ABSTRACT
In this paper, a robust control law is proposed for the tracking control problem of a class of uncertain Euler-Lagrange (EL) systems subjected to randomly varying input delay. EL systems represent a large class of real-world systems such as robotic manipulator, unmanned mobile robots etc. In comparison to the existing predictor based approaches, the proposed Robust Time-Delay Controller (ROTDC) can negotiate input delay within a specified range having an arbitrary variation. Razumikhin-type stability analysis is employed to derive the controller gain to maintain system stability for a given range of delay. Further, the closed loop uncertain system is shown to be Uniformly Ultimately Bounded (UUB) employing the proposed ROTDC. As a validation of the concept, comparative experimental results with predictor based methodology are also provided using a nonholonomic wheeled mobile robot with different time varying input delays, which demonstrate the efficacy of the proposed controller.
- R. Sipahi, S. I. Niculescu, C. Abdallah, W. Michiels, and K. Gu, Stability and stabilization of systems with time delay: Limitations and opportunities, IEEE Control System Magazine, vol. 31(1), pp. 38--65, 2011.Google ScholarCross Ref
- K. Gu and S. Niculescu, Survey on recent results in the stability and control of time-delay systems, ASME Journal of Dynamic Systems, Measurement, and Control, vol. 125, p. 158--165, 2003.Google ScholarCross Ref
- J. -P. Richard, Time-delay systems: an overview of some recent advances and open problems, Automatica, vol. 39(10), pp. 1667--1694, 2003. Google ScholarDigital Library
- V. L. Khartinov, Robust stability analysis of time delay systems: a survey, Annual Reviews in Control, vol. 23, pp. 185--196, 1999.Google ScholarCross Ref
- M. Krstic, Delay compensation for nonlinear, adaptive, and PDE systems, Birkhäuser, 2009.Google ScholarCross Ref
- O. M. Smith, A controller to overcome deadtime, ISA Journal, vol. 6, pp. 28--33, 1959.Google Scholar
- Z. Artstein, Linear systems with delayed controls: a reduction, IEEE Transactions on Automatic Control, vol. 27, pp. 869--876, 1982.Google ScholarCross Ref
- A. Z. Manitius, and A. W. Olbrot, Finite spectrum assignment problem for systems with delays, IEEE Transactions on Automatic Control, vol. 24, pp. 541--553, 1979.Google ScholarCross Ref
- V. L. Kharitonov, An extension of the prediction scheme to the case of systems with both input and state delay, Automatica, vol. 50, pp. 211--217, 2014. Google ScholarDigital Library
- R. Lozano, P. Castillo, P. Garcia, and A. Dzul, Robust prediction based control for unstable delay systems: Application to the yaw control of a mini-helicopter, Automatica, vol. 40(4), pp. 603--612, 2004. Google ScholarDigital Library
- D. Yue and Q. -L. Han, Delayed feedback control of uncertain systemswith time-varying input delay, Automatica, vol. 41(2), pp. 233--240, 2005. Google ScholarDigital Library
- Z. Wang, P. Goldsmith, and D. Tan, Improvement on robust control of uncertain systems with time-varying input delays, IET Control Theory and Applications, vol. 1(1), pp. 189--194, 2007.Google ScholarCross Ref
- A. Gonzalez, A. Sala, P. Garcia and P. Albertos, Robustness analysis of discrete predictor-based controllers for input-delay systems, International Journal of Systems Science, vol. 44(2), pp. 232--239, 2013. Google ScholarDigital Library
- A. Gonzalez, A. Sala and P. Albertos, Predictor-based stabilization of discrete time-varying input-delay systems, Automatica, vol. 48, pp. 454--457, 2012. Google ScholarDigital Library
- Z.-Y. Li, B. Zhou and Z. Lin, On robustness of predictor feedback control of linear systems with input delays, Automatica, vol. 50, pp. 1497--1506, 2014.Google ScholarCross Ref
- I. Karafyllis and M. Krstic, Delay-robustness of linear predictor feedback without restriction on delay rate, Automatica, vol. 49, pp. 1761--1767, 2013. Google ScholarDigital Library
