Quadratic controller for a chaotic micro-resonator

A model for a chaotic micro-oscillator is developed by adding a new control system to an electrostatic actuator consisting of two electrodes: the substrate and a cantilever beam on top. The electrostatic actuator itself has a single stable equilibrium over a range of voltage, whereas adding the controller, which has a quadratic function, creates a voltage range for bistability. The bi-stability represents a two well potential field that is used here to create chaos. The model of the beam actuator is a mathematical model of a continuous system with identified parameters from the experiments. The equations of motion are then descretized using the first mode shape of the beam and solved numerically to find the steady state oscillation. The range of the AC frequency and voltage excitation for sustained chaos creation is investigated through bifurcation diagrams which reveal two well chaos, periodic orbits and multiple periods. It is discovered that the proposed new controller has some important advantages over a previously introduced controller for creation of chaos. First, it has a simpler function making its implementation easier. Second, it has a larger bi-stability voltage range starting from zero that doubles the operating range for chaotic oscillation and decreases the actuation voltage by eleven times. At last but not least, the controller offers chaos in a three times wider AC voltage range than that of the previous controller.