基于微分平坦的旋转倒立摆双闭环抗扰 PID 控制
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TP13 TH701

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福建省自然科学基金(2019J01053,2022J01295)项目资助


Design and analysis of disturbance rejection PID control for the rotary inverted pendulum system based on differential flatness theory
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    摘要:

    针对一类不稳定、欠驱动二自由度旋转倒立摆系统, 提出一种基于微分平坦的双闭环抗扰 PID 控制方法。 首先, 建立倒 立摆的非线性动力学模型, 利用近似线性化分析系统的不稳定零动态与非最小相位特性; 然后, 结合微分平坦理论, 设计倒立摆 平坦输出,重构系统平坦状态, 并建立平坦状态与角度输出之间的转化关系,克服倒立摆的非最小相位影响; 进一步, 针对微分 平坦系统, 设计抗扰 PID 双闭环控制结构和带宽化调节方法, 在主动抗扰机制下实现对摆杆角度与悬臂角度的精准控制; 最后, 通过仿真与实验, 验证所提方法的有效性和实用性。 所提方法为欠驱动系统提供了一种结构简单、抗扰能力强的控制方案。

    Abstract:

    Considering an unstable and under-actuated two-degree-freedom rotary inverted pendulum system, this article proposes a double closed-loop disturbance rejection PID control method based on differential flatness theory. Firstly, a nonlinear dynamic model is formulated for the rotating inverted pendulum. The unstable zero-dynamics and non-minimum phase properties have been analyzed by the approximate linearization method. Then, the differential flatness theory is used to design flat output and derive state reconstruction. The relationship between the flat state and the angle out is established. In this way, the non-minimum phase can be removed by flatness transformation. The disturbance rejection PID control is developed for the designed flatness system with a dual closed-loop and the bandwidth tuning method is also derived. The two angles of the rotary inverted pendulum are controlled precisely based on active disturbance rejection mechanism. Finally, simulation and experiment are implemented to illustrate the effectiveness of the proposed method, which provides a simple and robust control scheme for underactuated systems.

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程 前,李赫然,聂卓赟,邵 辉,郑义民.基于微分平坦的旋转倒立摆双闭环抗扰 PID 控制[J].仪器仪表学报,2022,43(9):284-291

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  • 在线发布日期: 2023-02-06
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