Tracking control of a pendulum using a numerically efficient state estimation approach for polynomic non-linear systems

Abstract

This paper reports on the tracking control of a pendulum. The particular contributions of this paper lie in the development of a numerically efficient approach for the state estimation of a class of non-linear systems which fall under the extended generalized Wiener model structure and its application to the pendulum system. It details the estimation and control aspects for achieving the tracking control of the pendulum where attention is focused on Extended Kalman Filtering (EKF) methods based on Volterra series approximations of the non-linearity for the estimation of the pendulum states. Control is then effected by the Feedback Linearization (FL) technique and the Internal Model Principle (IMP). It is argued that this offers accuracy benefits over linear techniques while substantially reducing the computational burden associated with the standard EKF approaches. The arguments are supported by evidence from a case study system. It is demonstrated that this proposed approach is significantly faster and does not demand any additional hardware configurations. Estimation error and tracking error variance results are included for substantiating the numerical efficiency of the proposed approach.