Robust Adaptive Control of a Robotic Manipulator with Unknown Dead Zone and Friction Torques
The problem of controlling a two link robotic manipulator, consisting of a rotating and a prismatic links, is addressed. The actuations of both links are assumed to have unknown dead zone nonlinearities and friction torques modeled by LuGre friction model. Because of the existence of the unknown dead zone and friction torque at the actuations, unknown parameters and unmeasured states would appear to be part of the overall system dynamics that need for estimation. Unmeasured states observer, unknown parameters estimators, and robust adaptive control laws have been derived such that closed loop global stability is achieved. Simulation results have been performed to show the efficacy of the suggested approach.
[1] R. Johansson, "Quadratic optimization of motion coordination and
control ," IEEE Trans. on Automatic Control, vol. 35, no. 11, pp. 1197-
1208, November 1990.
[2] K. W, Lee, and, H. K. Khalil, " Adaptive output feedback control of robot
manipulators using high-gain observer," Int. J. Control, vol. 67, no. 6, pp.
869- 886, 1997.
[3] Y. C. Chang, and B. S. Cheng, "A nonlinear adaptive H Tracking control
design in robotic systems via neural networks," IEEE Trans. on Control
Systems Technology, vol. 5, no. 1, pp. 13-29, January 1997.
[4] Y. C. Chang, and B. S. Cheng, " A nonlinear adaptive H Tracking control
design in robotic systems via neural networks," IEEE Trans. on Control
Systems Technology, vol. 5, no. 1, pp. 13-29, January 1997.
[5] G. Tao, and P. V. Kokotovic, "Adaptive control of plants with unknown
dead zone ," IEEE Trans. on Automatic Control, vol. 39, no. 11, pp. 59-
68, November 1994.
[6] G. Tao, and P. V. Kokotovic, "Discrete- time adaptive control of plants
with unknown dead zone," Int. J. Control, vol. 61, pp. 1-17, 1995.
[7] H. Y. Cho, and E. W. Bai, "Convergence results for an adaptive dead
zone inverse," International Journal of Adaptive Control and Signal
Processing, 12, pp. 451- 466, 1998.
[8] F. L. Lewis, W. K. Tim, L. Z. Wang, and Z. X. Li, "Dead zone
compensation in motion control systems using adaptive fuzzy logic
control," IEEE Transactions on Control Systems Technology, Vol. 7, No.
6, pp. 731- 742, November, 1999.
[9] R. R. Selmic, and F. L. Lewis, "Dead zone compensation in motion
control systems using neural networks," IEEE Transactions on
Automatic Control, Vol. 45, No. 4, pp. 602- 613, April, 2000.
[10] S. X. Wang, C. Y.Su, and H.Y.Hong, "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, 2004.
[11] S. X. Wang, C. Y.Su, and H.Y. Hong, "Model reference adaptive control
of continuous-time systems with an unknown input dead zone," IEE
Proc. Control Theory Appl., 150, pp. 261- 266, 2003.
[12] S. X. Wang, C. Y.Su, and H.Y. Hong, "Robust adaptive control of a class
of nonlinear systems with unknown dead zone," Automatica, 40, pp.
407-413, 2004.
[13] J. Zhou, C. Wen, and Y. Zhang, "Adaptive output control of nonlinear
systems with uncertain dead zone nonlinearity," IEEE Transactions on
Automatic Control, Vol. 51, No. 3, pp. 504- 511, March, 2006.
[14] J. Zhou, and X. Z. Shen, "Robust adaptive control of nonlinear uncertain
plants with unknown dead zone," IET Control Theory Appl., Vol. 1,
No.1, pp. 25- 32, January, 2007.
[15] Y. Zhu, and P. R. Pagilla, "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, 2006.
[16] I. F. Jasim, "Stable robust adaptive controller and observer design for a
class of SISO nonlinear systems with unknown dead zone," World
Academy of Science, Engineering and Technology, vol. 59, pp. 209-215,
2009.
[17] C. C. Wit, H. Olsson, K. J. Astrom, and P. Lischinscky, "Dead zone
compensation in motion control systems using neural networks," A new
model for control of systems with friction," IEEE Trans. on Automatic
Control, vol. 40, no. 3, pp. 419-425, March 1995.
[18] D. Angeli, E. D. Sontag, and Y. Wang, "A characterization of input to
state stability," IEE Proc. Control Theory Appl., 150, pp. 261- 266, 2003.
[19] R. J. Schilling, "Fundamentals of robotics: analysis and control,"
Prentice-Hall, 1990.
[20] J.-J. E. Slotine, "Sliding Controller Design for Nonlinear Systems,"
International Journal of Control, vol. 40, pp. 435-448, 1984.J.-J. E.
Slotine, and J. A. Coetsee, "Adaptive Sliding Control Synthesis for
Nonlinear Systems," International Journal of Control, vol. 43, pp. 1631-
1651, 1986
[1] R. Johansson, "Quadratic optimization of motion coordination and
control ," IEEE Trans. on Automatic Control, vol. 35, no. 11, pp. 1197-
1208, November 1990.
