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A LQR Neural Network Control Approach for Fast Stabilizing Rotary Inverted Pendulums

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Abstract

Rotary inverted pendulum (RIP) is a well-known system that is commonly employed as an ideal benchmarking model for verifying linear and nonlinear control algorithms thanks to unique unstable and highly nonlinear natures. In this paper, an intelligent control method is developed for stabilizing such the RIP system in upright posture. The controller is structured from a linear quadratic regulator (LQR) and an online radial basis function (RBF) Neural-Network compensator. The LQR term plays a crucial role in yielding the nominal control signal based on a linearized model. Meanwhile, the neural control term is adopted to suppress the systematic deviation and external disturbances as the system is far from the equilibrium state. A damping segment-wise adaptation rule is proposed to activate the network operation. Stability of the closed-loop system is then proven by Lyapunov analyses. Effectiveness and feasibility of the advanced controller are confirmed throughout comparative simulation and real-time experiments.

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References

  1. Hartman, E. J., Keeler, J. D., & Kowalski, J. M. (1990). Layered neural networks with Gaussian hidden units as universal approximations. Neural Computation, 2(2), 210–215.

    Article  Google Scholar 

  2. Ge, S. S., Hang, C. C., & Zhang, T. (1999). Adaptive neural network control of nonlinear systems by state and output feedback. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), 29(6), 818–828.

    Article  Google Scholar 

  3. Ge, S. S., Hang, C. C., & Woon, L. C. (1997). Adaptive neural network control of robot manipulators in task space. IEEE Transactions on Industrial Electronics, 44(6), 746–752.

    Article  Google Scholar 

  4. Herwan, J., Kano, S., Ryabov, O., Sawada, H., & Misaka, N. K. T. (2021). Predicting surface roughness of dry cut grey cast iron based on cutting parameters and vibration signals from different sensor positions in CNC turning. International Journal of Automation Technology, 14(2), 217–228.

    Article  Google Scholar 

  5. Kato, D., Yoshitsugu, K., Hirogaki, T., Aoyama, E., & Takahashi, K. (2021). redicting positioning error and finding features for large industrial robots based on deep learning. International Journal of Automation Technology, 15(2), 206–214.

    Article  Google Scholar 

  6. Astrom, K. J., & Furuta, K. (2000). Swinging up a pendulum by energy control. Automatica, 36(2), 287–295.

    Article  MathSciNet  MATH  Google Scholar 

  7. Silik, Y., & Yaman, U. (2020). Control of rotary inverted pendulum by using on-off type of cold gas thrusters. Actuators, 9(4), 95.

    Article  Google Scholar 

  8. Zhang, L., & Dixon, R. (2021). Robust non-minimal state feedback control for a Furuta pendulum with parametric modelling errors. IEEE Transactions on Industrial Electronics, 68(8), 7341–7349.

    Article  Google Scholar 

  9. Elsayed, B. A., Hassan, M. A., & Mekhilef, S. (2014). Fuzzy swinging-up with sliding mode control for third order cart-inverted pendulum system. International Journal of Control, Automation and Systems, 13(1), 238–248.

    Article  Google Scholar 

  10. Saleem, O., & Mahmood-Ul-Hasan, K. (2020). Indirect adaptive state-feedback control of rotary inverted pendulum using self-mutating hyperbolic-functions for online cost variation. IEEE Access, 8, 91236–91247.

    Article  Google Scholar 

  11. Wadi, A., Lee, J. H., & Romdhane, L. (2018). Nonlinear sliding mode control of the Furuta pendulum. In 11th international symposium on mechatronics and its applications (pp. 1–5).

  12. Galan, D., Chaos, D., de la Torre, L., Aranda-Escolastico, E., & Heradio, R. (2019). Customized online laboratory experiments: a general tool and its application to the furuta inverted pendulum [focus on education]. IEEE Control Systems Magazine, 39(5), 75–87.

