Skip to main content
SpringerLink
Log in

Robust Stabilization of Inverted Pendulum Using ALQR Augmented by Second-Order Sliding Mode Control

  • Published:
Journal of Control, Automation and Electrical Systems Aims and scope Submit manuscript

Abstract

In this paper, a robust nonlinear control design strategy to solve the stabilization problem of an inverted pendulum system subject to parametric uncertainties and unmodeled dynamics is proposed. The control strategy is based on the combination of Amplified Linear Quadratic Regulator (ALQR) control with a high-order sliding mode algorithm. Differently from the standard ALQR controller, parametric uncertainties are considered in the design process. Linear matrix inequality conditions are provided to deal with the computational issues arising with the inclusion of this feature. A sliding mode term is added to the ALQR control law to mitigate the effect of unmodeled dynamics, such as dry friction, neglected in the system model. In order to prevent the occurrence of chattering, a high-order sliding mode approach was used, namely the second-order super-twisting algorithm. The effectiveness of the proposed strategy is evaluated through a real experiment performed using the Quanser inverted pendulum plant.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Cavalca, M., & Kienitz, K. (2009). Application of TFL/LTR robust control techniques to failure accommodation. ABCM Symposium Series in Mechatronics, 4, 189–197.

    Google Scholar 

  • Chalanga, A., Kamal, S., Fridman, L. M., Bandyopadhyay, B., & Moreno, J. A. (2016). Implementation of super-twisting control: Super-twisting and higher order sliding-mode observer-based approaches. IEEE Transactions on Industrial Electronics, 63(6), 3677–3685.

    Article  Google Scholar 

  • Chen, B.-S., Tseng, C.-S., & Uang, H.-J. (2000). Mixed \({H}_2\) / \({H}_{\infty }\) fuzzy output feedback control design for nonlinear dynamic systems: An LMI approach. IEEE Transactions on Fuzzy Systems, 8(3), 249–265.

    Article  Google Scholar 

  • Chen, C.-S., & Chen, W.-L. (1998). Robust adaptive sliding-mode control using fuzzy modeling for an inverted-pendulum system. IEEE Transactions on Industrial Electronics, 45(2), 297–306.

    Article  Google Scholar 

  • Das, S. K., & Paul, K. K. (2011). Robust compensation of a cart-inverted pendulum system using a periodic controller: Experimental results. Automatica, 47(11), 2543–2547.

    Article  MathSciNet  MATH  Google Scholar 

  • Fallaha, C., Saad, M., Kanaan, H., & Al-Haddad, K. (2011). Sliding-mode robot control with exponential reaching law. IEEE Transactions on Industrial Electronics, 58(2), 600–610.

    Article  Google Scholar 

  • Geromel, J., Korogui, R., & Bernussou, J. (2007). \({H}_2\) and \({H}_{\infty }\) robust output feedback control for continuous time polytopic systems. IEEE Transactions on Fuzzy Systems, 1(5), 1541–1549.

    Google Scholar 

  • Hadri-Hamida, A. (2015). Higher-order sliding mode control scheme with an adaptation low for uncertain power dc–dc converters. Journal of Control, Automation and Electrical Systems, 26(2), 125–133.

    Article  Google Scholar 

  • Kajiwara, H., Apkarian, P., & Gahinet, P. (1999). LPV techniques for control of an inverted pendulum. IEEE Control Systems, 19(1), 44–54.

    Article  Google Scholar 

  • Khalil, H. K. (2002). Nonlinear systems (3rd ed.). Upper Saddle River: Prentice Hall.

    MATH  Google Scholar 

  • Kleindienst, M., Reichhartinger, M., Horn, M., & Usai, E. (2014). An application of computer aided parameter tuning of a super-twisting sliding mode controller. In Proceedings of the 13th international workshop on variable structure systems (pp. 1–6).

  • Lee, J., Mukherjee, R., & Khalil, H. (2015). Output feedback stabilization of inverted pendulum on a cart in the presence of uncertainties. Automatica, 54, 146–157.

    Article  MathSciNet  MATH  Google Scholar 

  • Levant, A. (1993). Sliding order and sliding accuracy in sliding mode control. International Journal of Control, 58(6), 1247–1263.

    Article  MathSciNet  MATH  Google Scholar 

  • Levant, A. (1998). Robust exact differentiation via sliding mode technique. Automatica, 34, 379–384.

    Article  MathSciNet  MATH  Google Scholar 

  • Levant, A. (2003). Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control, 76(9/10), 924–941.

    Article  MathSciNet  MATH  Google Scholar 

  • Lin, S., Cai, Y., Yang, B., & Zhang, W. (2017). Electrical line-shafting control for motor speed synchronisation using sliding mode controller and disturbance observer. IET Control Theory Applications, 11(2), 205–212.

    Article  Google Scholar 

  • Medrano-Cersa, G. A. (1999). Robust computer control of an inverted pendulum. IEEE Control Systems, 19(3), 58–67.

