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

Hunek, Wojciech P.; Wach, Łukasz

doi:10.1109/cybconf.2017.7985817

Cited by 4 publications

(3 citation statements)

References 17 publications

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“…That approach gives the opportunity to impact on the perfect control strategy by influencing matrices obtained from SVD factorization in form of parameter or polynomial degrees of freedom as well. The tools mentioned above, previously employed to integer-order systems, are transferred to fractional-order perfect control of LTI MIMO discrete-time state-space systems [26]. It is remarkable that the concept of engaging the inverses of parameter matrices to increasing the robustness of multivariable discrete-time fractional-order perfect control structures in a state-space forms a new and original idea developed by these authors, not presented so far.…”

Section: Selection Of Nonunique Right Inversementioning

confidence: 99%

“…This fact is confirmed in a few reports in the area; however, the formal proof is still to be conducted. It turns out that the minimum-energy-based approach can improve the fractional-order closed-loop perfect control robustness [26]. The chosen degrees of freedom {β(q −1 )} for, e.g., σ-inverse substituted to the fractional-order perfect control law as in (15) can provide its stable/robust instance.…”

Section: Robustness Of Fractional-order Perfect Controlmentioning

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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Section: Selection Of Nonunique Right Inversementioning

confidence: 99%

Section: Robustness Of Fractional-order Perfect Controlmentioning

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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“…The issues involving the stability and robustness of MV/perfect control for LTI MIMO integer-order discrete-time systems in state-space framework become the field of intense scientific research [1][2][3][4][5][6][7]. Taking into account the integer-order perfect control the quest for advance takes the form of utilization different types of parameter of polynomial right inverses.…”

Section: Introductionmentioning

confidence: 99%

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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New interesting facts about minimum-energy perfect control for LTI nonsquare state-space systems

Hunek

2017

2017 22nd International Conference on Methods and Models in Automation and Robotics (MMAR)

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

Cited by 4 publications

References 17 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

New interesting facts about minimum-energy perfect control for LTI nonsquare state-space systems

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