Modeling and control of a redundantly actuated variable mass 3RRR planar manipulator controlled by a model-based feedforward and a model-based-proportional-derivative feedforward-feedback controller

摘要

In the paper, dynamics of a complex mechatronics system is considered. A redundantly actuated planar manipulator is the base of the mechanical part of it. It is a 3RRR(1) platform based parallel manipulator. To control its trajectory, a model-based feedforward controller is employed. Three aspects are fundamental in the presented investigations. The first focus is on development of an accurate numerical model used to solve the inverse dynamic problem in the controller loop of the model-based controller. As redundancies are present in actuation, traditional estimation techniques cannot be used to estimate the torques (a non-square matrix is present in the equation). Instead of the classical inverse, the right Moore-Penrose pseudo-inverse is used to estimate the torques. Passing to the second aspect, to realize the first run of the control algorithm, roughly estimated inertia parameters have to be implemented in the controller. Inertia parameters of the real object can differ from these implemented in the controller (the load of the platform is a variable mass element). As it is proofed in the paper, precision is a critical aspect of these estimations. When inappropriate estimation is proposed, significant trajectory errors are observed. To eliminate the consequences of the estimation errors, the control loop is extended with some additional PD (proportional-derivative) feedforward-feedback controller. Collaboration between these two controllers is the announced second objective of the paper. Intensive work of the PD controller is not required for a long time in the control loop, thus the third of the paper's fundamental objectives is dedicated to identification methods. Basing it in the PD signal value, some corrections are proposed for values of the inertia parameters and modification of the parameters is performed in the numerical description of the model-based controller. (C) 2015 Elsevier Ltd. All rights reserved.