodes serves as the controller, so there is no central controller in the system, and computations are distributed throughout the entire network. Since the controller is decentralized, there is a need for decentralized control tasks. To address this, this paper introduces a method for designing decentralized control tasks using periodic linear iteration. Each node in the network periodically broadcasts its own state and updates its next-step state as a weighted sum of its current state and the received current states of other nodes in the network. Each node in the network acts as a linear dynamic controller and maintains an internal state through information exchange with other nodes. We modeled the decentralized controller and obtained the model of the entire control system, and the workload of each obtained decentralized control task is balanced. Then, we obtained a parameter tuning method for each decentralized controller node based on Linear Matrix Inequalities (LMI) to stabilize the closed-loop system. Finally, the effectiveness of the proposed method was verified through digital simulation.

In recent years, small-scale microgrids have become popular in the power system industry because they provide an efficient electrical power generation platform to guarantee autonomy and independence from the power grid, which is a critical feature in cases of catastrophic events or remote areas. On the other hand, due to the short distances among multiple distribution generation systems in small-scale microgrids, the interconnection couplings among them increase significantly, which jeopardizes the stability of the entire system. Therefore, this work proposes a novel method to design decentralized robust controllers based on a retrofit model predictive control scheme to tackle the issue of instability due to the short distances among generation systems. In this approach, the retrofit model predictive controller receives the measured feedback signal from the interconnection current and generates a control command signal to limit the interconnection current to prevent instability. To design a retrofit controller, only the model of a robust closed-loop system, as well as an interconnection line, is required. The model predictive control signal is added in parallel to the control signal from the existing robust voltage source inverter controller. Simulation results demonstrate the superior performance of the proposed technique as compared with the virtual impedance and retrofit linear quadratic regulator techniques (benchmarks) with respect to peak-load demand, plug-and-play capability, nonlinear load, and inverter efficiency.

This study studies the problem of synchronisation control for spacecraft formation via extended state observer approach over directed communication topology. The attitude kinematics and dynamics of spacecraft are described by Lagrangian formulations, and the decentralised controller is designed with time-varying external disturbances and unmeasurable velocity information. In particular, the estimation of disturbances obtained via extended state observer is used for the decentralised controller design. A novel Lyapunov function is proposed to show that both static regulation and dynamic synchronisation are realised. Finally, simulation results are given to demonstrate the effectiveness of the controllers proposed in this study.