Research Paper:
Multi Strategy SA-PSO for Inverted Pendulum Identification Combined with Explicit Model Predictive Control
Zixu Li, Jingyuan Li, Yuhui Huang, Yiran Li, and Bin Xin
Beijing Institute of Technology
No.5 Zhongguancun South Street, Haidian District, Beijing 100081, China
In this paper, the inverted pendulum is controlled by Quanser universal benchtop equipment-direct current (QUBE DC) motor, and the motor inverted pendulum system is identified when the sinusoidal signal is input. However, there is a large error when the angle of the pendulum is pre-identified by numerical algorithms for subspace state space system identification algorithm. Therefore, this paper designs a multi strategy optimization simulated annealing particle swarm optimization algorithm, which can accurately identify the complex system with sinusoidal input signal. In the identification experiments of sinusoidal signals with multiple frequencies and amplitudes, this paper found that the algorithm performs relatively best at a frequency of 8 rad/s. Moreover, at a frequency of 8 rad/s, the algorithm can quickly reduce the error to 1.69% within 100 generations. Finally, based on the hardware model identified by particle swarm optimization, this paper designs an explicit model predictive control method to control the inverted pendulum, and tests the constraint processing and anti-disturbance performance of the system under the voltage pulse interference with different duty cycles, which realizes the inverted pendulum balance and has robustness under the interference.
- [1] J.-J. Wang, “Simulation studies of inverted pendulum based on PID controllers,” Simulation Modelling Practice and Theory, Vol.19, Issue 1, pp. 440-449, 2011. https://doi.org/10.1016/j.simpat.2010.08.003
- [2] B. Ninness, “Some system identification challenges and approaches,” IFAC Proc. Volumes, Vol.42, Issue 10, pp. 1-20, 2009. https://doi.org/10.3182/20090706-3-FR-2004.00001
- [3] B. L. Ho, “Effective construction of linear state-variable models from input/output functions,” Regelungstechnik, Vol.14, No.12, pp. 545-548, 1966.
- [4] K.-J. Åström and B. Torsten, “Numerical identification of linear dynamic systems from normal operating records,” IFAC Proc. Volumes, Vol.2, Issue 2, pp. 96-111, 1965. https://doi.org/10.1016/S1474-6670(17)69024-4
- [5] L. Ljung, “System identification,” A. Procházka, J. Uhlíř, P. W. J. Rayner, and N. G. Kingsbury (Eds.), “Signal analysis and prediction,” pp. 163-173, Springer, 1998. https://doi.org/10.1007/978-1-4612-1768-8
- [6] A. K. Tangirala, “Principles of system identification: Theory and practice,” CRC Press, 2018. https://doi.org/10.1201/9781315222509
- [7] M. Viberg, “Subspace-based methods for the identification of linear time-invariant systems,” Automatica, Vol.31, Issue 12, pp. 1835-1851, 1995. https://doi.org/10.1016/0005-1098(95)00107-5
- [8] T. Katayama, “Subspace methods for system identification,” Springer, 2005. https://doi.org/10.1007/1-84628-158-X
- [9] M. Verhaegen and V. Verdult, “Filtering and system identification: A least squares approach,” Cambridge University Press, 2007. https://doi.org/10.1017/CBO9780511618888
- [10] P. van Overschee and B. De Moor, “Subspace Identification for Linear Systems: Theory–Implementation–Applications,” Springer Science & Business Media, 2012. https://doi.org/10.1007/978-1-4613-0465-4
- [11] J. Kennedy and R. Eberhart, “Particle swarm optimization,” Proc. of Int. Conf. on Neural Networks (ICNN’95), Vol.4, pp. 1942-1948, 1995. https://doi.org/10.1109/ICNN.1995.488968
- [12] X. Xiang, R. Diao, S. Bernadin, S. Y. Foo, F. Sun, and A. S. Ogundana, “An Intelligent Parameter Identification Method of DFIG Systems Using Hybrid Particle Swarm Optimization and Reinforcement Learning,” IEEE Access, Vol.12, pp. 44080-44090, 2024. https://doi.org/10.1109/ACCESS.2024.3379146
- [13] P. Eswari, Y. Ramalakshmanna, and C. D. Prasad, “An Improved Particle Swarm Optimization-Based System Identification,” E. S. Gopi (Ed.), “Machine Learning, Deep Learning and Computational Intelligence for Wireless Communication,” Proc. of MDCWC 2020, pp. 137-142, Springer, 2021. https://doi.org/10.1007/978-981-16-0289-4_11
