Active control of nonlinear systems

Nonlinear systems do not obey the principle of superposition and would thus appear to be poor candidates for applying active control. Two classes of p roblem are considered for which active control can be usefully employed for nonlinear systems. In the first class the system under control is weakly n onlinear, often due to the nonlinearity of the actuator used to produce the secondary response. Such forms of nonlinearity can often be compensated fo r by pre-distortion in the control system, so that the output has the requi red waveform, and automatic methods of achieving such pre-distortion are di scussed for both tonal and random disturbances. Examples of the practical a pplication of these techniques include compressed-air loudspeakers and magn etostrictive vibration actuators. In the second class of problem, the nonli nearity generates the dominant part of the systems' response. A chaotic sys tem, for example, is extremely sensitive to small perturbations and this se nsitivity can be used to control the type of behaviour exhibited, using onl y very small control signals. A vibrating beam with a nonlinear stiffness i s used to illustrate various ways in which such control may be achieved. Th e ability of a control system to select between a rich variety of different behaviours encourages the hope that in some circumstances nonlinearity can be seen as a friend and not as an enemy. (C) 2001 Institute of Noise Contr ol Engineering.