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Nonlinear control of triple inverted pendulum based on GA–PIDNN

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Abstract

The triple inverted pendulum is a nonlinear, dynamic and unsteady system. The traditional control methods of triple inverted pendulum have problems of limited control accuracy, slow responding. This kind of pendulum system is difficult to control due to the inherent instability, nonlinear behavior and difficultly in establishing a precise mathematical model. In addition, the back-propagation (BP) algorithm has the shortage of easy trapped in local minimum. The triple inverted pendulum control based on GA–PIDNN is proposed. The PID neural network (PIDNN) is a new kind of feedforward multi-layer network. Besides multi-layer forward networks traditional merit, such as approach the ability proceed together the calculation nonlinear transformation, its middle layer has the proportional (P) integral, (I) derivative, (D) dynamic characteristic. Genetic algorithm (GA) has good parallel design structure and characteristics of global optimization. The nonlinear identification model is established, and controller is designed via GA–PIDNN based on the combination of the merits GA and PIDNN in the research of triple inverted pendulum. In simulation, through the comparative study of GA–PIDNN and PIDNN optimized by BP (BP–PIDNN), simulations results show that GA is more accurate and effective.

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Authors and Affiliations

  1. Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, 066004, China

    Xiu-Ling Zhang, Hong-Min Fan, Jia-Yin Zang, Liang Zhao & Shuang Hao

  2. National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Qinhuangdao, 066004, China

    Xiu-Ling Zhang

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  1. Xiu-Ling Zhang
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  2. Hong-Min Fan
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  3. Jia-Yin Zang
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  4. Liang Zhao
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  5. Shuang Hao
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Correspondence to Xiu-Ling Zhang.

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Zhang, XL., Fan, HM., Zang, JY. et al. Nonlinear control of triple inverted pendulum based on GA–PIDNN. Nonlinear Dyn 79, 1185–1194 (2015). https://doi.org/10.1007/s11071-014-1735-0

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  • DOI: https://doi.org/10.1007/s11071-014-1735-0

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