Transformation of two-dimensional model into two-dimensional decoupled model and decomposition into one-dimensional models

Abstract

Two-dimensional models are challenging to deals with because of their complex structure. Two-dimensional models can be separated into two sub-models only if they are represented in separable-denominator form. However, the separable-denominator form must satisfy the minimal rank-decomposition criteria to decompose the two-dimensional model into two sub-models. This research proposes a transformation that transforms the original two-dimensional general model into a two-dimensional decoupled model form without involving separable-denominator form and minimal rank-decomposition criteria and then decomposes into two one-dimensional sub-models (i.e. two cascaded one-dimensional models). Furthermore, the suggested transformation preserves the symmetry of the decomposed one-dimensional sub-models. These sub-models are used for ease in the design, analysis, control, and model reduction. Numerical outcomes show that the suggested transformation efficiently transforms the original two-dimensional model into decoupled model form, demonstrating the proposed transformation's effectiveness.

Keywords:

• Two-dimensional models
• decomposition of two-dimensional models
• causal recursive separable denominator
• two-dimensional decoupled model form
• model reduction
• non-symmetric algebraic riccati equation
• minimal rank-decomposition

Acknowledgments

Authors would like to thank the National University of Sciences & Technology (NUST) for supporting this research work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Additional information

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Notes on contributors

Muhammad Imran

Muhammad Imran, is received his B.S. in Electrical Engineering from, University of Engineering & Technology (UET) Taxila, Pakistan, in 2014. He received his M.S. and Ph.D. in Electrical Engineering Control Systems (Model/Controller Order Reduction) from, College of Electrical and Mechanical Engineering (CEME), and Military College of Signals (MCS), National University of Sciences and Technology (NUST), Islamabad, Pakistan, in 2017 and 2022, respectively. His research interests include model order reduction, control systems theory, nonlinear control systems, fuzzy control, simulation & optimisation of dynamical systems, systems, and signal processing, communication and biomedical algorithms.

Muhammad Imran

Muhammad Imran, is received his Masters and Ph.D. degrees in Electrical Engineering from MCS, NUST, Islamabad, Pakistan, in 2011 and 2014, respectively. He is an active researcher and produced many publications in well-reputed journals and conferences. Currently a faculty member at Military College of Signals, National University of Sciences & Technology as an Associate Prof and performing his duties as Associate Head of Department. His research interests include model/controller order reduction, control systems theory, communication systems, and signal processing, communication and biomedical algorithms.