ARX model decomposed on Meixner-Like orthonormal bases

The present study provides a new modeling of linear slowly starting systems. More precisely, this new approach extends the technique of filtering only the input using Meixner-Like (M-L) filters to filter both the output and input of the system outlined by an ARX model. Therefore, the idea is to develop the input and output parameters of ARX modeling over 2 M-L bases. So as to ensure an optimal representation, the two M-L poles are optimized using Newton-Raphson (N-R) and Genetic Algorithms (GA) methods. A new method is proposed for Model Predictive Control (MPC) using the obtained optimal model that is called ARXMeixner-Like (ARXM-L). A numerical example of system having delay and three examples of experimental research: A supersonic jet engine inlet, a Process Trainer PT326 and a Quanser aero experiment with one degree of freedom attitude control are made.