Least Squares Method for The Mathematical Model of an Automotive Window Mechanism
Keywords:
mathematical model, window mechanism, system identification, ultrasonic sensorAbstract
This research presents a system identification and mathematical modeling approach for an automotive window mechanism using Least Squares (LS) and Recursive Least Squares (RLS) estimation techniques due to the linearity of the automotive window mechanism system. The objective is to select the suitable dynamic model that can predict the position of the window mechanism and compare two parameter estimation methods between Least Squares (LS) and Recursive Least Squares (RLS) method. The experiment involves collecting input - output data using an ultrasonic sensor and Arduino-based data acquisition system. The collected data is used to estimate the system parameters for different model structures, including Autoregressive exogenous (ARX) and Autoregressive moving average exogenous inputs (ARMAX) models, at various model orders. The performance of each model is evaluated by comparing the simulated outputs with experimental data. The results indicate that the 4th order ARMAX model with Recursive Least Square achieves the highest accuracy of 95.563%. When the 4th order ARMAX model with Least Square achieves the accuracy of 94.862%. The findings of this research demonstrate that the selection of an appropriate model structure and estimation method significantly impacts the accuracy of system identification for an automotive window mechanism.
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