Nonlinear Dynamic States’ Estimation and Prediction Using Polynomial Predictive Modeling Estimation et prédiction d’états dynamiques non linéaires à l’aide d’une modélisation prédictive polynomiale

Abstract

In motion-control applications, noise and dynamic nonlinearities influence the performance of control systems and lead to unpredictable disturbances. The dc servo motors used in motion control applications should have precise control methods to achieve the desired responses. Therefore, predicting and compensating for the disturbance are essential for increasing system robustness and achieving high precision and fast reaction. This article introduces the polynomial predictive filtering (PPF) method to estimate the states of a system using polynomial extrapolation of consecutive and evenly spaced sensor data. Acceleration-/torque-based experiments are conducted to validate the effectiveness and viability of the proposed method. The difference between the real-time sensor data and the PPF-based predicted value shows a standard deviation of less than <inline-formula> <tex-math notation="LaTeX">$0.15$</tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">$1$</tex-math> </inline-formula> <inline-formula> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> <inline-formula> <tex-math notation="LaTeX">$10^{-5}$</tex-math> </inline-formula> for the velocity and disturbance torque, respectively.