Abstract
This article investigates the use of orthogonal basis functions, particularly Meixner-like functions, to streamline and optimize the parameter complexity in multi-input multi-output (MIMO) system modeling. We introduce a new optimal model for MIMO systems, developed by decomposing the auto-regressive MIMO model with external inputs (ARX) using orthonormal Meixner-like bases. This model, referred to as the MIMO ARX Meixner-like model, enables filtering of the system’s inputs and outputs with Meixner-like functions. Parameter reduction is achieved through the optimization of Meixner-like poles using an iterative technique based on the Newton-Raphson method. The proposed model’s efficacy is demonstrated through simulations on two experimental systems: a two-degrees-of-freedom (DOF) helicopter and a two-tank process. Results reveal that the model effectively reduces approximation errors with fewer parameters. Comparative analysis with the traditional MIMO ARX model confirms the superior performance of the MIMO ARX Meixner-like model.
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