Optimal Control of Wind Turbine Systems via Time-Scale Decomposition

Al-Iedani, Intessar; Gajić, Zoran

doi:10.3390/en13020287

Cited by 4 publications

(5 citation statements)

References 20 publications

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“…It is important to emphasize that there are many conference and journal publications on the control of processes in wind turbines, including wind farms, using concentrated (lumped) parameter systems; see for example [41,42] and the references therein. However, a very small number of papers use PDE-based control techniques to optimize dynamic processes in wind turbines and wind farms, and hence obtain more accurate and more efficient results.…”

Section: The Modeling and Control Of Wind Energy Systems Using Pdesmentioning

confidence: 99%

“…However, a very small number of papers use PDE-based control techniques to optimize dynamic processes in wind turbines and wind farms, and hence obtain more accurate and more efficient results. Even more, developing the corresponding PDE mathematical models of the well-established ODE mathematical models, like those in [41,42], will be an interesting area for future research.…”

Section: The Modeling and Control Of Wind Energy Systems Using Pdesmentioning

confidence: 99%

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The Modeling and Control of (Renewable) Energy Systems by Partial Differential Equations—An Overview

Radisavljevic-Gajic,

Karagiannis,

Gajic

2023

Energies

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Mathematical models of energy systems have been mostly represented by either linear or nonlinear ordinary differential equations. This is consistent with lumped-parameter dynamic system modeling, where dynamics of system state variables can be fully described only in the time domain. However, when dynamic processes of energy systems display both temporal and spatial evolutions (as is the case of distributed-parameter systems), the use of partial differential equations is necessary. Distributed-parameter systems, being described by partial differential equations, are mathematically (and computationally) much more difficult for modeling, analysis, simulation, and control. Despite these difficulties in recent years, quite a significant number of papers that use partial differential equations to model and control energy processes and systems have appeared in journal and conference publications and in some books. As a matter of fact, distributed-parameter systems are a modern trend in the areas of control systems engineering and some energy systems. In this overview, we will limit our attention mostly to renewable energy systems, particularly to partial differential equation modeling, simulation, analysis, and control papers published on fuel cells, wind turbines, solar energy, batteries, and wave energy. In addition, we will indicate the state of some papers published on tidal energy systems that can be modelled, analyzed, simulated, and controlled using either lumped or distributed-parameter models. This paper will first of all provide a review of several important research topics and results obtained for several classes of renewable energy systems using partial differential equations. Due to a substantial number of papers published on these topics in the past decade, the time has come for an overview paper that will help researchers in these areas to develop a systematic approach to modeling, analysis, simulation, and control of energy processes and systems whose time–space evolutions are described by partial differential equations. The presented overview was written after the authors surveyed more than five hundred publications available in well-known databases such as IEEE, ASME, Wiley, Google, Scopus, and Web of Science. To the authors’ best knowledge, no such overview on PDEs for energy systems is available in the scientific and engineering literature. Throughout the paper, the authors emphasize novelties, originalities, and new ideas, and identify open problems for future research. To achieve this goal, the authors reviewed more than five hundred journal articles and conference papers.

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Section: The Modeling and Control Of Wind Energy Systems Using Pdesmentioning

confidence: 99%

Section: The Modeling and Control Of Wind Energy Systems Using Pdesmentioning

confidence: 99%

The Modeling and Control of (Renewable) Energy Systems by Partial Differential Equations—An Overview

Radisavljevic-Gajic,

Karagiannis,

Gajic

2023

Energies

Self Cite

View full text Add to dashboard Cite

show abstract

“…where: 𝑹 ̅ > 𝟎 and 𝑸 ̅ ≥ 𝟎 are weighting matrices [30], [31]. Equation ( 27) is minimized under the model ( 24)…”

Section: Design Of a Linear Control For The Linearized Closed-loop Sy...mentioning

confidence: 99%

Development of a new linearizing controller using Lyapunov stability theory and model reference control

Mfoumboulou

Mnguni

2022

IJEECS

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<p><span>One of the most challenging aspects in the nonlinear control of a magnetic levitation (Maglev) system is to find an efficient control algorithm to achieve the stability and accuracy of the closed-loop system. The challenge is then to develop a linearizing control algorithm to maintain a steel ball at a desired position. In this paper, a novel linearizing control algorithm is proposed, which consists of the Lyapunov direct method (LDM) and the model reference control (MRC). The Lyapunov function is developed using the nonlinear equations of the magnetic levitation system, and the reference model is a linear second order system. Two control methods are developed to guarantee system robustness and output stability. Firstly, a new integral linear quadratic regulator (ILQR) is designed for the reference model. Then, an additional innovative proportional gain is combined with the linearizing controller to make the nonlinear control signal stronger. The simulation results indicate that the proposed linearizing controller has excellent set-point tracking, no time delay, fast rising and settling times, and achieves states stability.</span></p>

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“…Lomov's regularization method was generalized to examine the asymptotics of the solution to systems described by singularly perturbed integrodifferential equations with a rapidly oscillating right-hand side [14]. The optimal controller for a singularly perturbed wind turbine system was developed through time-scale decomposition with two reduced-order algebraic Riccati equations corresponding to the slow and fast time scales [15]. Glizer analyzed two types of singularly perturbed nonlinear time-dependent-controlled system with time delays (multiple point-wise and distributed) in the state variables [16].…”

Section: Introductionmentioning

confidence: 99%

Stabilization and the Design of Switching Laws of a Class of Switched Singularly Perturbed Systems via the Composite Control

2021

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This paper proves that the controller design for switched singularly perturbed systems can be synthesized from the controllers of individual slow–fast subsystems. Under the switching rules of individual slow–fast subsystems, switched singularly perturbed systems can be stabilized under a small value of ε. The switching rule is designed on the basis of state transformation of the individual subsystems.

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Optimal Control of Wind Turbine Systems via Time-Scale Decomposition

Cited by 4 publications

References 20 publications

The Modeling and Control of (Renewable) Energy Systems by Partial Differential Equations—An Overview

The Modeling and Control of (Renewable) Energy Systems by Partial Differential Equations—An Overview

Development of a new linearizing controller using Lyapunov stability theory and model reference control

Stabilization and the Design of Switching Laws of a Class of Switched Singularly Perturbed Systems via the Composite Control

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