Dynamics and control of a two link flexible planar manipulator

Abstract

<p>A lightweight manipulator has many desirable features. The structural flexibility associated with lightweight manipulators often results in mechanical vibrations and consequently leads to long settling times and position inaccuracy. The aim of the current study is to investigate the dynamics of a two degree of freedom manipulator with elastic joints and very flexible arms and develop a proper control strategy. The dynamic model of manipulator is derived with the Lagrangian formulation and the assumed-modes approach. The eigenvalues and eigen-functions of the flexible arms are determined by the transfer matrix method. The dynamic effects of friction at the joints, gear blacklash within the actuation, and internal structural damping of the arms are all considered. The derived theoretical model is verified by experiments.</p> <p>The parametric analysis is to designed to examine the effects of the major system parameters on the dynamic performance of the manipulator. The dynamic interactions between the members of the manipulator are also investigated.</p> <p>The power balancing technique is extended for distributed parameter systems and a new approach for model order reduction of nonlinear systems is proposed. Using the derived power elements of the original system states as a criterion, the model reduction is performed in the original physical coordinates. The proposed technique is applied to the manipulator. It is found that the bending vibrations of the flexible link are dominated by its first two natural modes. The contributions of the higher modes are negligible.</p> <p>A model reference adaptive control algorithm originally developed by Sobel is modified and used for the control of manipulator with an unknown payload. It is shown that the modification improves the algorithm's performance significantly. Computer simulations are performed to examine the algorithm's properties and select proper values for the gain matrices. Real-time testing is implemented to validate the theoretical analysis. It is found that the proposed algorithm provides satisfactory performance of the closed-loop system.</p>