In this work, we establish a convenient similarity between an adaptive backstepping control law and a standard proportional-integral-derivative (PID) controller for a class of second-order systems. The extracted similarity provides a deeper understanding of the adaptive backstepping design from a performance perspective via an intuitive method to select its otherwise abstract controller gains, on top of its traditional stability perspective. Such a similarity analysis opens the door for researchers to use well-established PID tuning methods to predict the performance of Lyapunov stability-based controllers. At the same time, the obtained formulation reveals how the corresponding PID control law can be linked to Lyapunov stability theory.

中文翻译：

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利用 PID 增益选择实现一类二阶系统的自适应反步控制

在这项工作中，我们为一类二阶系统建立了自适应反步控制律和标准比例积分微分 (PID) 控制器之间的便利相似性。提取的相似性通过直观的方法从性能角度提供了对自适应反推设计的更深入理解，以选择其在传统稳定性角度之上的抽象控制器增益。这种相似性分析为研究人员使用完善的 PID 调整方法来预测基于 Lyapunov 稳定性的控制器的性能打开了大门。同时，获得的公式揭示了相应的 PID 控制律如何与李雅普诺夫稳定性理论相关联。