Energy efficiency of pulsed actuations on linear resonators

Abstract

The objective of this paper is to show that under some circumstances, the sign of a sampled sinusoid sequences, briefly, is optimal to provide maximum energy transfer to linear resonators in the context of discrete-time pulsed actuation at periodic times with bounded sequences. It will be proven that there is an optimal sequence which maximizes the resonator amplitude at any given finite time, and that under some conditions, there is a sufficiently high time above which any sequence at the resonant frequency of the resonator also provides a locally unique maximum, in the case of a lossless or leaky resonator. The tool used to prove this last result is a theorem of quadratic programming. Since pulsed digital oscillators (PDOs) under certain conditions produce sequences, a variation of the standard PDO topology that simplifies these conditions is also proposed. It is proved that except for a set of initial conditions of the resonator of zero Lebesgue measure, the bitstream at the output of this topology produces a locally unique maximum in the total energy transferred to the resonator.