Adaptive Tuning Functions Tracking Control with Nonlinear Adaptive Observers

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Abstract

The paper is dedicated to the derivation of a unified approach for nonlinear adaptive closed loop system design with nonlinear adaptive state and parameter observers combined with tuning functions-based nonlinear adaptive control for trajectory tracking. The proposed approach guarantees asymptotic stability of the closed loop nonlinear adaptive system with respect to the tracking and state estimation errors and Lyapunov stability of the parameter estimator. The advantages of the approach are the lack of over-parametrization, resulting in a minimal number of estimator equations and the preservation of the overdamped performance specifications of the closed loop nonlinear adaptive system in its whole range of operation. The application of the approach to a permanent magnet synchronous motor driven inverted pendulum concludes with simulation of the closed loop nonlinear adaptive system time responses.

References

  • 1. Bastin, G., M. Gevers. Stable Adaptive Observers for Nonlinear Time-varying Systems. – IEEE Transactions on Automatic Control, 33, 1988, No. 7, 650-658.

  • 2. Besancon, G. Remarks on Nonlinear Adaptive Observer Design. – Systems & Control Letters, 41, 2000, No. 4, 271-280.

  • 3. Kanellakopoulos, I., M. Krstic, P. Kokotovic. Interlaced Controller-Observer Design for Adaptive Nonlinear Control. American Control Conference, 1992, 1337-1342.

  • 4. Kanellakopoulos, I., P. Kokotovic, R. Middleton. Observer-based Adaptive Control of Nonlinear Systems under Matching Conditions. American Control Conference, 1990, 549-555.

  • 5. Krstic, M., I. Kanellakopoulos, P. Kokotovic. Nonlinear and Adaptive Control Design. John Wiley and Sons Inc., 1995.

  • 6. Marino, R. Adaptive Observers for Single Output Nonlinear Systems. – IEEE Transactions on Automatic Control, 35, 1990, No. 9, 1054-1058.

  • 7. Marino, R., P. Tomei. Adaptive Observers with Arbitrary Exponential Rate of Convergence for Nonlinear Systems. – IEEE Transactions on Automatic Control, 40, 1995, No. 7, 1300-1304.

  • 8. Marino, R., P. Tomei. Global Adaptive Observers for Nonlinear Systems via Filtered Transformations. – IEEE Transactions on Automatic Control, 37,1992, No. 8, 1239-1245.

  • 9. Mishkov, R. L. Nonlinear Observer Design by Reduced Generalized Observer Canonical Form. – International Journal of Control, 78, 2005, No. 3, 172-185.

  • 10. Mishkov, R., S. Darmonski. Adaptive Nonlinear Trajectory Tracking Control for DC Motor Driven Inverted Pendulum. International Conference Automatics and Informatics'11, 2011, B-67–B-70.

  • 11. Mishkov, R., S. Darmonski. Adaptive Tuning Functions System Design for Inverted Pendulum. International Conference Engineering, Technologies and Systems TechSys, 2011, 16, book 1, 329-334.

  • 12. Mishkov, R., V. Petrov. Advanced Control Nonlinear State Space Models of Permanent Magnet Synchronous Motors. International Conference Automatics and Informatics' 12, 2012, 70-73.

  • 13. Mishkov, R., V. Petrov. Nonlinear Adaptive Observer Design in Combined Error Nonlinear Adaptive Control. Scientific Works “Food Science, Engineering and Technologies 2013”, Seventh National Conference with International Participation “Process Automation in the Food and Biotechnology Industries”, LX, 2013, No. 2, 95-99.

  • 14. Mishkov, R., V. Petrov. Strictly Orientated State Space Models of Permanent-magnet Synchronous Motors for Feedback Linearization Control. International Conference Engineering, Technologies and Systems TechSys 2011, 16, 2011, book 1, 335-340.

  • 15. Petrov, V., S. Darmonski. Observer Based Adaptive Nonlinear Control System Design for a Single Link Manipulator. Student Conference Electrical Engineering, Information and Communication Technologies EEICT 2012 Brno, Czech Republic, 2012, 116-120.

  • 16. Slotine, J.-J. & W. Li. Applied Nonlinear Control. Prentice-Hall International, 1991.

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