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首页> 中文期刊> 《力学学报：英文版》 >Optimal feedback gains of a delayed proportional-derivative (PD) control for balancing an inverted pendulum

Optimal feedback gains of a delayed proportional-derivative (PD) control for balancing an inverted pendulum

         
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摘要

In the dynamics analysis and synthesis of a con-trolled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a sys-tematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost charac-teristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial val-ues around the origin are fixed. The main results are checked by numerical simulation.

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  • 来源
    《力学学报：英文版》 |2017年第003期|635-645|共11页
  • 作者

    Qiang Wang; Zaihua Wang;

  • 作者单位

    Institute of Science, PLA University of Science and Technology, Nanjing 211101, China;

    Institute of Science, PLA University of Science and Technology, Nanjing 211101, China;

    State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;

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  • 正文语种 eng
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