An application of a new matrix inverse in stabilizing state-space perfect control of nonsquare LTI MIMO systems

Hunek, Wojciech P.; Latawiec, Krzysztof J.; Majewski, Paweł; Dzierwa, Piotr

doi:10.1109/mmar.2014.6957396

Cited by 17 publications

(12 citation statements)

References 35 publications

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“…Several methods of right/left inverses of nonsquare polynomial matrices, such as the classical minimum-norm right/left inverse, called T-inverse and τ-σ-S-inverses methods, have been studied in [27,32]. In this work, we focus on σ-inverse as follows:…”

Section: Inverses Of Nonsquare Polynomial Matrices and I (N) -Ilc Designmentioning

confidence: 99%

“…In the literature, there are control works that treated the nonsquare MIMO systems such as a Proportional Integrator Derivator (PID) controller cited in [25] which has been applied to a voltage model of Proton Exchange Membrane Fuel Cell (PEMFC); Model Predictive Control (MPC) was studied in [26] and has been applied to a Shell Heavy Oil Fractionator (SHOF); Minimum Variance Control (MVC) which is an inverse model control was studied in [27] and other examples of control strategies applied to nonsquare systems [28]. In the above cited works [25,26], the control schemes were achieved without a need to matrix inversion.…”

Section: Introductionmentioning

confidence: 99%

“…In the above cited works [25,26], the control schemes were achieved without a need to matrix inversion. However, in [27] the synthesis of the inverse model in the control procedure required a matrix inversion based on left and right inverses which are developed in [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New Iterative Learning Control Algorithm Using Learning Gain Based on σ Inversion for Nonsquare Multi-Input Multi-Output Systems

Noueili

Chagra

Ksouri

2018

Modelling and Simulation in Engineering

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Model inversion Iterative Learning Control (ILC) for a class of nonsquare linear time variant/invariant multi-input multi-output (MIMO) systems is considered in this paper. A new ILC algorithm is developed based on σ-right inversion of nonsquare learning gain matrices to resolve the matrix inversion problems appeared in the direct model inversion of nonsquare MIMO systems. Furthermore, a sufficient and necessary monotonic convergence condition is established. With rigorous analysis, the proposed ILC scheme guarantees the convergence of the tracking error. To prove the effectiveness and to illustrate the performance of the proposed approach for linear time-invariant (LTI) and time-varying nonsquare systems, two illustrative examples are simulated.

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Section: Inverses Of Nonsquare Polynomial Matrices and I (N) -Ilc Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New Iterative Learning Control Algorithm Using Learning Gain Based on σ Inversion for Nonsquare Multi-Input Multi-Output Systems

Noueili

Chagra

Ksouri

2018

Modelling and Simulation in Engineering

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“…A new approach implies the use of appropriate tools associated with systems described by matrix polynomial framework. A key role plays here the Smith-factorized the polynomial matrix Sinverse, which implements the so-called degrees of freedom [8][9][10][11][12][13][14][15]. As is shown by simulation studies, the new idea can restrain the negative influence of the propagation environment on the process of signal reconstruction/recovery.…”

Section: Introductionmentioning

confidence: 99%

New approach to wireless data communication in a propagation environment

Hunek

Majewski

2017

E3S Web Conf.

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Abstract. This paper presents a new idea of perfect signal reconstruction in multivariable wireless communications systems including a different number of transmitting and receiving antennas. The proposed approach is based on the polynomial matrix S-inverse associated with Smith factorization. Crucially, the above mentioned inverse implements the so-called degrees of freedom. It has been confirmed by simulation study that the degrees of freedom allow to minimalize the negative impact of the propagation environment in terms of increasing the robustness of whole signal reconstruction process. Now, the parasitic drawbacks in form of dynamic ISI and ICI effects can be eliminated in framework described by polynomial calculus. Therefore, the new method guarantees not only reducing the financial impact but, more importantly, provides potentially the lower consumption energy systems than other classical ones. In order to show the potential of new approach, the simulation studies were performed by author's simulator based on wellknown OFDM technique.

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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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An application of a new matrix inverse in stabilizing state-space perfect control of nonsquare LTI MIMO systems

Cited by 17 publications

References 35 publications

New Iterative Learning Control Algorithm Using Learning Gain Based on σ Inversion for Nonsquare Multi-Input Multi-Output Systems

New Iterative Learning Control Algorithm Using Learning Gain Based on σ Inversion for Nonsquare Multi-Input Multi-Output Systems

New approach to wireless data communication in a propagation environment

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

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