Bond Graph Modeling of Inter-Actuator Interactions in a Multi-Cylinder Hydraulic System

Authors: Mutuku Muvengei, John Kihiu

Abstract:

In this paper, a bond graph dynamic model for a valvecontrolled hydraulic cylinder has been developed. A simplified bond graph model of the inter-actuator interactions in a multi-cylinder hydraulic system has also been presented. The overall bond graph model of a valve-controlled hydraulic cylinder was developed by combining the bond graph sub-models of the pump, spool valve and the actuator using junction structures. Causality was then assigned in order to obtain a computational model which could be simulated. The causal bond graph model of the hydraulic cylinder was verified by comparing the open loop state responses to those of an ODE model which had been developed in literature based on the same assumptions. The results were found to correlate very well both in the shape of the curves, magnitude and the response times, thus indicating that the developed model represents the hydraulic dynamics of a valve-controlled cylinder. A simplified model for interactuator interaction was presented by connecting an effort source with constant pump pressure to the zero-junction from which the cylinders in a multi-cylinder system are supplied with a constant pressure from the pump. On simulating the state responses of the developed model under different situations of cylinder operations, indicated that such a simple model can be used to predict the inter-actuator interactions.

Keywords: Bond graphs, Inter-actuator interactions, Valvecontrolledhydraulic cylinder.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081987

References:

[1] M. Krishna, "Optimal Motion Generation for Hydraulic Robots". PhD. thesis, 1999.
[2] N. Singh, "Coordinated motion control of heavy duty industrial machines with redundancy," Journal of Robotica, vol. 13, pp. 623-633, 1995.
[3] H. M. Paynter, Analysis and Design of Engineering Systems. MIT Press Publishers, Cambridge, 1961.
[4] D. C. Karnopp, D. L Margolis, and R. C. Rosenberg, System Dynamics: Modelling and Simulation of Mechatronic Systems. John Wiley and Sons Publishers, Newyork, 2000.
[5] D. C. Karnopp, D. L. Margolis, and R. C. Rosenberg, System Dynamics; A Unified Approach. John Wiley and Sons Publishers, Newyork, 2nd ed., 1990.
[6] D .C. Karnopp and R. C. Rosenberg, Introduction to Physical System Dynamics. McGraw Hill Publishers, Newyork, 1983.
[7] P. Breedveld, "Bond graphs," in Encyclopedia of Life Support Systems, Modeling and Simulation, 2003.
[8] P. Gawthrop and L. Smith, Metamodeling: Bond Graphs and Dynamic Systems. Prentice Hall International Publishers, UK Limited, 1996.
[9] F. Fakri, A. Rocaries, and A. Carrierre, "A simple method for conversion of bond graph models in representation by block diagrams," in 1997 Proc. International Conference on Bond Graph Modeling and Simulation.
[10] J. F. Broenink, "Introduction to Physical Systems Modeling with Bond Graphs," Technical Report, Department of Electrical Engineering, University of Twente, Netherlands, 1996.
[11] H. Q. Nguyen, "Robust low level control of robotic excavation". PhD. thesis, Australian Centre for Field Robotics, The University of Sydney, 2000.
[12] M. Bin, "System modeling, identification and coordinated control design for an articulated forestry machine," MSc. thesis, Department of Mechanical Engineering, McGill University, 1996.
[13] S. Sarkar, "Dynamic modeling of an articulated forestry machine for simulation and control," MSc. thesis, Department of Mechanical Engineering, McGill University, Canada, 1996.
[14] R. G. Blackburn and J. Sheare, Fluid Power Control. Technology Press of M.I.T and John Wiley Publishers, 1960.
[15] H. E. Merritt, Hydraulic Control Systems. Wiley and Sons Publishers, Newyork, 1967.
[16] D. McCloy and H. R. Martin, Control of Fluid Power: Analysis and Design. Ellis Horwood Publishers Limited, England, 2 ed., 1980.
[17] W. Borutzky, "An energetically consistent bond graph model of a double acting hydraulic cylinder," in Proceedings of European Simulation Multiconference,, pp. 203-207, 1993.
[18] P. Dransfield and M. K. Teo, "Using Bond graphs in Simulating an Elecro-mechanical System," Journal of Franklin Institute, vol. 308, no. 3, pp. 173-184, 1984.
[19] B. W. Bernard, "Predicting the dynamic response of a hydraulic system using power bond graphs," MSc. thesis, Monach University, Melbourne, Australia, 1983.