Perfect Control for Fractional-Order Multivariable Discrete-Time Systems

Wach, Łukasz; Hunek, Wojciech P.

doi:10.1007/978-3-319-23039-9_19

Cited by 5 publications

(2 citation statements)

References 5 publications

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“…and y ref (k + 1) are the one-step deterministic output predictor and reference/setpoint, respectively, we obtain the perfect control law [19]…”

Section: Fractional-order Perfect Controlmentioning

confidence: 99%

“…Therefore, it is an attempt to synthesis of discrete-time fractional-order perfect control with regard of its stability and robustness. To obtain that objective, the recently devised a fractional-order multivariable discrete-time perfect control algorithm, in particular dedicated to the so-called nonsquare state-space systems, i.e., systems with different number of input and output variables, is used [19]. The simulations performed into perfect control involve parameter σ-inverse and H-inverse.…”

Section: Selection Of Nonunique Right Inversementioning

confidence: 99%

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

Hunek

Wach

2019

Symmetry

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The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Grünwald–Letnikov discrete-time state–space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due to an infinite number of solutions to the underlying inverse problem for nonsquare matrices. Therefore, the paper presents a new algorithm for fractional-order perfect control with corresponding stability formula involving recently given H- and σ -inverse of nonsquare matrices, up to now applied solely to the integer-order plants. On such foundation a new set of stability-related tools is introduced, among them the key role played by so-called control zeros. Control zeros constitute an extension of transmission zeros for nonsquare fractional-order LTI MIMO systems under inverse model control. Based on the sets of stable control zeros a minimum-phase behavior is specified because of the stability of newly defined perfect control law described in the non-integer-order framework. The whole theory is complemented by pole-free fractional-order perfect control paradigm, a special case of fractional-order perfect control strategy. A significant number of simulation examples confirm the correctness and research potential proposed in the paper methodology.

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“…and y ref (k + 1) are the one-step deterministic output predictor and reference/setpoint, respectively, we obtain the perfect control law [19]…”

Section: Fractional-order Perfect Controlmentioning

confidence: 99%

Section: Selection Of Nonunique Right Inversementioning

confidence: 99%

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

Hunek

Wach

2019

Symmetry

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New Approaches to Minimum-Energy Design of Integer- and Fractional-Order Perfect Control Algorithms

Hunek

Wach

2017

E3S Web Conf.

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Abstract. In this paper the new methods concerning the energy-based minimization of the perfect control inputs is presented. For that reason the multivariable integer-and fractional-order models are applied which can be used for describing a various real world processes. Up to now, the classical approaches have been used in forms of minimum-norm/least squares inverses. Notwithstanding, the above-mentioned tool do not guarantee the optimal control corresponding to optimal input energy. Therefore the new class of inversebased methods has been introduced, in particular the new σ-and H-inverse of nonsquare parameter and polynomial matrices. Thus a proposed solution remarkably outperforms the typical ones in systems where the control runs can be understood in terms of different physical quantities, for example heat and mass transfer, electricity etc. A simulation study performed in Matlab/Simulink environment confirms the big potential of the new energy-based approaches.

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Towards a New Stability Criterion for Fractional-Order Perfect Control of LTI MIMO Discrete-Time Systems in State-Space

Hunek¹,

Wach²

2017

2017 3rd IEEE International Conference on Cybernetics (CYBCONF)

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Perfect Control for Fractional-Order Multivariable Discrete-Time Systems

Cited by 5 publications

References 5 publications

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

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

New Approaches to Minimum-Energy Design of Integer- and Fractional-Order Perfect Control Algorithms

Towards a New Stability Criterion for Fractional-Order Perfect Control of LTI MIMO Discrete-Time Systems in State-Space

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