- [14] H. Issa and J. K. Tar, “Improvement of an Adaptive Robot Control by Particle Swarm Optimization-Based Model Identification,” Mathematics, Vol.10, Issue 19, Article No.3609, 2022. https://doi.org/10.3390/math10193609
- [15] M. Harati, A. A. Ghavifekr, and A. R. Ghiasi, “Model Identification of Single Rotary Inverted Pendulum Using Modified Practical Swarm Optimization Algorithm,” 2020 28th Iranian Conf. on Electrical Engineering (ICEE), 2020. https://doi.org/10.1109/ICEE50131.2020.9261035
- [16] S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, “Optimization by Simulated Annealing,” Science, Vol.220, No.4598, pp. 671-680, 1983. https://doi.org/10.1126/science.220.4598.671
- [17] C. E. Garcia, D. M. Prett, and M. Morari, “Model predictive control: Theory and practice—A survey,” Automatica, Vol.25, Issue 3, pp. 335-348, 1989. https://doi.org/10.1016/0005-1098(89)90002-2
- [18] S. J. Qin and T. A. Badgwell, “A survey of industrial model predictive control technology,” Control Engineering Practice, Vol.11, Issue 7, pp. 733-764, 2003. https://doi.org/10.1016/S0967-0661(02)00186-7
- [19] A. Bemporad and M. Morari, “Robust model predictive control: A survey,” A. Garulli and A. Tesi (Eds.), “Robustness in Identification and Control,” pp. 207-226, Springer, 2007. https://doi.org/10.1007/BFb0109870
- [20] J. Köhler, M. A. Müller, and F. Allgöwer, “Analysis and design of model predictive control frameworks for dynamic operation—An overview,” Annual Reviews in Control, Vol.57, Article No.100929, 2024. https://doi.org/10.1016/j.arcontrol.2023.100929
- [21] S. Yu, M. Hirche, Y. Huang, H. Chen, and F. Allgöwer, “Model predictive control for autonomous ground vehicles: A review,” Autonomous Intelligent Systems, Vol.1, Article No.4, 2021. https://doi.org/10.1007/s43684-021-00005-z
- [22] T. Gold, A. Völz, and K. Graichen, “Model Predictive Interaction Control for Industrial Robots,” IFAC-PapersOnLine, Vol.53, Issue 2, pp. 9891-9898, 2020. https://doi.org/10.1016/j.ifacol.2020.12.2696
- [23] F. Waheed, I. K. Yousufzai, and M. Valášek, “A TV-MPC Methodology for Uncertain Under-Actuated Systems: A Rotary Inverted Pendulum Case Study,” IEEE Access, Vol.11, pp. 103636-103649, 2023. https://doi.org/10.1109/ACCESS.2023.3318108
- [24] M. Askari, M. Moghavvemi, H. A. F. Almurib, and A. M. A. Haidar, “Stability of soft-constrained finite horizon model predictive control,” IEEE Trans. on Industry Applications, Vol.53, Issue 6, pp. 5883-5892, 2017. https://doi.org/10.1109/TIA.2017.2718978
- [25] A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, “The explicit linear quadratic regulator for constrained systems,” Automatica, Vol.38, Issue 1, pp. 3-20, 2002. https://doi.org/10.1016/S0005-1098(01)00174-1
- [26] J. Courts, A. G. Wills, T. B. Schön, and B. Ninness, “Variational system identification for nonlinear state-space models,” Automatica, Vol.147, Article No.110687, 2023. https://doi.org/10.1016/j.automatica.2022.110687
- [27] Y. Wang, W. Mao, Q. Wang, and B. Xin, “Fuzzy Cooperative Control for the Stabilization of the Rotating Inverted Pendulum System,” J. Adv. Comput. Intell. Intell. Inform., Vol.27, No.3, pp. 360-371, 2023. https://doi.org/10.20965/jaciii.2023.p0360
- [28] L. Fröhlich, “Data-Efficient Controller Tuning and Reinforcement Learning,” Ph.D. thesis, ETH Zürich, 2022. https://doi.org/10.3929/ethz-b-000545134
- [29] H. Xu, J. Zhang, H. Yang, and Y. Xia, “Extended State Functional Observer-Based Event-Driven Disturbance Rejection Control for Discrete-Time Systems,” IEEE Trans. on Cybernetics, Vol.52, Issue 7, pp. 6949-6958, 2021. https://doi.org/10.1109/TCYB.2020.3043385
- [30] J. Lofberg, “YALMIP: A toolbox for modeling and optimization in MATLAB,” 2004 IEEE Int. Conf. on Robotics and Automation, pp. 284-289, 2004. https://doi.org/10.1109/CACSD.2004.1393890
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