Oscillations of nonlinear multivariable feedback systems: A center manifold/normal form approach

Center manifolds and normal forms (CM/NF) of ordinary differential equations are applied to the oscillation analysis of multivariable feedback systems. The oscillations are regarded as being generated by a bifurcation. General bifurcations can be considered by the proposed approach, however, special emphasis is given to the monoharmonic case (Hopf bifurcation). A computer oriented recursive procedure for obtaining arbitrarily high order approximations is proposed. A frequency domain formulation is shown to be possible for lower order approximations. Compared to harmonic balance or describing function, the CM/NF approach gives as an additional information, the transient behaviour of the system.