## “Model Predictive Control of Low-Speed Partial Stroke Operated Digital Displacement Pump Unit”Authors: Niels Henrik Pedersen, Per Johansen, Anders Hedegaard Hansen and Torben Ole Andersen,
Affiliation: Aalborg University
Reference: 2018, Vol 39, No 3, pp. 167-177. |

**Keywords:**Digital Displacement Units, Fluid Power, Control, Non-smooth System, Hybrid Systems

**Abstract:**To enhance the use of the Digital Displacement Machine (DDM) technology as the future solution for low speed fluid power pump and motor units, a Model Predictive Control (MPC) strategy is presented. For a low speed DDM, the conventional full stroke operation strategy is unsuitable, since the control update rate is proportional to the machine speed. This creates an incentive to utilize sequential partial stroke operation where a fraction of the full stroke is used, which thereby increases the control update rate and control signal resolution. By doing this, the energy loss is increased and may become undesirable large if the control objective is purely set-point tracking, why a trade-off is considered advantageous. Discretizing the full stroke based on a chosen update rate results in a Discrete Linear Time Invariant (DLTI) model of the system with discrete input levels. In this paper, the Differential Evolution Algorithm (DEA) is used to determine the optimal control input based on the trade-off between set-point tracking and energy cost in the prediction horizon. The paper presents a flow and a pressure control strategy for a fixed speed digital displacement pump unit and shows the trade-off influence on the optimal solution through simulation. Results show the applicability of the control strategy and indicate that a much higher energy efficiency may be obtained with only a minor decrease in tracking performance for pressure control.

PDF (805 Kb) DOI: 10.4173/mic.2018.3.3

**References:**

[1] Armstrong, B. S.R. and Yuan, Q. (0). Armstrong, B, S.R. and Yuan, Q. Multi-level control of hydraulic gerotor motor and pumps. Proceedings of the 2006 American Control Conference Minneapolis, Minnesota, June 2006. doi:10.1109/ACC.2006.1657450

[2] Bech, M.M., Noergaard, C., Roemer, D.B., and Kukkonen, S. (2016). Bech, M, M., Noergaard, C., Roemer, D.B., and Kukkonen, S. A global multi-objective optimization tool for design of mechatronic compo- nents using generalized differential evolution. Proceedings of the 42nd Annual Conference of IEEE Industrial Electronics Society. doi:10.1109/IECON.2016.7793419

[3] Hansen, A.H., Asmussen, M.F., and Bech, M.M. (2017). Hansen, A, H., Asmussen, M.F., and Bech, M.M. Energy optimal tracking control with discrete fluid power systems using model predictive control. The Ninth Workshop on Digital Fluid Power, September 7-8, Aalborg, Denmark. .

[4] Heikkila, M. and Linjama, M. (2013). Heikkila, M, and Linjama, M. Displacement control of a mobile crane using digital hydraulic power management system. Mechatronics 23(4), pp. 452 - 461. doi:10.1016/j.mechatronics.2013.03.009

[5] Johansen, P. (2014). Johansen, P, Tribodynamic Modeling of Digital Fluid Power Motors. Ph.D. thesis, Department of Energy Technology, Aalborg University, 2014. .

[6] Johansen, P., Roemer, D.B., Pedersen, H.C., and Andersen, T.O. (2015). Johansen, P, , Roemer, D.B., Pedersen, H.C., and Andersen, T.O. Delta-sigma modulated displacement of a digital fluid power pump. Proceedings of the 7th Workshop on Digital Fluid Power, Linz, Austria. The Seventh Workshop on Digital Fluid Power, Linz, Austria. .

[7] Johansen, P., Roemer, D.B., Pedersen, H.C., and Andersen, T.O. (2017). Johansen, P, , Roemer, D.B., Pedersen, H.C., and Andersen, T.O. Discrete linear time invariant analysis of digital fluid power pump flow control. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, Vol. 139, Nr. 10, 101007. doi:10.1115/1.4036554

[8] Linjama, M. (2011). Linjama, M, Digital fluid power – state of the art. The Twelfth Scandinavian International Conference on Fluid Power, May 18-20, Tampere, Finland. .

[9] M.Ehsan, W.R. and Salter, S. (0). M, Ehsan, W.R. and Salter, S. Modeling of digital-displacement pump-motors and their application as hydraulic drives for nonuniform loads. ASME, Journal of dynamic system measurement and control, Vol. 122, pp. 210-215, March 2000. doi:10.1115/1.482444

[10] Merrill, K., Holland, M., and Lumkes, J. (2011). Merrill, K, , Holland, M., and Lumkes, J. Analysis of digital pump/motor operating strategies. Proceedings of the 52nd National Conference on Fluid Power, 2011. .

