VIBRATION CONTROL OF A CLASS OF GENERALIZED GRADIENT SYSTEMS

The suppression of oscillations in a class of generalized gradient systems using nonlinear dynamic output feedback is investigated. A class of controllers is considered which, in addition to a linear dynamic component, possess several types of nondynamic nonlinearities. Frequency domain conditions on the transfer matrix of the controller's linear component are presented that ensure the convergence of all closed-loop solutions to an equilibrium point in state space, thus eliminating the occurrence of sustained oscillations. Practically important technical applications include a.o. the set point control of mechanical systems described by the Euler–Lagrange equations and their equivalent Hamiltonian formulation. The obtained results constitute a systems theoretical basis for a new method of nonlinear vibration controller design.