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Adaptive stable control of manipulator system based on immersion and invariance

    Huapeng Wang Affiliation
    ; Nan Jiang Affiliation
    ; Ting Liu Affiliation
    ; Yangyang Cao Affiliation

Abstract

This work focused on the manipulator system containing uncertainties, and proposes an immersion and invariance (I&I) control strategy, in order to avoid the damage on the mechanical and the operation object caused by parameter uncertainty. A stable target system with lower dimension than the manipulator system was chosen to design the control law and estimation laws of uncertain parameters. Then finding an invariant and attractive manifold in state space with internal dynamics a copy of the desired closed-loop dynamics. Finally, design a control law that can steer the state of the system sufficiently close to the manifold. The immersion and invariance adaptive control does not rely on certainty equivalence. The whole uncertain parameter estimations are the sum of two terms. One is obtained by an iterative law like the traditional adaptive backstepping method. On the other hand, a nonlinear function is introduced. The role of this additional term makes the parameter estimations more exible and effective. Lyapunov function is not necessary for the process of designing adaptive controllers. So immersion and invariance can effectively avoid the 'computing expansion' of backstepping method. Compared with the traditional adaptive methods, simulation results show that the proposed immersion and invariance adaptive controller can improve the system performance, including dynamic response, stability and accuracy of parameter estimations.

Keyword : manipulator, immersion and invariance, adaptive control, uncertainty, nonlinear control

How to Cite
Wang, H., Jiang, N., Liu, T., & Cao, Y. (2018). Adaptive stable control of manipulator system based on immersion and invariance. Mathematical Modelling and Analysis, 23(3), 379-389. https://doi.org/10.3846/mma.2018.023
Published in Issue
Jun 14, 2018
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References

[1] A. Astolfi, D. Karagiannis and R. Ortegar. Tawards applied nonlinear adaptive control. Annual Reviews in Control, 32(2):136-148, 2008. https://doi.org/10.1016/j.arcontrol.2008.08.003.

[2] A. Astolfi, D. Karagiannis and R.Ortegar. Nonlinear and adaptive control with applications. Springer-Verlag London Limited, London, 2007.

[3] A. Astolfi and R. Ortegar. Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Transactions on Automatic Control, 48(4):590-606, 2003. https://doi.org/10.1109/TAC.2003.809820.

[4] S. Djebrani, A. Benali and F. Abdessemed. Modelling and feedback control of an omni-directional mobile manipulator. In The 7th IEEE Conference on Automation Science and Engineering, Trieste, Italy, 2011, pp. 785-791. IEEE, 2011. https://doi.org/10.1109/CASE.2011.6042441.

[5] Y. Hsiao, H. Tu and W. Hung. Sliding backstepping control design for robotic manipulator systems with motor dynamics. In The 11th IEEE International Conference on Control Automation, Taichung, Taiwan, 2014, pp. 667-672. IEEE, 2014. https://doi.org/10.1109/ICCA.2014.6870999.

[6] N. Jiang, S. Li and T. Liu. Nonlinear large disturbance attenuation controller design for power systems with STATCOM. Applied Mathematics and Computation, 219(20):10378-10386, 2013. https://doi.org/10.1016/j.amc.2013.04.011.

[7] IU Khan and R Dhaouadi. Nonlinear reduced order observer design for elastic drive systems using invariant manifolds. In 2015 IEEE International Conference on Mechatronics, Nagoya, Japan, 2015, pp. 58-63. IEEE, 2015. https://doi.org/10.1109/ICMECH.2015.7083948.

[8] X. Liu, G. Hong and H. Luo. The immersion and invariance adaptive control for a class of linear motor systems with its application. In The 27th Chinese Control and Decision Conference, Qingdao, China, 2015, pp. 1502-1507. IEEE, 2015. https://doi.org/10.1109/CCDC.2015.7162157.

[9] Z. Liu, X. Tan and R. Yuan. Nonlinear adaptive control for hypersonic vehicles via immersion and invariance. In The 32th Chinese Control Conference, Xian, China, 2013, pp. 2951-2956. IEEE, 2013.

[10] R. Mei, X. Wu and S. Jiang. Robust adaptive backstepping control for a class of uncertain nonlinear systems based on disturbance observers. China Information Sciences, 53(6):1201-1215, 2010. https://doi.org/10.1007/s11432-010-3116-s

[11] P. Rapp, M. Klunder and O. Sawodny. Nonlinear adaptive and tracking control of a pneumatic actuator via immersion and invariance. In IEEE 51st Annual Conference on Decision and Control, Maui, HI, USA, 2012, pp. 4145-4151. IEEE, 2012. https://doi.org/10.1109/CDC.2012.6426396.

[12] I. Sarras. On the stabilization of nonholonomic mechanical systems via immersion and invariance. IFAC Proceedings Volumes, 44(1):7227-7232, 2011. https://doi.org/10.3182/20110828-6-IT-1002.01537.

[13] Y. Wu, C. Lai and S. Chen. An adaptive neural network compensator for decoupling of dynamic effects of a macro-mini manipulator. In 2015 IEEE International Conference on Advanced Intelligent Mechatronics, Busan, South Korea, 2015, pp. 1427-1432. IEEE, 2015. https://doi.org/10.1109/AIM.2015.7222741.

[14] C. Zhang, A. Zhang and H. Zhang. RBF neural networks sliding mode controller design for static var compensator. In The 34th Chinese Control Conference, Hangzhou, China, 2015, pp. 3501-3506. IEEE, 2015. https://doi.org/10.1109/ChiCC.2015.7260179.

[15] B. Zhao, B. Xian and Y. Zhang. Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology. IEEE Transactions on Industrial Electronics, 62(5):2891-2902, 2015. https://doi.org/10.1109/TIE.2014.2364982.

[16] L. Zouari, H. Abid and M. Abid. Comparative study between PI and sliding mode controllers for exible joint manipulator driving by brushless DC motor. In The 14th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering, Sousse, Tunisia, 2013, pp. 294-299. IEEE, 2013. https://doi.org/10.1109/STA.2013.6783146.