    Article  Google Scholar 

  13. Park, J., & Sandberg, L. W. (1990). Universal approximation using radial-basis-function networks. Neural Computation, 3(2), 246–257.

    Article  Google Scholar 

  14. Ba, D. X. (2020). A flexible sliding mode controller for robot manipulators using a new type of neural-network predictor.

  15. Kharola, A., Tatil, P., Raiwani, S., & Rajput, D. (2016). A comparison study for control and stabilization of inverted pendulum on inclined surface (IPIS) using PID and fuzzy controller. Perspectives on Science, 8, 187–190.

    Article  Google Scholar 

  16. Chen, C. K., Lin, C. J., & Yao, L. C. (2008). Input-state linearization of a rotary inverted pendulum. Asian Journal of Control, 6(1), 130–135.

    Article  Google Scholar 

  17. Nguyen, N. P., Oh, H., Kim, Y., & Moon, J. (2021). A nonlinear hybrid controller for swinging-up and stabilizing the rotary inverted pendulum. Nonlinear Dynamics, 104, 1117–1137.

    Article  Google Scholar 

  18. Huang, J., Zhang, T., Fan, Y., & Sun, J. Q. (2019). Control of rotary inverted pendulum using model-free backstepping technique. IEEE Access, 7, 96965–96973.

    Article  Google Scholar 

  19. Nurcahyadi, T., & Blum, C. (2021). Adding negative learning to ant colony optimization: a comprehensive study. Mathematics, 9(4), 361.

    Article  Google Scholar 

  20. Hazem, Z. B., Fotuhi, M. J., & Bingül, Z. (2020). Development of a Fuzzy-LQR and Fuzzy-LQG stability control for a double link rotary inverted pendulum. Journal of the Franklin Institute, 357(15), 10529–10556.

    Article  MathSciNet  MATH  Google Scholar 

  21. Prasad, L. B., Tyagi, B., & Gupta, H. O. (2014). Optimal control of nonlinear inverted pendulum system using PID controller and LQR: Performance analysis without and with disturbance input. International Journal of Automation and Computing, 11, 661–670.

    Article  Google Scholar 

  22. Kim, J.-B., Lim, H.-K., Kim, C.-M., Kim, M.-S., Hong, Y.-G., & Han, Y.-H. (2020). Imitation reinforcement learning-based remote rotary inverted pendulum control in openflow network. IEEE Access, 7, 36682–36690.

    Article  Google Scholar 

  23. Mendeza, E., et al. (2020). ANN Based MRAC-PID controller implementation for a furuta pendulum system stabilization. Advances in Science, Technology and Engineering Systems Journal, 5(5), 324–333.

    Article  Google Scholar 

  24. Thanh, T. D. C., & Ahn, K. K. (2006). Nonlinear PID control to improve the control performance of 2 axes pneumatic artificial muscle manipulator using neural network. Mechatronics, 19(9), 577–587.

    Article  Google Scholar 

  25. Mehedi, I. M., Ansari, U., Bajodah, A. H., AL-Saggaf, U. M., Kada, B., & Rawa, M. J. (2020). Underactuated rotary inverted pendulum control using robust generalized dynamic inversion. Journal of Vibration and Control, 26(23), 2210–2220.

    Article  MathSciNet  Google Scholar 

  26. Jouila, A., & Nouri, K. (2020). An adaptive robust nonsingular fast terminal sliding mode controller based on wavelet neural network for a 2-DOF robotic arm. Journal of the Franklin Institute, 357(18), 13259–13282.

    Article  MathSciNet  MATH  Google Scholar 

  27. Sarkar, T. T., & Dewan, L. (2017). Application of LQR and MRAC for swing up control of inverted pendulum. In 4th international conference on power, control & embedded systems (ICPCES) (pp. 1–6).

  28. Karami, M., Tavakolpour-Saleh, A. R., & Norouzi, A. (2020). Optimal nonlinear PID control of a micro-robot equipped with vibratory actuator using ant colony algorithm: simulation and experiment. Journal of Intelligent and Robotic Systems, 99, 773–796.