[2] K. W, Lee, and, H. K. Khalil, " Adaptive output feedback control of robot
manipulators using high-gain observer," Int. J. Control, vol. 67, no. 6, pp.
869- 886, 1997.
[3] Y. C. Chang, and B. S. Cheng, "A nonlinear adaptive H Tracking control
design in robotic systems via neural networks," IEEE Trans. on Control
Systems Technology, vol. 5, no. 1, pp. 13-29, January 1997.
[4] Y. C. Chang, and B. S. Cheng, " A nonlinear adaptive H Tracking control
design in robotic systems via neural networks," IEEE Trans. on Control
Systems Technology, vol. 5, no. 1, pp. 13-29, January 1997.
[5] G. Tao, and P. V. Kokotovic, "Adaptive control of plants with unknown
dead zone ," IEEE Trans. on Automatic Control, vol. 39, no. 11, pp. 59-
68, November 1994.
[6] G. Tao, and P. V. Kokotovic, "Discrete- time adaptive control of plants
with unknown dead zone," Int. J. Control, vol. 61, pp. 1-17, 1995.
[7] H. Y. Cho, and E. W. Bai, "Convergence results for an adaptive dead
zone inverse," International Journal of Adaptive Control and Signal
Processing, 12, pp. 451- 466, 1998.
[8] F. L. Lewis, W. K. Tim, L. Z. Wang, and Z. X. Li, "Dead zone
compensation in motion control systems using adaptive fuzzy logic
control," IEEE Transactions on Control Systems Technology, Vol. 7, No.
6, pp. 731- 742, November, 1999.
[9] R. R. Selmic, and F. L. Lewis, "Dead zone compensation in motion
control systems using neural networks," IEEE Transactions on
Automatic Control, Vol. 45, No. 4, pp. 602- 613, April, 2000.
[10] S. X. Wang, C. Y.Su, and H.Y.Hong, "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, 2004.
[11] S. X. Wang, C. Y.Su, and H.Y. Hong, "Model reference adaptive control
of continuous-time systems with an unknown input dead zone," IEE
Proc. Control Theory Appl., 150, pp. 261- 266, 2003.
[12] S. X. Wang, C. Y.Su, and H.Y. Hong, "Robust adaptive control of a class
of nonlinear systems with unknown dead zone," Automatica, 40, pp.
407-413, 2004.
[13] J. Zhou, C. Wen, and Y. Zhang, "Adaptive output control of nonlinear
systems with uncertain dead zone nonlinearity," IEEE Transactions on
Automatic Control, Vol. 51, No. 3, pp. 504- 511, March, 2006.
[14] J. Zhou, and X. Z. Shen, "Robust adaptive control of nonlinear uncertain
plants with unknown dead zone," IET Control Theory Appl., Vol. 1,
No.1, pp. 25- 32, January, 2007.
[15] Y. Zhu, and P. R. Pagilla, "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, 2006.
[16] I. F. Jasim, "Stable robust adaptive controller and observer design for a
class of SISO nonlinear systems with unknown dead zone," World
Academy of Science, Engineering and Technology, vol. 59, pp. 209-215,
2009.
[17] C. C. Wit, H. Olsson, K. J. Astrom, and P. Lischinscky, "Dead zone
compensation in motion control systems using neural networks," A new
model for control of systems with friction," IEEE Trans. on Automatic
Control, vol. 40, no. 3, pp. 419-425, March 1995.
[18] D. Angeli, E. D. Sontag, and Y. Wang, "A characterization of input to
state stability," IEE Proc. Control Theory Appl., 150, pp. 261- 266, 2003.
[19] R. J. Schilling, "Fundamentals of robotics: analysis and control,"
Prentice-Hall, 1990.
[20] J.-J. E. Slotine, "Sliding Controller Design for Nonlinear Systems,"
International Journal of Control, vol. 40, pp. 435-448, 1984.J.-J. E.
Slotine, and J. A. Coetsee, "Adaptive Sliding Control Synthesis for
Nonlinear Systems," International Journal of Control, vol. 43, pp. 1631-
1651, 1986
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:59551", author = "Ibrahim F. Jasim and Najah F. Jasim", title = "Robust Adaptive Control of a Robotic Manipulator with Unknown Dead Zone and Friction Torques", abstract = "The problem of controlling a two link robotic manipulator, consisting of a rotating and a prismatic links, is addressed. The actuations of both links are assumed to have unknown dead zone nonlinearities and friction torques modeled by LuGre friction model. Because of the existence of the unknown dead zone and friction torque at the actuations, unknown parameters and unmeasured states would appear to be part of the overall system dynamics that need for estimation. Unmeasured states observer, unknown parameters estimators, and robust adaptive control laws have been derived such that closed loop global stability is achieved. Simulation results have been performed to show the efficacy of the suggested approach.
", keywords = "Adaptive Robust Control, Dead Zone, Friction Torques, Robotic Manipulators.", volume = "4", number = "8", pages = "681-8", }
