Controlling Regular and Chaotic Dynamics in the Duffing-Ueda Oscillator

This paper investigates the control of a forced nonlinear-oscillator which is composed of a series-connected resonant circuit with a nonlinear inductor commonly known as Duffing's oscillator. Two control strategies are suggested. The first is primarily concerned with suppressing chaos by means of adding an external weak force to the input driving the oscillator. The second procedure uses a reference model to produce appropriate reference, chaotic and nonchaotic signals for the the oscillator to track. It is shown that this control scheme is effective in both regulating and tracking problems. Although it is possible to disperse with the reference model in many applications, it is often highly desirable to obtain a model of the system. A practical and effective procedure for determining the model is therefore discussed. A discrete model of the oscillator, which had been previously obtained from the system with no prior information is used in several simulated examples provided to illustrate the main points of the paper.