Can simple systems be regulated by simple controllers? Engineering experience indicates that this is often the case. Certainly, the overwhelming majority of industrially deployed controllers are proportional-integral-derivative (PID) controllers, many of which are tuned without detailed models. This is often in disappointing contrast with the controllers produced using model-based approaches. This article takes a slightly different approach. (For a nontechnical summary of the approach taken in this article, see “Nontechnical Summary.”) Rather than imposing structural constraints on the controller (which is difficult and diminishes the level of achievable performance), we instead look for structural features in system models that naturally yield simpler optimal controllers. This is similar in philosophy to the work of [7], in which the property of spatial invariance is shown to simplify the realization and synthesis of optimal controllers for a class of optimal control problems. However, rather than using spatial invariance to define the notion of a “simple system,” we instead turn to passivity and reciprocity.

中文翻译：

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无源互易网络：从简单模型到简单最优控制器


简单的系统可以用简单的控制器来调节吗？工程经验表明这种情况经常发生。当然，绝大多数工业部署的控制器都是比例积分微分 (PID) 控制器，其中许多控制器是在没有详细模型的情况下进行调整的。这通常与使用基于模型的方法生成的控制器形成令人失望的对比。本文采用了略有不同的方法。 （有关本文所采用方法的非技术摘要，请参阅“非技术摘要”。）我们不是对控制器施加结构约束（这很困难并且会降低可实现的性能水平），而是在系统模型中寻找结构特征这自然会产生更简单的最优控制器。这在原理上类似于[7]的工作，其中空间不变性的性质被证明可以简化一类最优控制问题的最优控制器的实现和综合。然而，我们没有使用空间不变性来定义“简单系统”的概念，而是转向被动性和互惠性。