A New Stability Theory for Grünwald–Letnikov Inverse Model Control in the Multivariable LTI Fractional-Order Framework

Hunek, Wojciech P.; Wach, Łukasz

doi:10.3390/sym11101322

Cited by 3 publications

(2 citation statements)

References 36 publications

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“…Remark 1. Naturally, the right inverse of the CB matrix used in the perfect control law can be obtained in different numeric procedures described, e.g., in [12,16,20].…”

Section: Perfect Controlmentioning

confidence: 99%

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Switching Perfect Control Algorithm

2020

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The application of the switching control framework to the perfect control algorithm is presented in this paper. Employing the nonunique matrix inverses, the different closed-loop properties are obtained and further enhanced with possible switching methodology implementation. Simulation examples performed in the MATLAB/Simulink environment clearly show that the new framework can lead to benefits in terms of the control energy, speed, and robustness of the perfect control law. The possibility of transferring the new obtained results to the symmetrical nonlinear plants seems to be immediate.

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“…Remark 1. Naturally, the right inverse of the CB matrix used in the perfect control law can be obtained in different numeric procedures described, e.g., in [12,16,20].…”

Section: Perfect Controlmentioning

confidence: 99%

“…With the application of the so-called degrees of freedom, almost an infinite number of possible solutions could be employed in different control strategies [14], including the perfect control design. Properties connected with minimum energy or maximum speed were established using, e.g., the arbitrary σ-or H-inverse [15,16].…”

Section: Introductionmentioning

confidence: 99%

Switching Perfect Control Algorithm

2020

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Robust Fractional-Order Perfect Control for Non-Full Rank Plants Described in the Grünwald-Letnikov IMC Framework

Hunek

Feliks

2021

Fract Calc Appl Anal

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The advanced analytical study in the field of fractional-order non-full rank inverse model control design is presented in the paper. Following the recent results in this matter it is certain, that the inverse model control-oriented perfect control law can be established for the non-full rank integer-order systems being under the discrete-time state-space reference with zero value. It is shown here, that the perfect control paradigm can be extended to cover the multivariable non-full rank plants governed by the more general Grünwald-Letnikov discrete-time state-space model. Indeed, the postulated approach significantly reduces both iterative and non-iterative computational effort, mainly derived from the approximation of the Moore-Penrose inverse of the non-full rank matrices to finally be inverted. A prevention provided by the new method excludes the detrimental matrix behavior in the form of singularity, often avoided due to the observed ill-conditioned sensitivity. Thus, the new defined robust fractional-order non-full rank instance of such control strategy, supported by the pole-free mechanism, gives rise to the introduction of the general unified non-full rank perfect control-originated theory. Numerical algorithms with simulation investigation clearly confirm the innovative peculiarities provided by the manuscript.

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A Survey of Fractional Order Calculus Applications of Multiple-Input, Multiple-Output (MIMO) Process Control

Almeida

Lenzi

2020

Fractal Fract

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Multiple-input multiple-output (MIMO) systems are usually present in process systems engineering. Due to the interaction among the variables and loops in the MIMO system, designing efficient control systems for both servo and regulatory scenarios remains a challenging task. The literature reports the use of several techniques mainly based on classical approaches, such as the proportional-integral-derivative (PID) controller, for single-input single-output (SISO) systems control. Furthermore, control system design approaches based on derivatives and integrals of non-integer order, also known as fractional control or fractional order (FO) control, are frequently used for SISO systems control. A natural consequence, already reported in the literature, is the application of these techniques to MIMO systems to address some inherent issues. Therefore, this work discusses the state-of-the-art of fractional control applied to MIMO systems. It outlines different types of applications, fractional controllers, controller tuning rules, experimental validation, software, and appropriate loop decoupling techniques, leading to literature gaps and research opportunities. The span of publications explored in this survey ranged from the years 1997 to 2019.

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A New Stability Theory for Grünwald–Letnikov Inverse Model Control in the Multivariable LTI Fractional-Order Framework

Cited by 3 publications

References 36 publications

Switching Perfect Control Algorithm

Switching Perfect Control Algorithm

Robust Fractional-Order Perfect Control for Non-Full Rank Plants Described in the Grünwald-Letnikov IMC Framework

A Survey of Fractional Order Calculus Applications of Multiple-Input, Multiple-Output (MIMO) Process Control

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