A New LQR Optimal Control for a Single-Link Flexible Joint Robot Manipulator Based on Grey Wolf Optimizer

Razmjooy, Navid; Ramezani, Mehdi; Namadchian, Ali

Document Type : Review Article

Authors

¹ Department of Electrical Engineering, University of Tafresh, Tafresh, Iran.

² Department of Mathematics, University of Tafresh, Tafresh, Iran.

Abstract

Flexible manipulators are very commonly used in industries. In this paper a single-link flexible joint robot is modeled firstly by using Euler–Lagrange energy equation. An optimized Linear Quadratic Regulator is employed to control the manipulator. After that, a Linear Quadratic Regulator (LQR) controller is used for optimal control of the manipulator. For optimizing the LQR, the regulator term weighting of the LQR is achieved by using the newly introduced grey wolf optimizer technique. With the optimized LQR controller based on the proposed performance index, it is tried to have a system with the minimum overshoot and settling time. By considering the proposed performance index and comparing with the PSO-based controller as a popular algorithm, the superiority of the proposed LQR controller in improving the stability and performance of the manipulator is shown. The simulations are performed in MATLAB environment and the results confirm the efficiency of the proposed controller.

Keywords

References

[1] Rivin, Eugene I. Mechanical design of robots, McGraw-Hill, Inc., 1987.

[2] Kelly, Rafael, Victor Santibañez Davila, and Julio Antonio Loria Perez, “Control of robot manipulators in joint space,” Springer Science & Business Media, 2006.

[3] Eppinger, Steven D., and Warren P. Seering. “Three dynamic problems in robot force control,” in Proc. IEEE International Conference on Robotics and Automation, 1989.

[4] Ortega, Romeo, Rafael Kelly, and Antonio Loria, “A class of output feedback globally stabilizing controllers for flexible joints robots.” IEEE Trans. robotics and automation. Vol. 11, no. 5, pp. 766-770, 1995.

[5] Tomei, Patrizio. “A simple PD controller for robots with elastic joints.” IEEE Trans. Automatic Control, vol. 36, no. 10, pp. 1208-1213, 1991.

[6] Ulrich, S. and Sasiadek, J.Z., “Modeling and direct adaptive control of a flexible-joint manipulator”, Journal of Guidance, Control, and Dynamics, vol. 35, no. 1, pp. 25–39, 2012.

[7] Ailon, A. and Ortega, R., “An observer-based set-point controller for robot manipulators with flexible joints,” Systems and Control Letters, vol. 21, pp. 329–335, 1993.

[8] Aldu-Schäffer, A., Ott, C. and Hirzinger, G., “A unified passivity-based framework for position, torque and impedance control of flexible joint robots,” The International Journal of Robotics Research, vol. 26, no. 1, pp. 23–39, 2007.

[9] Ozgoli, S., and H. D. Taghirad, “A survey on the control of flexible joint robots,” Asian Journal of Control, vol. 8, no.4, pp. 332-344, 2006.

[10] Wang, W.S. and C.H. Liu, “Implementation of H2 Optimal Controller for a Single Link FJR,” in Proc. 1990 IEEE Int. Conf. Rob. Autom., Site??, pp. ??, 1990.

[11] Lin, L.C. and K. Yuan, “Control of FJRs via External Linearization Approach,” J. Rob. Syst., 1990.

[12] Berger, R.M. and H.A. ElMaraghy, “Feedback Linearization Control of Flexible Joint Robots,” Rob. Comput. Integr. Manuf., vol. 9 (3), pp. 239-246, 1992.

[13] Huang, A.C. and Y.C. Chen, “Adaptive Sliding Control for Single-Link Flexible-Joint Robot with Mismatched Uncertainties,” IEEE Trans. Contr. Syst. Technol., vol. 12, no. 5, pp. 770-776, 2004.

[14] Taghirad, H.D. and Gh. Bakhshi, “Composite Hinf Controller Sythesis for FJRs,” In Proc. 2002 IEEE Int. Conf. Intell. Rob. Syst., IROS’02, pp. 2073-2078.

[15] Ozgoli, S. and H.D. Taghirad, “Robust Controller for Flexible Joint Robot Using H2/H∞ and Mixed Sensitivity Approaches,” Iranian Int. Seminar Mech. Eng., Isfahan, Iran,2005.

[16] Drapeau V., Wang D. “Verification of a closed-loop shaped-input controller for a five-bar-linkage manipulator,” in Proc. 1993 IEEE International Conference on Robotics and Automation, pp. 216-221.

[17] Akyuz IH, Yolacan E, Ertunc HM, Bingul Z. “PID and state feedback control of a single-link flexible joint robot manipulator,” in Proc. 2011 IEEE International Conference Mechatronics (ICM), pp. 409-414.

[18] Issai Schur, “Neue Begründung der Theorie der Gruppencharaktere,” Neue begründung der theorie der gruppencharaktere, pp. 406-432.

[19] Golub, G. H. and Van Loan, C. F. “Matrix Computations,” 3rd ed., Baltimore, MD: Johns Hopkins University Press, 1996, pp. 312-314.

[20] Schur, I. “On the Characteristic Roots of a Linear Substitution with an Application to the Theory of Integral Equations,” Math. Ann., vol. 66, pp. 488-510, 1909.

[21] Razmjooy, Navid, Ali Madadi, Hamid-Reza Alikhani, and Mahmood Mohseni. “Comparison of LQR and Pole Placement Design Controllers for Controlling the Inverted Pendulum,” Journal of World’s Electrical Engineering and Technology vol. 2322 (2014): p.5114.

[22] Kobayashi, Iwase, Suzuki, Furuta. “Swinging-up and Balancing Control of Double Fututa Pendulum by Using State-Dependent Riccati Equation. Graduate School of Systems Engineering,” Tokyo Denki University.

[23] Razmjooy, Navid, Mohsen Khalilpour, and Mehdi Ramezani. “A New Meta-Heuristic Optimization Algorithm Inspired by FIFA World Cup Competitions: Theory and Its Application in PID Designing for AVR System,” Journal of Control, Automation and Electrical Systems, vol.27, no.4, pp. 349-472, 2016.

[24] Kennedy J. and Eberhart R, “Particle swarm optimization,” in Proc. 1995 IEEE Int. Conf. Neural Networks, vol. 4, pp. 1942-1948, 1995.

[25] Mirjalili, Seyedali, Seyed Mohammad Mirjalili, and Andrew Lewis. “Grey wolf optimizer,” Advances in Engineering Software, vol. 69, pp. 46-61, 2014.

[26] Zitzler, Eckart, and Simon Künzli. “Indicator-based selection in multiobjective search,” In 2004 International Conference on Parallel Problem Solving from Nature, pp. 832-842 Springer Berlin Heidelberg.

Majlesi Journal of Electrical Engineering

A New LQR Optimal Control for a Single-Link Flexible Joint Robot Manipulator Based on Grey Wolf Optimizer

References

References

Volume 10, Issue 3 - Serial Number 3
September 2016

A New LQR Optimal Control for a Single-Link Flexible Joint Robot Manipulator Based on Grey Wolf Optimizer

References

References

Volume 10, Issue 3 - Serial Number 3September 2016

Volume 10, Issue 3 - Serial Number 3
September 2016