{"title":"Stable Robust Adaptive Controller and Observer Design for a Class of SISO Nonlinear Systems with Unknown Dead Zone","authors":"Ibrahim F. Jasim","volume":35,"journal":"International Journal of Biomedical and Biological Engineering","pagesStart":338,"pagesEnd":342,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/3236","abstract":"
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.<\/p>\r\n","references":"[1] Tao, G., and Kokotovic, P. V., 1994, \"Adaptive Control of Plants With\r\nUnknown Dead Zone,\" IEEE Trans. Automatic Control, 39, pp. 59-68.\r\n[2] Tao, G., and Kokotovic, P. V., 1995, \"Discrete-time Adaptive Control of\r\nSystems With Unknown Dead Zone,\" International Journal of Control,\r\n61, pp. 1- 17.\r\n[3] Cho, H. Y., and Bai, E. W., 1998, \"Convergence Results for An\r\nAdaptive Dead Zone Inverse,\" International Journal of Adaptive Control\r\nand Signal Processing, 12, pp. 451- 466.\r\n[4] Lewis, F. L., Tim, W. K., Wang, L. Z., and Li, Z. X., 1999, \"Dead Zone\r\nCompensation in Motion Control Systems Using Adaptive Fuzzy Logic\r\nControl\", IEEE Trans. Control Systems Technology, 7, pp. 731- 742.\r\n[5] Selmic, R. R., and Lewis, F. L., 2000, \"Dead Zone Compensation in\r\nMotion Control Systems Using Neural Networks\", IEEE Trans.\r\nAutomatic Control, 45, pp. 602- 613.\r\n[6] Zhou, J., Wen, C., and Zhang, Y., 2006, \" Adaptive Output Control of\r\nNonlinear Systems Wuth Unknown Dead Zone\", IEEE Trans. Automatic\r\nControl, 51, pp. 504-511.\r\n[7] Zhou, J., and Shen, X. Z., 2007, \"Robust Adaptive Control of Nonlinear\r\nUncertain Plants With Unknown Dead Zone\", IET Control Theory\r\nAppl., 1, pp. 25-32.\r\n[8] Wang, S. X., Su, C. Y., and Hong, H.Y., 2004, \"Robust Adaptive\r\nControl of a Class of Nonlinear Systems With Unknown Dead Zone\",\r\nProc. 40th IEEE Conf. on Decision and Control, Orlando, Florida, USA,\r\npp. 1627- 1632.\r\n[9] Wang, S. X., Su, C. Y., and Hong, H.Y., 2003, \"Model Reference\r\nAdaptive Control of Continuous-Time Systems With an Unknown Input\r\nDead Zone\", IEE Proc. Control Theory Appl., 150, pp. 261- 266.\r\n[10] Wang, S. X., Su, C. Y., and Hong, H.Y., 2004, \"Robust Adaptive\r\nControl of a Class of Nonlinear Systems With Unknown Dead Zone\",\r\nAutomatica, 40, pp. 407-413.\r\n[11] Zhu, Y., and Pagilla, P. R., 2006, \"Adaptive Controller and Observer\r\nDesign for a Class of Nonlinear Systems\", Trans. Of ASME, Journal of\r\nDyn. Syst., Meas., and Control, 128, pp. 712- 717.\r\n[12] Slotine, J.-J. E., 1984, \"Sliding Controller Design for Nonlinear\r\nSystems\", International Journal of Control, 40, pp. 435-448.\r\n[13] Slotine, J.-J. E., and Coetsee, J. A., 1986, \"Adaptive Sliding Control\r\nSynthesis for Nonlinear Systems\", International Journal of Control, 43,\r\npp. 1631- 1651.\r\n[14] M. Serruya, N. Hatsopoulos, M. R. Fellows, L. Paninski, J.\r\nDonoghue, \\Robustness of neuroprosthetic decoding algorithms,\" Biological Cybernetics, vol. 88, no. 3, pp. 219{228,\r\nMar 2003.\r\n[15] M. Jazayeri and J. A. Movshon, \\Optimal representation of sensory information by neural populations,\" Nature\r\nNeuroscience, vol. 9, no. 5, pp. 690-696, May 2006.\r\n[16] M. H. Schieber \\Individuated \fnger movements of rhesus monkeys: a means of quantifying the independence of\r\nthe digits,\" Journal of Neurophysiology, vol. 65, no. 6,\r\npp. 1381{1391, June 1991.\r\n[17] M. C. Schieber and L. S. Hibbard, \\How somatotopic is\r\nthe motor cortex hand area?,\" Science, vol. 261, pp. 489{492, July 1993.\r\n[18] A. V. Poliakov and M. H. Schieber, \\Limited functional\r\ngrouping of neurons in the motor cortex hand area during\r\nindividuated \fnger movements: a cluster analysis,\" Journal of Neurophysiology, vol. 82, no. 6, pp. 3488{3505, Dec.\r\n1999.\r\n[19] A. P. Georgopolous, G. Pellizzer, A. V. Poliakov and M.\r\nH. Schieber, \\Neural coding of \fnger and wrist movements,\" Journal of Computational Neuroscience, vol. 6,\r\nno. 3, pp. 279{288, May 1999.\r\n[20] M. N. Shadlen and W. T. Newsome, \\The variable discharge implications for connectivity, computation and information coding,\" Journal of Neuroscience, vol. 18,\r\npp. 3870{3896, 1998.\r\n[21] J. G. Skellam, \\The frequency distribution of the difference between two Poissn variables belonging to di\u000berent populations,\" Journal of the Royal Statistical Society:\r\nSereis A, vol. 109, no. 3 pp. 296, 1946.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 35, 2009"}