[11] Noergaard, C. (2017). Noergaard, C, Design, Optimization and Testing of Valves for Digital Displacement Machines. Ph.D. thesis, Aalborg University. doi:10.5278/vbn.phd.eng.00013

[12] Payne, G.S., Stein, U. P.P., Ehsan, M., Caldwell, N.J., and Rampen, W. H.S. (2005). Payne, G, S., Stein, U. P.P., Ehsan, M., Caldwell, N.J., and Rampen, W. H.S. Potential of digital displacement hydraulics for wave energy conversion. In Proc. of the 6th European Wave and TIdal Energy Conference, Glasgow UK.. .

[13] Pedersen, N.H., Johansen, P., and Andersen, T.O. (2017). Pedersen, N, H., Johansen, P., and Andersen, T.O. Event-driven control of a speed varying digital displacement machine. Proceedings of ASME/BATH FPMC Symposium on Fluid Power and Motion Control, Sarasota, Florida, USA, 2017. doi:10.1115/FPMC2017-4260

[14] Pedersen, N.H., Johansen, P., and Andersen, T.O. (2017). Pedersen, N, H., Johansen, P., and Andersen, T.O. Lqr-feedback control development for wind turbines featuring a digital fluid power transmission system. 9th FPNI PhD symposium on fluid power, Florianópolis, Brazil, 2017. doi:10.1115/FPNI2016-1537

[15] Pedersen, N.H., Johansen, P., and Andersen, T.O. (2018). Pedersen, N, H., Johansen, P., and Andersen, T.O. Challenges with respect to control of digital displacement hydraulic units. Modeling, Identification and Control, Vol 39, 2018. doi:10.4173/mic.2018.2.4

[16] Pedersen, N.H., Johansen, P., and Andersen, T.O. (2018). Pedersen, N, H., Johansen, P., and Andersen, T.O. Optimal control of a wind turbine with digital fluid power transmission. Nonlinear Dynamics, 2018. doi:10.1007/s11071-017-3896-0

[17] Rampen, W. (2010). Rampen, W, The development of digital displacement technology. In Proceedings of Bath/ASME FPMC Symposium. .

[18] Roemer, D.B. (2014). Roemer, D, B. Design and Optimization of Fast Switching Valves for Large Scale Digital Hydraulic Motors. Ph.D. thesis. Department of Energy Technology, Aalborg University. .

[19] Sniegucki, M., Gottfried, M., and Klingauf, U. (2013). Sniegucki, M, , Gottfried, M., and Klingauf, U. Optimal control of digital hydraulic drives using mixed-integer quadratic programming. 9th IFAC Symposium on Nonlinear Control System, Toulouse, 2013. doi:10.3182/20130904-3-FR-2041.00013

[20] Song, X. (2008). Song, X, Modeling an active vehicle suspension system with application of digital displacement pump motor. Proceedings of the ASME 2008 International Design Engineering Techical Conference/Computers and Information in Enegineering Conference, Brooklyn, New York. doi:10.1115/DETC2008-49035

[21] Stephens, M.A., Manzie, C., and Good, M.C. (2013). Stephens, M, A., Manzie, C., and Good, M.C. Model predictive control for reference tracking on an industrial machine tool servo drive. IEEE Transactions on Industrial Informatics, Vol. 9. doi:10.1109/TII.2012.2223222

[22] Wilfong, G., Batdorff, M., and Lumkes, J. (2010). Wilfong, G, , Batdorff, M., and Lumkes, J. Design and dynamic analysis of high speed on/off poppet valves for digital pump/motors. In Proceedings of the 6th FPNI-PhD Symposium. .

[23] Wilfong, G., Holland, M., and Lumkes, J. (2011). Wilfong, G, , Holland, M., and Lumkes, J. Design and analysis of pilot operated high speed on/off valves for digital pump/motors. In Proceedings of the 52nd National Conference on Fluid Power, 2011. .

**BibTeX:**

@article{MIC-2018-3-3,

title={{Model Predictive Control of Low-Speed Partial Stroke Operated Digital Displacement Pump Unit}},

author={Pedersen, Niels Henrik and Johansen, Per and Hansen, Anders Hedegaard and Andersen, Torben Ole},

journal={Modeling, Identification and Control},

volume={39},

number={3},

pages={167--177},

year={2018},

doi={10.4173/mic.2018.3.3},

publisher={Norwegian Society of Automatic Control}

};