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Robust Proportional Control for Trajectory Tracking of a Nonlinear Robotic Manipulator: LMI Optimization Approach

  • Research Article - Computer Engineering and Computer Science
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Abstract

This paper proposes a new control configuration that is simple, model free and robust for trajectory tracking control of a multi-input–multi-output nonlinear robotic manipulator system. The proposed controller consists of two terms. The first term is a linear controller in proportional (P) control structure, and the second term is a nonlinear robustness term in sliding mode structure. This combined nonlinear controller exploits the simplicity and easy implementation properties of proportional-integral-derivative control and robustness properties of the sliding mode control (SMC) against system uncertainties and parameter variations. Important feature of the proposed controller is avoiding the need to determine the accurate dynamic model of the plant, which is a necessity in standard SMC. Stability analysis is performed, and stability in closed loop is proved for the proposed control method. A control problem is restated as a convex optimization problem based on linear matrix inequality technique, and optimal gain of P controller is obtained. A simulation model of the plant is built in MATLAB–Simulink environment for testing the proposed controller. Closed-loop system performances are observed for standard SMC, computed torque control, SMC with proportional-derivative control and proposed control. Simulation results reveal the effectiveness of proposed method in response to system uncertainties, random noise and external disturbance.

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References

  1. Sharma S., Rana K.P.S., Kumar V.: Performance analysis of fractional order fuzzy PID controllers applied to a robotic manipulator. Expert Syst. Appl. 41(9), 4274–4289 (2014)

    Article  Google Scholar 

  2. Kolhe J.P., Shaheed M., Chandar T.S., Talole S.E.: Robust control of robot manipulators based on uncertainty and disturbance estimation. Int. J. Robust Nonlinear Control 23(1), 104–122 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Reznik L., Ghanayem O., Bourmistrov A.: PID plus fuzzy controller structures as a design base for industrial applications. Eng. Appl. Artif. Intell. 13(4), 419–430 (2000)

    Article  Google Scholar 

  4. Ouyang P.R., Acob J., Pano V.: PD with sliding mode control for trajectory tracking of robotic system. Robot. Comput. Integr. Manuf. 30(4), 189–200 (2014)

    Article  Google Scholar 

  5. Rahman M.H., Saad M., Kenne J., Archambault P.S.: Control of an exoskeleton robot arm with sliding mode exponential reaching law. Int. J. Control Autom. Syst. 11(1), 92–104 (2013)

    Article  Google Scholar 

  6. Liu H.T., Zhang T.: Neural network-based robust finite-time control for robotic manipulators considering actuator dynamics. Robot. Comput. Integr. Manuf. 29(2), 301–308 (2013)

    Article  Google Scholar 

  7. Liang Y.-W., Xu S.-D., Liaw D.-C., Chen C.-C.: A study of T-S model based SMC scheme with application to robot control. IEEE Trans. Ind. Electron. 55(11), 3964–3971 (2008)

    Article  Google Scholar 

  8. Parra-Vega V., Arimoto S., Liu Y.H., Hirzinger G., Akella P.: Dynamic sliding PID control for tracking of robot manipulators: theory and experiments. IEEE Trans. Robot. Autom. 19(6), 967–976 (2003)

    Article  Google Scholar 

  9. Islam S., Liu X.: Robust Sliding Mode Control for Robot Manipulators. IEEE Trans. Ind. Electron. 58(6), 2444–2453 (2011)

    Article  Google Scholar 

  10. Zhang, A.; She, J.; Lai, X.; Wu, M.; Qiu, J.; Chen, X.: Robust tracking control of robot manipulators using only joint position measurements. Math. Probl. Eng. Article ID 719474 (2013)

  11. Slotine J.E., Coetsee J.A.: Adaptive sliding controller synthesis for non-linear systems. Int. J. Control 43, 1631–1635 (1986)

    Article  MATH  Google Scholar 

  12. Yao, B.; Tomizuka, M.: Robust adaptive motion and force control of robot manipulators in unknown stiffness environments. In: Proceedings of the 32nd IEEE Conference on Decision Control, pp. 142–147 (1993)

