Stable Robust Adaptive Controller and Observer Design for a Class of SISO Nonlinear Systems with Unknown Dead Zone

This paper presents a new stable robust adaptive controller and observer design for a class of nonlinear systems that contain i. Coupling of unmeasured states and unknown parameters ii. Unknown dead zone at the system actuator. The system is firstly cast into a modified form in which the observer and parameter estimation become feasible. Then a stable robust adaptive controller, state observer, parameter update laws are derived that would provide global adaptive system stability and desirable performance. To validate the approach, simulation was performed to a single-link mechanical system with a dynamic friction model and unknown dead zone exists at the system actuation. Then a comparison is presented with the results when there is no dead zone at the system actuation.

• Ibrahim F. Jasim

• Dead Zone
• Nonlinear Systems
• Observer
• Robust Adaptive Control.

[1] Tao, G., and Kokotovic, P. V., 1994, "Adaptive Control of Plants With
Unknown Dead Zone," IEEE Trans. Automatic Control, 39, pp. 59-68.
[2] Tao, G., and Kokotovic, P. V., 1995, "Discrete-time Adaptive Control of
Systems With Unknown Dead Zone," International Journal of Control,
61, pp. 1- 17.
[3] Cho, H. Y., and Bai, E. W., 1998, "Convergence Results for An
Adaptive Dead Zone Inverse," International Journal of Adaptive Control
and Signal Processing, 12, pp. 451- 466.
[4] Lewis, F. L., Tim, W. K., Wang, L. Z., and Li, Z. X., 1999, "Dead Zone
Compensation in Motion Control Systems Using Adaptive Fuzzy Logic
Control", IEEE Trans. Control Systems Technology, 7, pp. 731- 742.
[5] Selmic, R. R., and Lewis, F. L., 2000, "Dead Zone Compensation in
Motion Control Systems Using Neural Networks", IEEE Trans.
Automatic Control, 45, pp. 602- 613.
[6] Zhou, J., Wen, C., and Zhang, Y., 2006, " Adaptive Output Control of
Nonlinear Systems Wuth Unknown Dead Zone", IEEE Trans. Automatic
Control, 51, pp. 504-511.
[7] Zhou, J., and Shen, X. Z., 2007, "Robust Adaptive Control of Nonlinear
Uncertain Plants With Unknown Dead Zone", IET Control Theory
Appl., 1, pp. 25-32.
[8] Wang, S. X., Su, C. Y., and Hong, H.Y., 2004, "Robust Adaptive
Control of a Class of Nonlinear Systems With Unknown Dead Zone",
Proc. 40th IEEE Conf. on Decision and Control, Orlando, Florida, USA,
pp. 1627- 1632.
[9] Wang, S. X., Su, C. Y., and Hong, H.Y., 2003, "Model Reference
Adaptive Control of Continuous-Time Systems With an Unknown Input
Dead Zone", IEE Proc. Control Theory Appl., 150, pp. 261- 266.
[10] Wang, S. X., Su, C. Y., and Hong, H.Y., 2004, "Robust Adaptive
Control of a Class of Nonlinear Systems With Unknown Dead Zone",
Automatica, 40, pp. 407-413.
[11] Zhu, Y., and Pagilla, P. R., 2006, "Adaptive Controller and Observer
Design for a Class of Nonlinear Systems", Trans. Of ASME, Journal of
Dyn. Syst., Meas., and Control, 128, pp. 712- 717.
[12] Slotine, J.-J. E., 1984, "Sliding Controller Design for Nonlinear
Systems", International Journal of Control, 40, pp. 435-448.
[13] Slotine, J.-J. E., and Coetsee, J. A., 1986, "Adaptive Sliding Control
Synthesis for Nonlinear Systems", International Journal of Control, 43,
pp. 1631- 1651.
[14] M. Serruya, N. Hatsopoulos, M. R. Fellows, L. Paninski, J.
Donoghue, \Robustness of neuroprosthetic decoding algorithms," Biological Cybernetics, vol. 88, no. 3, pp. 219{228,
Mar 2003.
[15] M. Jazayeri and J. A. Movshon, \Optimal representation of sensory information by neural populations," Nature
Neuroscience, vol. 9, no. 5, pp. 690-696, May 2006.
[16] M. H. Schieber \Individuated nger movements of rhesus monkeys: a means of quantifying the independence of
the digits," Journal of Neurophysiology, vol. 65, no. 6,
pp. 1381{1391, June 1991.
[17] M. C. Schieber and L. S. Hibbard, \How somatotopic is
the motor cortex hand area?," Science, vol. 261, pp. 489{492, July 1993.
[18] A. V. Poliakov and M. H. Schieber, \Limited functional
grouping of neurons in the motor cortex hand area during
individuated nger movements: a cluster analysis," Journal of Neurophysiology, vol. 82, no. 6, pp. 3488{3505, Dec.
1999.
[19] A. P. Georgopolous, G. Pellizzer, A. V. Poliakov and M.
H. Schieber, \Neural coding of nger and wrist movements," Journal of Computational Neuroscience, vol. 6,
no. 3, pp. 279{288, May 1999.
[20] M. N. Shadlen and W. T. Newsome, \The variable discharge implications for connectivity, computation and information coding," Journal of Neuroscience, vol. 18,
pp. 3870{3896, 1998.
[21] J. G. Skellam, \The frequency distribution of the difference between two Poissn variables belonging to dierent populations," Journal of the Royal Statistical Society:
Sereis A, vol. 109, no. 3 pp. 296, 1946.