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摘要: Pendubot是以电机转矩为输入，主动臂角度和欠驱动臂角度为输出的强非线性、多变量、欠驱动机械系统，受到具有时变不确定性的摩擦影响，且模型参数随摆臂质量与长度的改变而变化.本文将上述被控对象采用确定线性模型与未知高阶非线性项来描述，设计消除前一时刻高阶非线性项及其变化率对系统输出影响的补偿器，叠加于基于确定线性模型设计的PD控制器，提出了补偿信号法驱动的自适应平衡控制方法，并对所提方法进行了稳定性和收敛性分析.仿真和物理对比实验表明，当Pendubot系统模型参数改变时，所提控制算法可以有效地消除摩擦的影响，将两摆臂输出角度稳定在目标位置.Abstract: The Pendubot system is a strong nonlinear multivariable underactuated mechanical system with the motor torque as the input, angles of the actuated link and the underactuated link as outputs. The model parameters, such as the length of the link, the center of mass, change with the system mechanical structure. Moreover, the system is influenced by the friction, which is uncertain, nonlinear and time varying. In this paper, a novel compensation signal driven adaptive controller is developed by representing the controlled object as the combination of a determinate low-order linear model and unknown high-order nonlinear terms. In the proposed controller design, two compensation signals are constructed and added onto the control signal obtained from the linear deterministic model based PD control design. Such two compensation signals aim at eliminating the effects of the previous sample high-order nonlinearity and its changing rate, respectively. The performance analysis of the algorithm is given, and simulations and physical experiments are carried out, where it has been shown that the two output angles of the Pendubot can be stabilized at their targeted positions when the system is subjected to unknown variations of its parameters.1) 本文责任编委 梅生伟
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图 2 补偿信号法驱动的Pendubot自适应平衡控制结构图
Fig. 2 Structure diagram of Pendubot adaptive balance control using the compensation signal based approach
表 1 本文控制方法与文献[15]控制方法的性能指标
Table 1 Performance indexes of the control method in [15] and the proposed control method
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表 2 常规PD、文献[15]及本文控制方法的性能指标
Table 2 Performance indexes of the conventional PD method, the method in [15] and the proposed method
绝对误差累积和 误差均方差 常规PD 17 950.004 1.780 文献[15] 33 762.650 2.656 本文 11 233.987 1.762
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