    Article  Google Scholar 

  29. Susanto, E., Wibowo, A. S., & Rachman, E. G. (2020). Fuzzy swing up control and optimal state feedback stabilization for self-erecting inverted pendulum. IEEE Access, 8, 6496–6504.

    Article  Google Scholar 

  30. Ba, D. X., Ahn, K. K., & Tai, N. T. (2014). Adaptive Integral-type neural sliding mode control for pneumatic muscle actuator. International Journal of Automation Technology, 8(6), 888–895.

    Article  Google Scholar 

  31. Ahmmed, T., Akhter, I., Karim, S. M. R., & Ahamed, F. A. S. (2020). Genetic Algorithm based PID parameter optimization. American Journal of Intelligent Systems, 10(1), 8–13.

    Article  Google Scholar 

  32. Jayachitra, A., & Vinodha, R. (2014). Genetic algorithm based PID controller tuning approach for continuous stirred tank reactor. Advances in Artificial Intelligence, 2014, 1–8.

    Article  Google Scholar 

  33. Park, J.-Y., & Han, S.-Y. (2013). Swarm intelligence topology optimization based on artificial bee colony algorithm. International Journal of Precision Engineering and Manufacturing, 14, 115–121.

    Article  Google Scholar 

  34. Guo, C., Tang, H., Niu, B., & Lee, C. B. P. (2021). A survey of bacterial foraging optimization. Neurocomputing, 452(10), 728–746.

    Article  Google Scholar 

  35. Gautam, P. (2016). Optimal control of inverted pendulum system using adaline artificial neural network with LQR.

  36. Zabihifar, S. H., Yushchenko, A. S., & Navvabi, H. (2020). Robust control based on adaptive neural network for Rotary inverted pendulum with oscillation compensation. Neural Computing and Applications, 32, 1–13.

    Article  Google Scholar 

  37. Hfaiedh, A.,, Chemori, A., & Abdelkrim, A. (2020). Disturbance observer-based super-twisting control for the inertia wheel inverted pendulum.

  38. Vu, V.-P., Nguyen, M.-T., Nguyen, A.-V., Tran, V.-D., & Nguyen, T.-M.-N. (2021). Disturbance observer-based controller for inverted pendulum with uncertainties: Linear matrix inequality approach. International Journal of Electrical and Computer Engineering, 11(6), 4907–4921.

    Google Scholar 

  39. Yang, X., & Zheng, X. (2018). Swing-up and stabilization control design for an underactuated rotary inverted pendulum system: Theory and experiments. IEEE Transactions on Industrial Electronics, 65(9), 7229–7238.

    Article  Google Scholar 

  40. Arnaldo De Carvalho, J., Justo, J. F., Angelico, B. A., De Oliveira, A. M., & Filho, J. I. D. S. (2021). Rotary inverted pendulum identification for control by paraconsistent neural network. IEEE Access, 9, 74155–74167.

    Article  Google Scholar 

  41. Han, C., Bin Kim, K., Lee, S. W., Jun, M. B.-G., & Jeong, Y. H. (2021). Thrust force-based tool wear estimation using discrete wavelet transformation and artificial neural network in CFRP drilling. International Journal of Precision Engineering and Manufacturing. doi: https://doi.org/10.1007/s12541-021-00558-2

  42. Jung, S., & Kim, S. S. (2007). Hardware implementation of a real-time neural network controller with a DSP and an FPGA for nonlinear systems. IEEE Transactions on Industrial Electronics, 54(1), 265–271.

    Article  Google Scholar 

  43. Jung, S., & Kim, S. S. (2008). Control experiment of a wheel-driven mobile inverted pendulum using neural network. IEEE Transactions on Automatic Control, 16(2), 297–303.

    MathSciNet  Google Scholar 

  44. Moreno-Valenzuela, J., Aguilar-Avelar, C., Puga-Guzmán, S. A., & Santibáñez, V. (2016). Adaptive neural network control for the trajectory tracking of the furuta pendulum. IEEE Transactions on Cybernetics, 46(12), 3439–3452.

