STEADY-STATE BEHAVIOR IN THE VIBRATIONAL CONTROL OF A CLASS OF NONLINEAR-SYSTEMS BY AP-FORCING

Vibrational control is an open-loop control technique that uses zero m ean parametric vibrations for shaping the response of a linear or nonl inear dynamical system. Several theoretical results are available, bas ed on averaging techniques, assuring the possibility of modifying the equilibrium properties of a system. For nonlinear systems, computation al difficulties arise and theoretical results cannot easily be applied . In this note, the stationary behavior of a class of nonlinear system s vibrationally controlled by AP-forcing is investigated. A practical formula linking the amplitude and the frequency of the vibration and t he amplitude of the steady-state oscillation in the controlled variabl e is obtained. As test cases, the well-known Rayleigh equation, a cata lytic reactor equation, and the phase locked loop equation are conside red.