A procedure for an "upgrade" of a linear PID controller to a non-linear homogeneous one is developed and verified by real experiments with quadrotor. The controller design is based on a generalized homogeneity (dilation symmetry) of the system. Its parameters are obtained from the gains of linear controller. The issues of digital implementation of the proposed controller are discussed. Finally, the stability and robustness properties of the homogeneous PID controller are validated on the quadrotor QDrone platform of Quanser .

中文翻译：

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线性控制器的广义同质化：理论与实验

开发了一种将线性 PID 控制器“升级”为非线性齐次控制器的程序，并通过四旋翼的实际实验进行了验证。控制器设计基于系统的广义同质性（膨胀对称性）。它的参数是从线性控制器的增益中获得的。讨论了所提出的控制器的数字实现问题。最后，在 Quanser 的四旋翼 QDrone 平台上验证了齐次 PID 控制器的稳定性和鲁棒性。