In this article, we develop proportional, fractional‐integral, and derivative () controllers for the regulation and tracking problems of nonlinear systems. The analytic results are obtained by extending the passivity‐based approach to include fractional operators. Robustness under parametric uncertainty is dealt with by a combination with an adaptive scheme. It is also shown their robustness under additive noise and their robustness under uncertainty in the derivation order. The advantages in the controlled system performance and in the control energy consumption in comparison to classic PI and proportional integral derivative controllers are illustrated for the quadratic boost converter and a benchmark system in the literature.

中文翻译：

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鲁棒的自适应无源PIλD控制

在本文中，我们开发了比例，分数-积分和微分（）控制器，用于非线性系统的调节和跟踪问题。通过将基于无源性的方法扩展为包括分数算符，可以获得分析结果。参数不确定性下的鲁棒性可通过与自适应方案相结合来解决。还显示了它们在加性噪声下的鲁棒性和在推导阶数不确定性下的鲁棒性。与经典的PI和比例积分微分控制器相比，在传统的PI和比例积分微分控制器中，在受控系统性能和控制能耗方面的优势已在文献中有所说明。