- M. Jankovic, Control Lyapunov-Razumikhin Functions and Robust Stabilization of Time Delay Systems, IEEE Transactions On Automatic Control, vol. 46(7), pp. 1048--1060,2001.Google ScholarCross Ref
- C. Hua, G. Feng and X. Guan, Robust controller design of a class of nonlinear time delay systems via backstepping method, Automatica, vol. 44, pp. 567--573, 2008. Google ScholarDigital Library
- M. Krstic, Input delay compensation for forward complete and strict feedforward nonlinear systems, IEEE Transactions on Automatic Control, vol. 55, pp. 287--303, 2010.Google ScholarCross Ref
- A. Ailon, Asymptotic stability in a flexible-joint robot with model uncertainty and multiple time delays in feedback, Journal of the Franklin Institute, vol. 341(6), pp. 519--531,2004.Google ScholarCross Ref
- Z. Zhang, S. Xu and B. Zhang, Exact tracking control of nonlinear systems with time delays and dead-zone input, Automatica, vol. 52, pp. 272--276, 2015. Google ScholarDigital Library
- N. Sharma, S. Bhasin, Q. Wang and W. E. Dixon, Predictor based control for an uncertain euler-lagrange system with input delay, Automatica, vol. 47(11), pp. 2332--2342, 2011. Google ScholarDigital Library
- N. Fischer, R. Kamalpurkar, N. Fitz-Coyand and W. E. Dixon, Lyapunov-based control of an uncertain euler-lagrange system with time varying input delay, American Control Conference, pp. 3919--3924, 2012.Google ScholarCross Ref
- R. Kamalpurkar, N. Fischer, S. Obuz and W. E. Dixon, Time-varying input and state delay compensation for uncertain nonlinear systems, IEEE Transactions on Automatic Control, vol. 61(3), pp. 834--839, 2016.Google ScholarCross Ref
- H. Yousef, Design of adaptive fuzzy-based tracking control of input time delay nonlinear systems, Nonlinear Dynamics, vol. 79, pp. 417--426, 2015.Google ScholarCross Ref
- A. Safa, M. Baradarannia, H. Kharrati and S. Khanmohammadi, Global attitude stabilization of rigid spacecraft with unknown input delay, Nonlinear Dynamics, 2015.Google Scholar
- J. K. Hale, Theory of functional differential equation, Springer-Verlag, 1977.Google ScholarCross Ref
- S. Roy, S. Nandy, R. Ray and S. N. Shome, Time delay sliding mode control nonholonomic wheeled mobile robot: experimental validation, IEEE International Conference on Robotics and Automation, pp. 2886--2892, 2014.Google ScholarCross Ref
- S. Roy, S. Nandy, I. N. Kar, R. Ray and S. N. Shome, Robust control of nonholonomic wheeled mobile robot with past information: Theory and experiment, Journal of Systems and Control Engineering, vol. 231(3), pp. 178--188, 2017.Google Scholar
- P. Coelho and U. Nunes, Path-following control of mobile robots in presence of uncertainties, IEEE Transactions on Robotics and Automation, vol. 21, no. 2, pp. 252--261, 2005. Google ScholarDigital Library
Index Terms
- Robust Control of Uncertain Euler-Lagrange Systems with Time-Varying Input Delay
Recommendations
Observer-Based adaptive neural network controller for uncertain nonlinear systems with unknown control directions subject to input time delay and saturation
This paper addresses the design of an observer based adaptive neural controller for a class of strict-feedback nonlinear uncertain systems subject to input delay, saturation and unknown direction. The input delay has been handled using an integral ...
Predictor-based control for an uncertain Euler-Lagrange system with input delay
Controlling a nonlinear system with actuator delay is a challenging problem because of the need to develop some form of prediction of the nonlinear dynamics. Developing a predictor-based controller for an uncertain system is especially challenging. In ...
Robust adaptive tracking controller design for non-affine non-linear systems with state time-varying delay and unknown dead-zone
A novel Neural Network (NN)-based dead-zone compensation scheme for a class of non-affine Multiple-Input Multiple-Output (MIMO) non-linear systems with state time-varying delay is presented. A static NN is introduced to approximate and adaptively cancel ...
Comments