Oscillator control based on energy feedback

Oscillations and waves are important phenomena that are encountered in many different areas of physics. An oscillation is a disturbance in a physical system that is repetitive in time. A wave is a disturbance in an extended physical system that is both repetitive in time and periodic in space. In general, an oscillation involves a continuous back and forth flow of energy between two different energy types: e.g., kinetic and potential energy, in the case of a mechanical systems. Oscillatory behaviors are often found in the life sciences too; these include the beats of the heart, and the oscillations of the membrane potential in the axons of the neurons, among many others. A wave involves similar repetitive energy flows to an oscillation, but, in addition, is capable of transmitting energy and information from place to place. The study of the dynamical behavior of oscillating systems, oscillators for short, is therefore a central issue in physics and in mathematics. Then, these sciences provide basic and general results that found major applications not only in physics, but also in all the other branches of science, as well as in technology. In this paper a new design method based on state energy concept is proposed. It is shown that linear system controlled by a linear controller with energy feedback can generate required types of signals. Depending on parameters of the controller the generated output signal can be harmonic, quasi-periodic or even chaotic.