Modelling and control of a two-link flexible manipulator using finite element modal analysis

Abstract

This thesis focuses on Finite Element (FE) modeling and robust control of a two-link flexible manipulator based on a high resolution FE model and the system vibration modes. A new FE model is derived using Euler-Bernoulli beam elements, and the model is validated using commercial software Abaqus CAE. The frequency and time domain analysis reveal that the response of the FE model substantially varies with changing the number of elements, unless a high number of elements (100 elements in this work) is used. The gap between the complexity of the high order FE model capable of predicting dynamics of the multibody system, and suitability of the model for controller design is bridged by designing control schemes based on the reduced order models obtained using modal truncation/H8 techniques. Two reduced order multi-input multi-output modal control algorithms composed of a robust feedback controller along with a feed-forward compensator are designed. The first controller, Inversion-based Two Mode Controller (ITMC), is designed using a mixed-sensitivity H8 synthesis and a modal inversion-based compensator. The second controller, Shaping Two-Mode Controller (STMC), is designed with H8 loopshaping using the modal characteristics of the system. Stability robustness against unmodelled dynamics due to the model reduction is shown using the small gain theorem. Performance of the feedback controllers are compared with Linear Quadratic Gaussian designs and are shown to have better tracking characteristics. Effectiveness of the control schemes is shown by simulation of rest-to-rest maneuver of the manipulator to a set of desired points in the joint space. The ITMC is shown to have more precise tracking performance, while STMC has higher control over vibration of the tip, at the expense of more tracking errors.