Limit Cycle Generation by Inducing the Controllable Hopf Bifurcation
摘要
This work presents a methodology for the design of a controller that induces the normal form of the controllable Hopf bifurcation on a class of nonlinear second-order differential equations in order to endow the system with limit cycles of desired amplitude and frequency. The controller is designed as a vector function for its state-space representation, and the equivalent scalar function controller for the differential equation is derived. The controller design is implemented as a circuit, and the performance of the design is verified.