Arabian Journal for Science and Engineering

, Volume 44, Issue 8, pp 6757–6768 | Cite as

Optimal Nonlinear Model Reference Controller Design for Ball and Plate System

  • Hazem I. Ali
  • Haider M. JassimEmail author
  • Amjad F. Hasan
Research Article - Electrical Engineering


This paper presents a new design procedure of an optimal nonlinear controller using the model reference approach. The ball and plate system is used as nonlinear, uncertain, and MIMO system to verify the effectiveness of the proposed controller. The main goal of the proposed design is to assure a desirable performance despite the presence of the coupling among control loops and uncertainty. The invasive weed optimization (IWO) method, which is one of the metaheuristic optimization algorithms, is used to obtain the optimal parameters of the proposed controller. The feasibility and efficiency of the proposed nonlinear controller are illustrated experimentally using real ball and plate system.


Nonlinear control Optimal control Model reference Ball and plate IWO 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Liu, D.; Tian, Y.; Duan, H.: Ball and plate control system based on sliding mode control with uncertain items observe compensation. In: 2009 IEEE International Conference on Intelligent Computing and Intelligent Systems. ICIS 2009, Vol. 2, pp. 216-221. IEEE (2009)Google Scholar
  2. 2.
    Liu, H.; Liang, Y.: Trajectory tracking sliding mode control of ball and plate system. In: 2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR), vol. 3, pp. 142–145. IEEE (2010)Google Scholar
  3. 3.
    Awtar, S.; Bernard, C.; Boklund, N.; Master, A.; Ueda, D.; Craig, K.: Mechatronic design of a ball-on-plate balancing system. Mechatronics 12(2), 217–228 (2002)CrossRefGoogle Scholar
  4. 4.
    Zhao, B.Y.; Li, X. L.: On multiple model adaptive control strategy research of ball and plate system. In: Advanced Materials Research, vol. 898, pp. 501–505. Trans Tech Publ. (2014)Google Scholar
  5. 5.
    Han, K.; Tian, Y.; Kong, Y.; Li, J.; Zhang, Y.: Tracking control of ball and plate system using a improved PSO on-line training PID neural network. In: 2012 International Conference on Mechatronics and Automation (ICMA), pp. 2297–2302. IEEE (2012)Google Scholar
  6. 6.
    Das, A.; Roy, P.: Improved performance of cascaded fractional-order SMC over cascaded SMC for position control of a ball and plate system. IETE J. Res. 63(2), 238–247 (2017)CrossRefGoogle Scholar
  7. 7.
    Debono, D.; Bugeja, M.: Application of sliding mode control to the ball and plate problem. In: 2015 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO), vol. 1, pp. 412–419. IEEE (2015)Google Scholar
  8. 8.
    Yuan, D.; Zhang, Z.: Modelling and control scheme of the ball-plate trajectory-tracking pneumatic system with a touch screen and a rotary cylinder. IET Control Theory Appl. 4(4), 573–589 (2010)CrossRefGoogle Scholar
  9. 9.
    Aguilar-Ibanez, C.; Sira-Ramirez, H.; Suarez-Castanon, M.S.: A linear active disturbance rejection control for a ball and rigid triangle system. Math. Probl. Eng. 2016(5), 1–11 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Galvan-Colmenares, S.; Moreno-Armendáriz, M.A.; Rubio, JdJ; Ortíz-Rodriguez, F.; Yu, W.; Aguilar-Ibáñez, C.F.: Dual PD control regulation with nonlinear compensation for a ball and plate system. Math. Probl. Eng. 2014, 10 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Su, X.; Sun, Z.-S.; Zhao, S.-M.: Fuzzy control method for ball and plate system. Comput. Simul. 23(9), 165–167 (2006)Google Scholar
  12. 12.
    Bai, M.; Tian, Y.; Wang, Y.: Intelligence switching control of ball and plate system based on feedback linearization. In: 2011 30th Chinese Control Conference (CCC), pp. 688–693. IEEE (2011)Google Scholar
  13. 13.
    de Jesús Rubio, J.: Robust feedback linearization for nonlinear processes control. ISA Trans. 74, 155–164 (2018)CrossRefGoogle Scholar
  14. 14.
    Ming, B.; Yantao, T.; Yongxiang, W.: Decoupled fuzzy sliding mode control to ball and plate system. In: 2011 2nd International Conference on Intelligent Control and Information Processing (ICICIP), vol. 2, pp. 685–690. IEEE (2011)Google Scholar
  15. 15.
    Duan, H.; Han, K. W.; Zhang, Y.; Tian, Y.: Control for ball and plate system based on RBF-ADRC. In: 2012 International Conference on Mechatronics and Automation (ICMA), pp. 434–439. IEEE (2012)Google Scholar
  16. 16.
    Borah, M.; Roy, P.; Roy, B.K.: Enhanced performance in trajectory tracking of a ball and plate system using fractional order controller. IETE J. Res. 64(1), 76–86 (2018)CrossRefGoogle Scholar
  17. 17.
    Hussein, S.; Muhammed, B.; Sikiru, T.; Umoh, I.; Salawudeen, A.: Trajectory tracking control of ball on plate system using weighted Artificial Fish Swarm Algorithm based PID. In: 2017 IEEE 3rd International Conference on Electro-Technology for National Development (NIGERCON), pp. 554–561. IEEE (2017)Google Scholar
  18. 18.
    Fan, X.; Zhang, N.; Teng, S.: Trajectory planning and tracking of ball and plate system using hierarchical fuzzy control scheme. Fuzzy Sets Syst. 144(2), 297–312 (2004)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Knuplez, A.; Chowdhury, A.; Svecko, R.: Modeling and control design for the ball and plate system. In: 2003 IEEE International Conference on Industrial Technology, vol. 2, pp. 1064–1067. IEEE (2003)Google Scholar
  20. 20.
    Mehrabian, A.R.; Lucas, C.: A novel numerical optimization algorithm inspired from weed colonization. Ecol. Inform. 1(4), 355–366 (2006)CrossRefGoogle Scholar
  21. 21.
    Basak, A.; Pal, S.; Das, S.; Abraham, A.; Snasel, V.: A modified invasive weed optimization algorithm for time-modulated linear antenna array synthesis. In: 2010 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2010)Google Scholar
  22. 22.
    Mallahzadeh, A.R.R.; Oraizi, H.; Davoodi-Rad, Z.: Application of the invasive weed optimization technique for antenna configurations. Prog. Electromagn. Res. 79, 137–150 (2008)CrossRefGoogle Scholar
  23. 23.
    Oravec, M.; Jadlovská, A.: Model predictive control of a ball and plate laboratory model. In: 2015 IEEE 13th International Symposium on Applied Machine Intelligence and Informatics (SAMI), pp. 165–170. IEEE (2015)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • Hazem I. Ali
    • 1
  • Haider M. Jassim
    • 1
    Email author
  • Amjad F. Hasan
    • 1
  1. 1.University of TechnologyBaghdadIraq

Personalised recommendations