International Journal of Control and Automation Vol. 9, No. 11 (2016), pp.315-326 http//dx.doi.org/10.14257/ijca.2016.9.11.27 ISSN: 2005-4297 IJCA Copyright © 2016 SERSC Nonlinear One – Link Flexible Manipulator State Estimation Using the Extended Kalman Filter Mohammed Bakhti and Badr Bououlid Idrissi Moulay Ismaïl University, Ecole Nationale Supérieure d’Arts et Métiers, BP 4024, Marjane II, Beni Hamed, 50000, Meknès, Morocco mdbakhti@yahoo.fr, badr.bououlid@gmail.com Abstract Flexible manipulators active vibration control has been subject to a large number of research papers due to its high potential for industrial applications. However, this approach generally requires the feedback of state variables that are not always available via direct measurements. The present study proposes a state estimation scheme for a nonlinear one – link flexible manipulator based on the Extended Kalman Filter. First, the flexible manipulator, seen as an Euler-Bernoulli cantilever beam, is modeled using The Hamilton’s principle, the elastic movement is approximated using the assumed modes method and the system non linear equations are introduced and converted into the matrix form. Then, the observability of the system is proven and the Extended Kalman Filter scheme is detailed. This article compares, via the numerical simulation results included, the efficiency of the state estimate, reflected by the estimation error and the time required by the filter to converge, relatively to the assumptions on the available measurements. Keywords: Non linear State Estimation, one – link flexible manipulator, System observability, Extended Kalman Filter 1. Introduction Having potential advantages of greater payload to manipulator weight ratio, lower energy consumption and faster response, the flexible manipulators are increasingly utilized in many modern applications such as aircraft, and space structures. However, their modeling approaches and their control/observation systems must consider both the rigid body and the flexible degrees of freedom [1]. One of the common used approaches, for modeling the one-link flexible manipulator, which is essential for the understanding of general multiple-link flexible manipulators, rely on the Hamilton’s principle or the Lagrange equations of movement. Many research papers [2 – 7] have used the Euler – Bernoulli beam theory to derive the deformation model, while the elastic degree of freedom is approximated using either the assumed mode method or the finite element method. Previous nonlinear observer formulations for the flexible manipulator have been investigated. An extended state observer was proposed for the trajectory tracking control of a flexible-joint robotic system in [8]. A nonlinear high gain observer has been developed to estimate the elastic degrees of freedom and their time derivatives in [9], and the Extended Kalman Filter has been used in [9] to give an estimate of the environmental forces. The sliding mode theory has been investigated in [11] to design both a controller and an observer for the tip positioning problem. Distributed observers have been presented in [12, 13] to estimate infinite dimensional states requiring only the boundary values measured by sensors. The principal contribution of this paper is to formulate the Extended Kalman filter, based on the nonlinear model of the one-link flexible manipulator, to give an estimate of its state variables. The analyzed motion of the flexible one-link manipulator consists of Online Version Only. Book made by this file is ILLEGAL.