Optimal actuation of nonlinear resonant systems

In this study, we examine a new approach for actuation of dynamical systems with minimum work and maximum amplitude while maintaining constraints on the actuation force. Two methodology issues are addressed in the paper: sensitivity analysis about the nonlinear transient response and exploration of the strongly nonlinear relationship between the two objectives and the actuation design variables. The optimization analysis is carried out on lightly damped Duffing systems. The formulation of the optimization problem is found ideally suited to resolve the difficulty of dependence of response on initial conditions. The tradeoff curve of work and amplitude is computed. The optimal actuation strove to compensate for the limited force amplitude by an abrupt change in the force in time. Finally the optimization procedure is demonstrated on the kinematic design of hovering insect flight. The optimal design gives 50% reduction in power consumption, with a larger cutback for an actuation with high acceleration.