|
|
基于模糊控制的多体系统动力学约束违约稳定方法
|
Abstract:
提出了一种基于模糊逻辑控制的多体动力学约束违约稳定方法。该方法以位置约束方程及其导数的误差作为模糊输入，通过模糊推理机制计算反馈输出，精准控制多体系统的约束违约。与传统方法不同，该方法不受积分算法选择、时间步长设置等因素的限制，在长时间实时仿真场景中展现出良好的适应性与稳定性。通过平面三摆和曲柄滑块两个典型仿真算例，有效验证了该方法在约束违约控制中的可靠性与有效性，为多体系统动力学仿真提供了新的技术路径。
A constraint violation stabilization method of multibody system dynamics is presented using fuzzy logic control. The method uses the errors of position constraint equations and their derivatives as fuzzy inputs, and calculates feedback outputs through a fuzzy inference mechanism to accurately control constraint violations in multibody systems. Unlike traditional methods, this approach is not limited by factors, such as the choice of integration algorithm or the setting of time steps, demonstrating good adaptability and stability in long-term real-time simulation scenarios. The reliability and effectiveness of the proposed method in constraint violation control are validated through two typical simulation cases: a planar triple pendulum and a crank-slider mechanism, providing a new technical pathway for multibody system dynamics simulation.
| [1] | Marques, F., Souto, A.P. and Flores, P. (2017) On the Constraints Violation in Forward Dynamics of Multibody Systems. Multibody System Dynamics, 39, 385-419. https://doi.org/10.1007/s11044-016-9530-y |
| [2] | Wehage, R.A. and Haug, E.J. (1982) Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems. Journal of Mechanical Design, 104, 247-255. https://doi.org/10.1115/1.3256318 |
| [3] | Wehage, K.T., Wehage, R.A. and Ravani, B. (2015) Generalized Coordinate Partitioning for Complex Mechanisms Based on Kinematic Substructuring. Mechanism and Machine Theory, 92, 464-483. https://doi.org/10.1016/j.mechmachtheory.2015.06.006 |
| [4] | Zahariev, E. and McPhee, J. (2003) Stabilization of Constraints of Multibody System Dynamics. Mechanics Based Design of Structures and Machines, 31, 25-55. https://doi.org/10.1081/sme-120017108 |
| [5] | Zahariev, E. and Mcphee, J. (2003) Stabilization of Multiple Constraints in Multibody Dynamics Using Optimization and a Pseudo-Inverse Matrix. Mathematical and Computer Modelling of Dynamical Systems, 9, 417-435. https://doi.org/10.1076/mcmd.9.4.417.27898 |
| [6] | Baumgarte, J. (1972) Stabilization of Constraints and Integrals of Motion in Dynamical Systems. Computer Methods in Applied Mechanics and Engineering, 1, 1-16. https://doi.org/10.1016/0045-7825(72)90018-7 |
| [7] | Müller, A. (2012) Motion Equations in Redundant Coordinates with Application to Inverse Dynamics of Constrained Mechanical Systems. Nonlinear Dynamics, 67, 2527-2541. https://doi.org/10.1007/s11071-011-0165-5 |
| [8] | Nikravesh, P.E. (1987) Computer Aided Analysis of Mechanical Systems. N J Prentice-Hall. |
| [9] | Nada, A. and Bayoumi, M. (2024) Development of a Constraint Stabilization Method of Multibody Systems Based on Fuzzy Logic Control. Multibody System Dynamics, 61, 233-265. https://doi.org/10.1007/s11044-023-09921-9 |
| [10] | Zhao, W.J., Pan, Z.K. and Wang, Y.B. (2000) An Automatic Constraint Violation Stabilization Method for Differential/Algebraic Equations of Motion in Multibody System Dynamics. Applied Mathematics and Mechanics, 21, 103-108. https://doi.org/10.1007/bf02458546 |
| [11] | Lin, S. and Huang, J. (2002) Stabilization of Baumgarte’s Method Using the Runge-Kutta Approach. Journal of Mechanical Design, 124, 633-641. https://doi.org/10.1115/1.1519277 |
| [12] | Lin, S. and Chen, M. (2011) A PID Type Constraint Stabilization Method for Numerical Integration of Multibody Systems. Journal of Computational and Nonlinear Dynamics, 6, Article 044501. https://doi.org/10.1115/1.4002688 |
| [13] | Guizhi, L. and Rong, L. (2018) Determination of Stability Correction Parameters for Dynamic Equations of Constrained Multibody Systems. Mathematical Problems in Engineering, 2018, Article 8945301. https://doi.org/10.1155/2018/8945301 |
| [14] | Flores, P. and Seabra, E. (2009) Influence of the Baumgarte Parameters on the Dynamics Response of Multibody Mechanical Systems. Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications and Algorithms, 16, 415-432. |
| [15] | 刘杰, 李允公, 刘宇, 等. 智能控制与MATLAB实用技术[M]. 北京: 科学出版社, 2017. |
| [16] | Siddique, N.H. and Adeli, H. (2013) Computational Intelligence: Synergies of Fuzzy Logic, Neural Networks, and Evolutionary Computing. Wiley. https://doi.org/10.1002/9781118534823 |
