Multi-objective optimal tuning and performance comparison of the LQR controller for an underactuated motion control system with GA, ABC, VPS, and BB-BC algorithms
Abstract
The presented study is organized to provide details on the design and performance analysis of multi-objective optimization of LQR controller parameters for an underactuated motion (pendulum type gantry crane) system. The objective of the optimization is to design an LQR controller to eliminate pendulum oscillations caused by the motion of the system. In line with this objective, a new multi-objective function has been designed by considering the important parameters of control responses. The VPS and BB-BC algorithms have been utilized for the first time in the design and development of motion control for single pendulum gantry systems and compared with traditional GA and ABC algorithms. The six different populations or particle size values of GA, ABC, VPS, and BB BC algorithms were examined over 100 iterations to achieve the most successful optimization results. Furthermore, the configurations of the GA, ABC, VPS, and BB-BC algorithms yielding the best control performance were compared amongst themselves and against conventionally designed LQR controllers. Preliminary design findings indicated the elimination of steady-state error in the pendulum cart system, along with a considerable improvement of 51.54\% in settling time. Additionally, a substantial enhancement of up to 67.57\% was achieved in the settling time of the pendulum angle.
Keywords
multi-objective optimization, linear quadratic regulator, genetic algorithm, artificial bee colony, vibrating particles system algorithm, big bang-big crunch algorithm
References
- [1] Conker, C., Kilic, A., Mistikoglu, S., Kapucu, S. and Yavuz, H. An enhanced control technique for the elimination of residual vibrations in flexible-joint manipulators. Strojniški vestnikJournal of Mechanical Engineering, 60(9), 592-599, (2014).
- [2] Abdel-Rahman, E.M., Nayfeh, A.H. and Masoud, Z.N. Dynamics and control of cranes: A review. Journal of Vibration and Control, 9(7), 863-908, (2003).
- [3] Xie, X., Huang, J. and Liang, Z. Using continuous function to generate shaped command for vibration reduction. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 227(6), 523-528, (2013).
- [4] Conker, C., Yavuz, H. and Bilgic, H.H. A review of command shaping techniques for elimination of residual vibrations in flexible-joint manipulators. Journal of Vibroengineering, 18(5), 2947-2958, (2016).
- [5] Masoud, Z.N. and Nayfeh, A.H. Sway reduction on container cranes using delayed feedback controller. Nonlinear Dynamics, 34, 347-358, (2003).
- [6] Burul, I., Kolonic, F. and Matuško, J. The control system design of a gantry crane based on H∞ control theory. In Proceedings, The 33rd International Convention MIPRO, pp. 183-188, Opatija, Croatia, (2010, May).
- [7] Bakhtiari-Nejad, F., Nazemizadeh, M. and Arjmand, H. Tracking control of an underactuated gantry crane using an optimal feedback controller. International Journal of Automotive and Mechanical Engineering, 7, 830-839, (2013).
- [8] Ospina-Henao, P.A. and Lopez-Suspes, F. Dynamic analysis and control PID path of a model type gantry crane. In Proceedings, 5th Colombian Conference of Engineering Physics (V CNIF), pp. 26-30, Medellin, Colombia, (2016, September).
- [9] Fang, Y., Ma, B., Wang, P. and Zhang, X. A motion planning-based adaptive control method for an underactuated crane system. IEEE Transactions on Control Systems Technology, 20(1), 241-248, (2012).
- [10] Tuan, L.A., Moon, S.C., Lee, W.G. and Lee, S.G. Adaptive sliding mode control of overhead cranes with varying cable length. Journal of Mechanical Science and Technology, 27, 885-893, (2013).