Equations with Advanced Arguments in Stick Balancing Models

机译：杆平衡模型中带有高级参数的方程

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A stick balancing problem is considered, where the output for the feedback controller is provided by an accelerometer attached to the stick. This output is a linear combination of the stick's angular displacement and its angular acceleration. If the output is fed back in a PD controller with feedback delay, then the governing equation of motion is an advanced functional differential equation, since the third derivative of the angular displacement (the angular jerk) appears with a delayed argument through the derivative term. Equations with advanced arguments are typically non-causal and are unstable with infinitely many unstable poles. It is shown that the sampling of the controller may still stabilize the system in spite of its advanced nature. In the paper, different models for stick balancing are considered and discussed by analyzing the corresponding stability diagrams.

机译：考虑到杆平衡问题，其中反馈控制器的输出由连接到杆的加速度计提供。该输出是杆的角位移及其角加速度的线性组合。如果在具有反馈延迟的PD控制器中反馈输出，则运动的控制方程式是高级功能微分方程式，因为角位移的三阶导数（角加速度）出现在通过导数项的延迟参数上。具有高级自变量的方程式通常是非因果的，并且在具有多个不稳定极点的情况下是不稳定的。结果表明，尽管控制器具有先进性，但采样仍可以使系统稳定。在本文中，通过分析相应的稳定性图，考虑并讨论了用于杆平衡的不同模型。

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《Time delay systems: methods, applications and new trends》|2010年|p.161-172|共12页
会议地点 Prague(CZ);Sinaia(RO)
作者
Tamas Insperger; Richard Wohlfart; Janos Turi; Gabor Stepan;
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作者单位

Budapest University of Technology and Economics, Department of Applied Mechanics,Budapest, Hungary;

Budapest University of Technology and Economics, Department of Applied Mechanics,Budapest, Hungary;

Programs in Mathematical Sciences, University of Texas at Dallas, Richardson, TX, USA;

Budapest University of Technology and Economics, Department of Applied Mechanics,Budapest, Hungary;

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正文语种 eng
中图分类时间与频率计量;
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Equations with Advanced Arguments in Stick Balancing Models

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