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

This paper reports on the tracking control of a pendulum. The particular co ntributions of this paper lie in the development of a numerically efficient approach for the state estimation of a class of non-linear systems which f all under the extended generalized Wiener model structure and its applicati on to the pendulum system. It details the estimation and control aspects fo r achieving the tracking control of the pendulum where attention is focused on Extended Kalman Filtering (EKF) methods based on Volterra series approx imations of the non-linearity for the estimation of the pendulum states. Co ntrol is then effected by the Feedback Linearization (FL)I technique and th e Internal Model Principle (IMP). It is argued that this offers accuracy be nefits over linear techniques while substantially reducing the computationa l burden associated with the standard EKF approaches. The arguments are sup ported by evidence from a case study system. It is demonstrated that this p roposed approach is significantly faster and does not demand any additional hardware configurations. Estimation error and tracking error variance resu lts are included for substantiating the numerical efficiency of the propose d approach.