    Article  Google Scholar 

  • Moreno, J. A., & Osorio, M. (2012). Strict lyapunov functions for the super-twisting algorithm. IEEE Transactions on Automatic Control, 57(4), 1035–1040.

    Article  MathSciNet  Google Scholar 

  • Nagesh, I., & Edwards, C. (2014). A multivariable super-twisting sliding mode approach. Automatica, 50, 984–988.

    Article  MathSciNet  MATH  Google Scholar 

  • Olalla, C., Leyva, R., El Aroudi, A., & Queinnec, I. (2009). Robust LQR control for PWM converters: An LMI approach. IEEE Transactions on Industrial Electronics, 56(7), 2548–2558.

    Article  Google Scholar 

  • Oliveira, C., Aguiar, M., Monteiro, J., Pereira, W., Paula, G. T., & Almeida, T. (2016). Vector control of induction motor using an integral sliding mode controller with anti-windup. Journal of Control, Automation and Electrical Systems, 27(2), 169–178.

    Article  Google Scholar 

  • Oucheriah, S., & Guo, L. (2013). PWM-based adaptive sliding-mode control for boost dc–dc converters. IEEE Transactions on Industrial Electronics, 60(8), 3291–3294.

    Article  Google Scholar 

  • Pereira, R.L., Afonso, R.J.M., & Kienitz, K.H. (2015). Sliding mode control via ALQR for uncertain systems: An LMI approach. In Proceedings of the 23rd ABCM international congress of mechanical engineering.

  • Pilloni, A., Pisano, A., & Usai, E. (2012). Parameter tuning and chattering adjustment of super-twisting sliding mode control system for linear plants. In Proceedings of the 12th international workshop on variable structure systems (pp. 479–484).

  • Prakash, R. (1990). Target feedback loop/loop transfer recovery (TFL/LTR) robust control design procedures. In Proceedings of the 29th conference on decision and control (pp. 1203–1209).

  • Quanser. (2012). Linear inverted pendulum: User’s manual. Technical report.

  • Shyu, K. K., & Lai, C. K. (2002). Incremental motion control of synchronous reluctance motor via multisegment sliding mode control method. IEEE Transactions on Control System Technology, 10(2), 169–176.

    Article  Google Scholar 

  • Slotine, J.-J. E., & Wi, L. (1991). Applied nonlinear control. Upper Saddle River: Prentice Hall.

    Google Scholar 

  • Teixeira, H., de Mattos Siqueira, V., & Munaro, C. J. (2013). Closed-loop quantification and compensation of friction in an inverted pendulum. Journal of Control, Automation and Electrical Systems, 24(6), 794–805.

    Article  Google Scholar 

  • Trivedi, P. K., Bandyopadhyay, B., Mahata, S., & Chaudhuri, S. (2015). Roll stabilization: A higher-order sliding-mode approach. IEEE Transactions on Aerospace and Electronic Systems, 51(3), 2489–2496.

    Article  Google Scholar 

  • Utkin, V. I. (1977). Variable structure systems with sliding modes. IEEE Transactions on Automatic Control, 22(2), 212–222.

    Article  MathSciNet  MATH  Google Scholar 

  • Utkin, V. I. (1993). Sliding mode control design principles and applications to electric drives. IEEE Transactions on Industrial Electronics, 40(1), 23–36.

    Article  Google Scholar 

  • Utkin, V.I., & Shi, J. (1996). Integral sliding modes in systems operating under uncertainty conditions. In Proceedings of the 35th conference on decision and control (pp. 4591–4596).

  • van der Linden, G.W., & Lambrechts, P.F. (1992). \({H}_{\infty }\) control of an experimental inverted pendulum with dry friction. In Proceedings of the 1st IEEE conference on control applications (Vol. 1, pp. 123–128).

  • Young, K. D., Utkin, V. I., & Ozguner, U. (1999). A control engineer’s guide to sliding mode control. IEEE Transactions on Control System Technology, 7(3), 328–342.

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support provided by the anonymous reviewers for their helpful suggestions on this paper.

Author information

Authors and Affiliations

  1. UNIFEI, Federal University of Itajubá, Campus Itabira, Rua Irmã Ivone Drumond, 200, Distrito Industrial II, Itabira, MG, 35903-087, Brazil

    Fernando H. D. Guaracy & Renan L. Pereira

  2. UNIFEI, Federal University of Itajubá, Institute of Systems Engineering and Information Technology, Av. BPS, 1303, Pinheirinho, Itajubá, MG, 37500-903, Brazil

    Caio F. de Paula

Authors
  1. Fernando H. D. Guaracy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Renan L. Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Caio F. de Paula
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fernando H. D. Guaracy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guaracy, F.H.D., Pereira, R.L. & de Paula, C.F. Robust Stabilization of Inverted Pendulum Using ALQR Augmented by Second-Order Sliding Mode Control. J Control Autom Electr Syst 28, 577–584 (2017). https://doi.org/10.1007/s40313-017-0332-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40313-017-0332-0

Keywords

Search

Navigation