State-feedback control with a full-state estimator for a cart-inverted pendulum system

  • Abstract
  • Keywords
  • References
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  • Abstract

    A Cart Inverted Pendulum System is an unstable, nonlinear and underactuated system. This makes a cart inverted pendulum system used as a benchmark for testing many control method. A cart must occupy the desired position and the angle of the pendulum must be in an equilibrium point. System modeling of a cart inverted pendulum is important for controlling this system, but modeling using assumptions from state-feedback control is not completely valid. To minimize unmeasured state variables, state estimators need to be designed. In this paper, the state estimator is designed to complete the state-feedback control to control the cart inverted pendulum system. The mathematical model of the cart inverted pendulum system is obtained by using the Lagrange equation which is then changed in the state space form. Mathematical models of motors and mechanical transmissions are also included in the cart inverted pendulum system modeling so that it can reduce errors in a real-time application. The state gain control parameter is obtained by selecting the weighting matrix in the Linear Quadratic Regulator (LQR) method, then added with the Leuenberger observer gain that obtained by the pole placement method on the state estimator. Simulation is done to determine the system performance. The simulation results show that the proposed method can stabilize the cart inverted pendulum system on the cart position and the desired pendulum angle.


  • Keywords

    Cart Inverted Pendulum; Lagrange Equation; LQR; State Estimator; State-Feedback Control

  • References

      [1] I. Siradjuddin, Z. Amalia, B. Setiawan, F. Ronilaya, E. Rohadi, A. Setiawan, S. Adhisuwignjo, ”Stabilising a cart inverted pendulum with an augmented PID control scheme,” In MATEC Web of Conferences, EDP Sciences, 2018, Vol. 197, p. 11013.

      [2] I. Siradjuddin, B. Setiawan, A. Fahmi, Z. Amalia, E. Rohadi, ”State space control using LQR method for a cart-inverted pendulum linearised model,” International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS, 2017, Vol:17, No:01

      [3] I. Siradjuddin, Z. Amalia, B. Setiawan, R. P. Wicaksono and E. Yudaningtyas, ”Stabilising a cart inverted pendulum system using pole placement control method,” 2017 15th International Conference on Quality in Research (QiR) : International Symposium on Electrical and Computer Engineering, Nusa Dua, 2017, pp. 197-203.

      [4] Zhenkai Guo, Jianqin Mao and Ping Wang, ”An Approach of Adaptive Fuzzy Modeling and Application to Inverted Pendulum Control,” 2006 6th World Congress on Intelligent Control and Automation, Dalian, 2006, pp. 1594-1598.

      [5] L. Ye, ”Secondary Pendulum Control System Based on Genetic Algorithm and Neural Network,” 2006 Chinese Control Conference, Harbin, 2006, pp. 1152-1155.

      [6] E. S. Sazonov, P. Klinkhachorn and R. L. Klein, ”Hybrid LQG-neural controller for inverted pendulum system,” Proceedings of the 35th Southeastern Symposium on System Theory, Morgantown, WV, USA, 2003, pp. 206-210.

      [7] Y. Kado, Y. Pan and K. Furuta, ”Control System for Skill Acquisition- Balancing Pendulum based on Human Adaptive Mechatronics-,” 2006 IEEE International Conference on Systems, Man and Cybernetics, Taipei, 2006, pp. 4040-4045.

      [8] I. Park, J. Kim and J. Oh, ”Online Biped Walking Pattern Generation for Humanoid Robot KHR-3(KAIST Humanoid Robot - 3: HUBO),” 2006 6th IEEE-RAS International Conference on Humanoid Robots, Genova, 2006, pp. 398-403.

      [9] B. A. Sharif and A. Ucar, ”State feedback and LQR controllers for an inverted pendulum system,” 2013 The International Conference on Technological Advances in Electrical, Electronics and Computer Engineering (TAEECE), Konya, 2013, pp. 298-303.

      [10] Z. Jie and R. Sijing, ”Sliding mode control of inverted pendulum based on state observer,” 2016 Sixth International Conference on Information Science and Technology (ICIST), Dalian, 2016, pp. 322-326. doi:10.1109/ICIST.2016.7483432

      [11] C. Mahapatra and S. Chauhan, ”Tracking control of inverted pendulum on a cart with disturbance using pole placement and LQR,” 2017 International Conference on Emerging Trends in Computing and Communication Technologies (ICETCCT), Dehradun, 2017, pp. 1-6.




Article ID: 26985
DOI: 10.14419/ijet.v7i4.44.26985

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