On the Feasibility of Self-Powered Linear Feedback Control

A control system is called
self-powered
if the only energy it requires for operation is that which it absorbs from the plant. For a linear feedback law to be feasible for a self-powered control system, its feedback signal must be colocated with the control inputs, and its input–output mapping must satisfy an associated passivity constraint. The imposition of such a feedback law can be viewed equivalently as the imposition of a linear passive shunt admittance at the actuation ports of the plant. In this article, we consider the use of actively-controlled electronics to impose a self-powered linear feedback law. To be feasible, it is insufficient that the imposed admittance be passive, because parasitic losses must additionally be overcome. We derive sufficient feasibility conditions, which explicitly account for these losses. In the finite-dimensional, time-invariant case, the feasibility condition distills to a more conservative version of the positive-real lemma, which is parametrized by various loss parameters. Three examples are given, in which this condition is used to determine the least-efficient loss parameters necessary to realize a desired feedback law.