Robust overwhelming control of a hydraulically driven three-degrees-of-freedom parallel manipulator through a simplified fast inverse model

Abstract

An overwhelming controller-based implicit system inversion scheme is proposed in this work to control a hydraulically driven planar (three-degrees-of-freedom) parallel manipulator. The physical model-based design of the controller is developed by using bond graphs. The electro-hydraulic actuator in the leg is modelled by including the dynamics of the servo-valve and the cylinder. A leg-space force-feedback controller is proposed for controlling the hydraulic pressures acting on the pistons of the actuators. The objective is to develop a fast inverse model which is suitable for real-time implementation in the controller. It is shown that an approximate inverse model which correctly represents the kinematics of motion but has incorrect representation of inertias is sufficient for the controller design because of the high feedback gains used in the overwhelming control strategy. This controller, based on the approximate simple inverse model, generates the right driving forces for the actual system whose model is much more complicated and uncertain. Finally, the controller design for a planar vehicle simulator is considered as an example and the corresponding simulation results are used to validate the robustness of the model-based overwhelming controller to the modelling uncertainties.

Bond graph modelling of a hydraulic cylinder-actuated planar manipulator

“…(20) This method of modelling dynamics from kinematics viewpoint is referred to flow mapping [20]. The kinematic equations of the hydraulic cylinder are given in the subsequent paragraphs.…”

“…9. The elements k p and r p are assigned very high values, so that they yield a highfrequency oscillation at the beginning and decay rapidly [5,11,20]. Use of this model to resolve the problem of differential causality at different joints is shown in Fig.…”

“…These advantages of bond graph were recognized and applied to model various multibody systems decades ago [16][17][18][19]. However, no attention is paid towards BG modelling of the multibody dynamics of the hydraulic cylinder constrained by revolute joint until recently when this task is accomplished and applied to many applications by [20,21]. The applications reported in these references are on modelling and dynamic analysis of a V-twin engine mount system, an axially flexible conical pendulum, and three-dimensional active and passive prismatic joints.…”

“…The same concept of modelling prismatic joint can be employed in various kinds of manipulators, such as forklifts, excavators, dumpers, etc. Control application was also demonstrated with the help of a Stewart platform model, in which the developed model was inverted to solve inverse dynamics for force and impedance control [20]. In those articles, the multibody dynamics of the hydraulic cylinder was modelled by considering it to be two interconnected links (i.e., cylinder barrel and piston rod) constrained by prismatic joint to produce the linear sliding movement.…”

“…The obtained model is validated by comparing its responses with those of the actual system in a complete duty cycle. Although simple kinematic relations are used to construct the BG model, the model can itself calculate the Coriolis and centrifugal forces because of power conservative feature of bond graph [13,20,21]. …”