    Article  Google Scholar 

  45. Nghi, H. V., Nhien, D. P., Nguyet, N. T. M., Duc, N. T., Luu, N. P., Thanh, P. S., Lam, L. T. H., & Ba, D. X. (2021). A LQR-based neural-network controller for fast stabilizing rotary inverted pendulum. In 2021 International conference on system science and engineering (ICSSE) (pp. 19–22).

  46. Craig, J. J. (2005). Introduction to robotics: Mechanics and control (3rd ed.). Pearson Prentice Hall.

    Google Scholar 

  47. Harris, D. M., & Harris, S. L. (2007). Digital design and computer architecture (1st ed.). Morgan Kaufmann.

    Google Scholar 

  48. Apolloni, B., Ghosh, A., Alpaslan, F., & Patnaik, S. (2011). Machine learning and robot perception. Springer-Verlag.

  49. Li, S., Huo, C., Liu, Y. (2008). Inverted pendulum system control by using modified PID neural network.

  50. Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323, 533–536.

    Article  MATH  Google Scholar 

  51. Ba, D. X., Dinh, T. Q., & Ahn, K. K. (2016). An integrated intelligent nonlinear control method for pneumatic artificial muscle. IEEE/ASME Transaction in Mechatronics, 21(4), 1835–1845.

    Article  Google Scholar 

  52. Chen, M., & Ge, S. S. (2015). Adaptive neural output feedback control of uncertain nonlinear systems with unknown hysteresis using disturbance observer. IEEE Transactions on Industrial Electronics, 62(12), 7706–7716.

    Article  MathSciNet  Google Scholar 

  53. Hinton, G., Deng, L., Yu, D., Dahl, G., Mohamed, A., Jaitly, N., Senior, A., Vanhoucke, V., Nguyen, P., Sainath, T., & Kingsbury, B. (2012). Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups. IEEE Signal Processing Magazine, 29(6), 82–97.

    Article  Google Scholar 

  54. LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521, 436–444.

    Article  Google Scholar 

  55. Sun, W., Wu, Y., & Lv, X. (2021). Adaptive neural network control for full-state constrained robotic manipulator with actuator saturation and time-varying delays. IEEE Transactions on Neural Networks and Learning Systems .

  56. He, W., Sun, Y., Yan, Z., Yang, C., Li, Z., & Kaynak, O. (2020). Disturbance observer-based neural network control of cooperative multiple manipulators with input saturation. IEEE Transactions on Neural Networks and Learning Systems, 31(5), 1735–1746.

    Article  MathSciNet  Google Scholar 

  57. Yaskawa. (2014). YASKAWA Minertia motor—F series. In A breakthrough in office automation: Yaskawa’s DC servromotors with encoders.

  58. Thegioiic. (2021). HI216 600W 15A H-bridge.

  59. STMicroelectronics. (2020). Datasheet of STM32F4 series. DS8626 Rev 9. https://www.st.com/resource/en/datasheet/dm00037051.pdf.

  60. L. Aimagin Co. (2021). Waijung blockset. https://waijung1.aimagin.com/?fbclid=IwAR24kEDGkGf.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.01-2020.10.

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Vietnam National Foundation for Science and Technology Development (NAFOSTED), 107.01–2020.10,Dang Xuan Ba.

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  1. Ho Chi Minh City University of Technology and Education (HCMUTE), Ho Chi Minh City, Vietnam

    Huynh Vinh Nghi, Dinh Phuoc Nhien & Dang Xuan Ba

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  1. Huynh Vinh Nghi
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  2. Dinh Phuoc Nhien
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Nghi, H.V., Nhien, D.P. & Ba, D.X. A LQR Neural Network Control Approach for Fast Stabilizing Rotary Inverted Pendulums. Int. J. Precis. Eng. Manuf. 23, 45–56 (2022). https://doi.org/10.1007/s12541-021-00606-x

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