Abstract In this brief note we pose, and solve, the problem of robustification of controller designs where the actuator dynamics was neglected. This situation is very common in applications where, to validate the assumption that the actuator dynamics can be neglected, a high-gain inner-loop that enforces a time-scale separation between the actuator and the plant dynamics is implemented. Of course, the injection of the high-gain has well-known deleterious effects. Moreover, a stability, and robustness, analysis of such a control configuration is usually unavailable. Our first main contribution is to provide an alternative to such a scheme, with provable robust stability properties. The second contribution is to, applying this result, propose a robustification procedure to the industry standard field-oriented control of current-fed induction motors, which is usually implemented neglecting the actuator dynamics, with no rigorous proof of stability available to date. Finally, we propose the first solution of smooth, time-invariant regulation of the dynamic model of a class of nonholonomic systems, that includes the widely popular unicycle example. Simulation examples prove the superior performance of the proposed controller compared with the existing switching and/or time-varying alternatives reported in the literature.

中文翻译：

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非线性控制系统相对于执行器动力学的鲁棒化：浸入式和不变性方法

摘要 在这篇简短的笔记中，我们提出并解决了忽略执行器动力学的控制器设计的鲁棒性问题。这种情况在应用中非常常见，为了验证可以忽略执行器动力学的假设，实施了一个高增益内环，强制执行器和设备动力学之间的时间尺度分离。当然，高增益的注入具有众所周知的有害影响。此外，通常无法对这种控制配置进行稳定性和稳健性分析。我们的第一个主要贡献是提供这种方案的替代方案，具有可证明的稳健稳定性特性。第二个贡献是，应用这一结果，提出了一种针对电流馈送感应电机的工业标准磁场定向控制的鲁棒性程序，这通常是在忽略执行器动力学的情况下实现的，迄今为止没有严格的稳定性证明。最后，我们提出了一类非完整系统的动态模型的平滑、时不变调节的第一个解决方案，其中包括广泛流行的独轮车示例。与文献中报道的现有切换和/或时变替代方案相比，仿真示例证明了所提出的控制器的优越性能。