Abstract
This paper focuses on the uncertainty bound parameter (UBP) to design the robust control of electrical manipulators. The UBP is commonly obtained by considering the worst case of uncertainties in bounding functions. However, too high estimation of UBP may cause saturation of input, higher frequency of chattering in the switching control laws, and thus a bad behavior of the whole system, while too low estimation of UBP may cause a higher tracking error. A proper UBP is preferred to improve the performance of robust control system. A simple, less dependent and proper UBP is proposed based on the nominal model of electrical manipulator and feedbacks of joint accelerations. This work is motivated by recent experimental results in measuring acceleration by optical encoder. Modeling of an electrical manipulator with presence of uncertainties is presented for control purposes. The proposed robust control is justified by stability analysis.
Similar content being viewed by others
References
Abdallah, C., Dawson, D., Dorato, P., Jamshidi, M.: Survey of robust control for rigid robots. IEEE Control Syst. Mag. 11, 24–30 (1991)
Corless, M.J.: Control of uncertain nonlinear systems. ASME Trans. J. Dyn. Syst. Meas. Control 115(2B), 362–372 (1993)
Qu, Z., Dawson, D.M.: Robust Tracking Control of Robot Manipulators. IEEE Press, New York (1996)
Sage, H.G., De Mathelin, M.F., Ostertag, E.: Robust control of robot manipulators: a survey. Int. J. Control 72(16), 1498–1522 (1999)
Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice Hall International, Englewood Cliffs (1991)
Liu, C., Cheah, C.C., Slotine, J.J.E.: Adaptive Jacobian tracking control of rigid-link electrically driven robots based on visual task-space information. Automatica 42, 1491–1501 (2006)
Fateh, M.M.: On the voltage-based control of robot manipulators. Int. J. Control Autom. Syst. 6(5), 702–712 (2008)
Corless, M., Leitmann, G.: Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamics systems. IEEE Trans. Autom. Control 26, 1139–1144 (1981)
Leitmann, G.: On the efficacy of nonlinear control in uncertain linear systems. ASME Trans. J. Dyn. Syst. Meas. Control 102, 95–102 (1981)
Spong, M.W.: Motion control of robot manipulators. In: Handbook of Control, pp. 1339–1350. CRC Press, Boca Raton (1996)
Spong, M.W.: On the robust control of robot manipulators. IEEE Trans. Automat. Control 37, 1782–1786 (1992)
Torres, S., Mendez, J.A., Acosta, L., Becerra, V.M.: On improving the performance in robust controllers for robot manipulators with parametric disturbances. Control Eng. Pract. 15, 557–566 (2007)
Burkan, R., Uzmay, I.: Upper bounding estimation for robustness to the parameter uncertainty in trajectory control of robot arm. Robot. Autonom. Syst. 45, 99–110 (2003)
Dawson, D.M., Qu, Z., Carroll, J.J.: Tracking control of rigid link electrically-driven robot manipulators. Int. J. Control 56, 991–1006 (1992)
Miro, J.V., White, A.S.: Modelling an industrial manipulator a case study. Simul. Pract. Theory 9, 293–319 (2002)
Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modelling and Control. Wiley, New York (2006)
Klafter, R.D., Chmielewski, T.A., Negin, M.: Robotic Engineering: An Integrated Approach. Prentice-Hall, New York (1989)
Jaritz, A., Spong, M.W.: An experimental comparison of robust control algorithms on a direct drive manipulator. IEEE Trans. Control Syst. Technol. 6(4), 627–640 (1996)
Mcinroy, J.E., Saridis, G.N.: Acceleration and torque feedback for robotic control: experimental results. J. Robot. Syst. 7, 813–832 (1990)
Dumetz, E., Dieulot, J.Y., Barre, P.J., Colas, F., Delplace, T.: Control of an industrial robot using acceleration feedback. J. Intell. Robot. Syst. 46, 111–128 (2006)
Tsuji, T., Kobayashi, H.: Robust acceleration control based on acceleration measurement using optical encoder. In: IEEE International Symposium on Industrial Electronics, 4–7 June 2007, Vigo, Spain, pp. 3108–3113 (2007)
Tsuji, T., Mizuochi, M., Nishi, H., Ohnishi, K.: A velocity measurement method for acceleration control. In: Proceedings of International Conference on Industrial Electronics, Control and Instrumentation, pp. 1943–1948 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fateh, M.M. Proper uncertainty bound parameter to robust control of electrical manipulators using nominal model. Nonlinear Dyn 61, 655–666 (2010). https://doi.org/10.1007/s11071-010-9677-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-010-9677-7