Optimal Design of LQR Controller for Single Inverted Pendulum

Abstract:

Aiming to the multi-variable, non-linear, high-order, close coupled, inverted pendulum system, a mathematical model of the inverted pendulum was established. The LQR controller was put forwards according to this model. In the LQR controller, the selection of the weight matrix Q and R directly impact on structural dynamic response and controlling force. How to determine the optimal Q and R to obtain the global optimal control is still a problem. The matrix Q and R were optimized based on genetic algorithm with different objective functions and the results were verified here. The simulation results show that the optimal preference weighting coefficient were obtained by genetic algorithm and the satisfactory factors can be selected by the designer according to the preference, while the subjectivity and blindness of the conventional method have been overcame.

• Periodical: Advanced Materials Research (Volumes 472-475)
• Pages: 1505-1509
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.472-475.1505
• Online since: February 2012
• Authors: Yong Peng, Zhi Neng Liu
• Keywords: Genetic Algorithm (GA), LQR Controller, Optimization, Single Inverted Pendulum

References

[1] Ziegler,J. G.,Nichols N.B. Optimum setting for automatic controllers [J] .ASME Trans, 1942, 64 (8) :759~768 .

[2] Y.B He,H.Zhaoy,Y.zhu. Neural network self-learning variable-robustness adaptive tracking control for eleetro-hydraulic servo system .3nd International SymPosiumon Test and Measurement. Xi'an. June 1999, :265-268 .

[3] CHANG C S,XU D Y,QUEK H B. Pareto-optimal setbased multiobjective tuning of fuzzy automatic train opera-tion for mass transit system[C] .IEE Proceedings on Elec-tric Power Applications. London: IEE, 1999, :577-583 .

DOI: 10.1049/ip-epa:19990481

[4] X.huan,X.Xia. Speed regulation with measured output feedback in the control of heavy haul .Elsevier Ltd, 2007, :242-247 .

[5] Kim Min Young,Lee Chung-Oh. An experimental study onthe optimization of controller gains for an electro-hydraulicservo system using evolution strategies[J] .Control Engi-neering Practice, 2006, 43 (14) :137-147 .

DOI: 10.1016/j.conengprac.2005.01.010

[6] Hiroshi Wakuya,Yoichiro Sankai,Yuzuru Morita. Sea-sonal variation of euro-controller training period observed in the control task of inverted pendulum[C] .Interna-tional Congress Series. 2007, :114-118 .

DOI: 10.1016/j.ics.2006.12.007

[7] Yasar Becerikli,B Koray Celik. Fuzzy Control of Inverted Pendulum and Concept of Stability Using Java Application[J] .Mathematical and Computer Modelling, 2007, (46) :24～37 .

DOI: 10.1016/j.mcm.2006.12.004

[8] B.Srinivasan,P.Huguenin,D.Bonvin. Global stabilization of an inverted pendulum-Control strategy and experimental verification .Artomatica, 2008, (7) :1-5 .

DOI: 10.1016/j.automatica.2008.07.004

[9] Jenkins W M. Plane frame optimum design environment based on genetic algorithm .J. Struct. Engng. ASCE, 1992, 118 (11) :3103-3112 .

DOI: 10.1061/(asce)0733-9445(1992)118:11(3103)

[10] Kirkpatrick S, Gelatt CD Jr, Vecchi MP. Optimization by simulated annealing .Science, 1983, 220 (4598) :671-680 .

DOI: 10.1126/science.220.4598.671

[11] R. Hinterding. Gaussian Mutation and Self-adaption for Numeric Genetic Algorithms .Proceedings of the 1995 IEEE International Conference on Evolutionary Computation. November29-December1,1995, :384-389 .

DOI: 10.1109/icec.1995.489178