Further Result on Fast Search Method for NMPCs by Mixed Objective-Physical Nondimensionalizations for Mechatonic Systems

Authors

Satoru Sakai, Takumu Takagi, Kohei Sawada, Tomoya Yokogawa, Ryo Arai

Abstract

Many nonlinear model predictive controls (NMPCs) are suffering from the computational cost as well as the stability for mechatonic systems in several situations. The paper proposes a simple but general fast search method of design parameters for stable NMPCs. The computational cost is reduced, that is, each closed-loop simulation runs faster and the number of the (stable or unstable) closed-loop simulations is decreased. First, we introduce dimensions (SI units) for the objective function which is usually dimensionless unlike the physical dynamics and constraints. Second, we propose a fast search method by mixing a nondimensionalization for the objective function and another nondimensionalization for the physical dynamics and constraints. Finally, the effectiveness of the proposed method is confirmed by a numerical experiment via an actual hydraulic cylinder. Almost 20% reduction of the computational cost is achieved to find good design parameters for the stable NMPCs. Remarkably, the proposed method is generally applicable to many NMPCs and is not restricted to a specific one.

Keywords

nondimensionalization; nonlinear model predictive control; port-Hamiltonian modeling

Citation

• Journal: IFAC-PapersOnLine
• Year: 2023
• Volume: 56
• Issue: 2
• Pages: 7529–7535
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2023.10.652
• Note: 22nd IFAC World Congress- Yokohama, Japan, July 9-14, 2023

BibTeX

@article{Sakai_2023,
  title={{Further Result on Fast Search Method for NMPCs by Mixed Objective-Physical Nondimensionalizations for Mechatonic Systems}},
  volume={56},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2023.10.652},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Sakai, Satoru and Takagi, Takumu and Sawada, Kohei and Yokogawa, Tomoya and Arai, Ryo},
  year={2023},
  pages={7529--7535}
}

Download the bib file

References

• Using a scale testbed: Controller design and evaluation. IEEE Control Systems vol. 21 15–26 (2001) – 10.1109/37.924794
• Siano, D. B. Orientational analysis, tensor analysis and the group properties of the SI supplementary units—II. Journal of the Franklin Institute vol. 320 285–302 (1985) – 10.1016/0016-0032(85)90032-8
• Buckingham, On physically similar systems. Physics review (1931)
• Curtis, W. D., Logan, J. D. & Parker, W. A. Dimensional analysis and the pi theorem. Linear Algebra and its Applications vol. 47 117–126 (1982) – 10.1016/0024-3795(82)90229-4
• Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters vol. 42 217–227 (2001) – 10.1016/s0167-6911(00)00091-8
• Ghanekar, M., Wang, D. W. L. & Heppler, G. R. Scaling laws for linear controllers of flexible link manipulators characterized by nondimensional groups. IEEE Transactions on Robotics and Automation vol. 13 117–127 (1997) – 10.1109/70.554352
• Grabmair, Energy-based nonlinear control of hydraulically actuated mechanical systems. (2005)
• Hailu, Use of dimensional analysis to reduce the parametric space for gain-scheduling. (2005)
• Heybroek, K. & Sjoberg, J. Model Predictive Control of a Hydraulic Multichamber Actuator: A Feasibility Study. IEEE/ASME Transactions on Mechatronics vol. 23 1393–1403 (2018) – 10.1109/tmech.2018.2823695
• Huang, J. et al. Model Predictive Trajectory Tracking Control of Electro-Hydraulic Actuator in Legged Robot With Multi-Scale Online Estimator. IEEE Access vol. 8 95918–95933 (2020) – 10.1109/access.2020.2995701
• Kugi, A. & Kemmetmüller, W. New Energy-based Nonlinear Controller for Hydraulic Piston Actuators. European Journal of Control vol. 10 163–173 (2004) – 10.3166/ejc.10.163-173
• Mattila, J., Koivumaki, J., Caldwell, D. G. & Semini, C. A Survey on Control of Hydraulic Robotic Manipulators With Projection to Future Trends. IEEE/ASME Transactions on Mechatronics vol. 22 669–680 (2017) – 10.1109/tmech.2017.2668604
• Morari, M. & H. Lee, J. Model predictive control: past, present and future. Computers & Chemical Engineering vol. 23 667–682 (1999) – 10.1016/s0098-1354(98)00301-9
• Nezu, (1993)
• Ohtsuka, A continuation/GMRES method for fast computation of nonlinear receding horizon control. Auto-matica (2004)
• Sakai, Fast computation by simplification of a class of hydro-mechanical system. (2012)
• Sakai, Casimir based fast computation for hydraulic robot optimizations. (2013)
• Sakai, A new method for parameter identification for n-dof hydraulic robots. (2014)
• Sakai, S., Osuka, K., Maekawa, T. & Umeda, M. Robust Control Systems of a Heavy Material Handling Agricultural Robot: A Case Study for Initial Cost Problem. IEEE Transactions on Control Systems Technology vol. 15 1038–1048 (2007) – 10.1109/tcst.2007.899710
• Sakai, Fast search method for stable nmpc by objective nondimensionalizations of mechatonic systems. (2022)
• Sakai, S. & Stramigioli, S. Visualization of Hydraulic Cylinder Dynamics by a Structure Preserving Nondimensionalization. IEEE/ASME Transactions on Mechatronics vol. 23 2196–2206 (2018) – 10.1109/tmech.2018.2854751
• Summers, S., Jones, C. N., Lygeros, J. & Morari, M. A Multiresolution Approximation Method for Fast Explicit Model Predictive Control. IEEE Transactions on Automatic Control vol. 56 2530–2541 (2011) – 10.1109/tac.2011.2146990
• van der Schaft, Port-Hamiltonian systems: an introductory survery. (2006)
• Wang, Y. & Boyd, S. Fast Model Predictive Control Using Online Optimization. IEEE Transactions on Control Systems Technology vol. 18 267–278 (2010) – 10.1109/tcst.2009.2017934
• Zohuri, (2015)