Passive and Reciprocal Networks: From Simple Models to Simple Optimal Controllers

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 aNontechnical Summary.a) 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 asimple system,a we instead turn to passivity and reciprocity.