  13. Yao B., Tomizuka M.: Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form. Automatica 33(5), 893–900 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yao B., Fanping B., Reedy J., Chiu G.T.: Adaptive robust motion control of single-rod hydraulic actuators: theory and experiments. IEEE/ASME Trans. Mechatron. 5(1), 79–91 (2000)

    Article  Google Scholar 

  15. Zeinali M., Notash L.: Adaptive sliding mode control with uncertainty estimator for robot manipulators. Mech. Mach. Theory 45(1), 80–90 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ge S.S., Lee T.H., Harris C.J.: Adaptive Neural Network Control of Robotic Manipulator. World Scientific, Singapore (1998)

    Book  Google Scholar 

  17. Sun, T.; Pei, H.; Pan, Y.P.; Zhang, C.: Neural network-based sliding mode adaptive control for robot manipulators. Neurocomputing 74(Issue 14–15), 2377–2384 (2011)

  18. Han S., Lee J.: Decentralized neural network control for guaranteed tracking error constraint of a robot manipulator. Int. J. Control Autom. Syst. 13(4), 906–915 (2015)

    Article  Google Scholar 

  19. Yuangang, T.; Fuchun, S.; Zengqi, S.: Neural network control of flexible-link manipulators using sliding mode. Neurocomputing 70(Issues 1–3), 288–295 (2006)

  20. Nekoukar V., Erfanian A.: Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems. Fuzzy Sets Syst. 179(1), 34–49 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Rajamani, R.; Cho Y.: Observer Design for Nonlinear Systems: Stability and Convergence. In: Proceedings of the 34th IEEE Conference of Decision and Control, pp. 93–94 (1995)

  22. Khalil H.: Nonlinear Systems. Prentice Hall, Englewood Cliffs (2002)

    MATH  Google Scholar 

  23. Siljak D.D., Stipanovic D.M.: Robust stabilization of nonlinear systems: the LMI approach. Math. Prob. Eng. 6, 461–493 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  24. Romero, G.; Alcorta, E.; Lara, D.; Perez, l.; Betancourt, R.; Ocampo, H.: New method for tuning robust controller applied to robot manipulator. Int. J Adv. Robot. Syst. A (2012). DOI:10.5772/53734

  25. Utkin V., Guldner J., Shi J.: Sliding Mode Control in Electro-Mechanical Systems, 2nd edn. CRC Press, Boca Raton (2009)

    Book  Google Scholar 

  26. Slotine J., Li W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

  27. Ayala H.V., Coelho L.D.: Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator. Expert Syst. Appl. 39(10), 8968–8974 (2012)

    Article  Google Scholar 

  28. Islam R., Iqbal J., Khan Q.: Design and comparison of two control strategies for multi-DOF articulated robotic arm manipulator. Control Eng. Appl. Inf. 16(2), 28–39 (2014)

    Google Scholar 

  29. Acob, J.M.; Pano, V.; Quyang, P.R.: Hybrid PD sliding mode control of a two degree-of-freedom parallel robotic manipulator. In: Proceeding of the 2013 10th IEEE International Conference on Control and Automation (ICCA), pp. 12–14, June (2013)

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Authors and Affiliations

  1. Al-Khwarizmi College of Engineering, University of Baghdad, Baghdad, Iraq

    Ali Hussien Mary

  2. Department of Electrical and Electronics Engineering, University of Gaziantep, Gaziantep, Turkey

    Tolgay Kara

Authors
  1. Ali Hussien Mary
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  2. Tolgay Kara
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Correspondence to Ali Hussien Mary.

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Mary, A.H., Kara, T. Robust Proportional Control for Trajectory Tracking of a Nonlinear Robotic Manipulator: LMI Optimization Approach. Arab J Sci Eng 41, 5027–5036 (2016). https://doi.org/10.1007/s13369-016-2221-4

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  • DOI: https://doi.org/10.1007/s13369-016-2221-4

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