Modeling and sliding-mode control of flexible-link robotic structures for vibration suppression

Abstract

In many applications, the use of slender and light flexible structures has increased due to the requirement of more energetically efficient structures. This kind of structures is easily prone to vibrate due to external forces or due to forces generated in the inner structure during the movement. One objective of this work is to generate models of flexible-link structures: cantilever beam, one flexible-link robot and two flexible-link robot; which include rotational actuators, piezoelectric actuators, and different kinds of sensors (acceleration and deformation). The models are obtained under a classical mechanics approach of Lagrange Euler energy balance; the assumed mode method is used to approximate the flexibility of the elastic components. In the model formulation, new rotation angles are introduced in the distal joints and the joint inertia is separated according to this new kinematic consideration. Some parts of the resulting model involving integral terms are calculated using symbolic programming software; whereas other parts are implemented and calculated dynamically during simulation. The resulting models are programmed in Matlab/Simulink subjected to a novel verification methodology and then validated experimentally in a platform constructed for the implementation. The second objective is to develop, from simplified models of the flexible-link structures, robust controllers for joint tracking and active vibration suppression. Therefore, robust control is used with two basic purposes: to face the model uncertainties due to the discrepancies between the models and real systems and to suppress the vibration of the flexible-link structures. Three control strategies are proposed: Dual loop control approach, decentralized and centralized Lyapunov model-based sliding mode control approach. The values required for the implementation of the controller are obtained from the formulated models. The controllers were implemented in a dSPACE rapid prototyping control card and the experimental results show the effectiveness of the proposed control strategies in terms of joint tracking and vibration suppression.