Necessary Conditions for Feasibility of Linear, Time-Invariant Self-Powered Feedback Control Laws

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. In this paper we consider the use of actively-controlled electronics to impose a self-powered linear feedback law. In this case, the feasibility of a linear feedback law must account for parasitic losses in the electronics and energy storage system. For the case in which the feedback law is linear and time-invariant, this paper derives necessary feasibility conditions which explicitly account for these losses. This feasibility condition is then illustrated in a simple example.