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1
An application of parameter matrix right H-inverse into fractional-order perfect control law
Wach Ł.
Zeszyty Naukowe. Elektryka / Politechnika Opolska
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2017
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z. 75
121--124
EN
The paper presents a possibility of employment of right nonunique parameter H-inverse to LTI MIMO nonsquare fractional-order perfect control systems in state-space. On the basis of Grünwald–Letnikov definition and Hinverse formula applied, until now, to the classical perfect control a formula for fractional-order perfect control is presented here. The potential of H-inverse to stabilize nonsqure fractional-order perfect control is emphasized.
2
Fractional-order discrete-time perfect control of LTI MIMO STATE-SPACE SYSTEMS – new stability remarks
Wach Ł.
Zeszyty Naukowe. Elektryka / Politechnika Opolska
|
2016
|
z. 72
105--106
EN
In this paper a preliminary study on the perfect control stability in fractional-order framework is presented. A new formula that allows delimiting the stability area for LTI MIMO discrete-time fractional-order systems in state-space corresponds to the one dedicated to classical integer-order systems. The new approach opens the possibility for illustrating the perfect control stability areas for such systems under numerical method.
3
Contribution of σ-inverse to stabilization of fractional-order perfect control for lti mimo state-space systems
Wach Ł., Hunek W. P.
Zeszyty Naukowe. Elektryka / Politechnika Opolska
|
2016
|
z. 74
185--190
EN
The paper presents a study on possibilities of application of the parameter matrix σ-inverse for stabilization the fractional-order discrete-time perfect control in state-space. Basing on Grünwald–Letnikov definition and a new fractional-order perfect control law for LTI MIMO systems the simulation research illustrates the prospects of utilisation the σ-inverse for stabilization of mentioned control strategy. The simulation example shows that σ-inverse outperforms the classical minimum-norm right inverse so called T-inverse.
4
Content available Contribution of New Parameter Inverses to Robustification of Fractional-Order Perfect Control for LTI MIMO Discrete-Time State-Space Systems
Wach Ł., Hunek W. P.
Journal of Automation Mobile Robotics and Intelligent Systems
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2016
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Vol. 10, No. 3
29--33
EN
The paper presents results of application of various right inverses to fractional-order discrete-time perfect control in terms of improving its stability and robustness. For that reason the newly introduced σ-inverse and H-inverse are applied finally to obtain the mentioned above control strategy strictly dedicated to LTI MIMO nonsquare systems described by state-space framework. It is highlighted that parameter σ-inverse and H-inverse with different so called ‘degrees of freedom’ outperform the typical minimum-norm right T-inverse. Moreover, this new approach deals with the same class of problems concerning integer-order systems. The simulation studies performed in Matlab/Simulink environment confirm high potential of proposed here method.
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