Prediction of limit cycles in nonlinear systems with reset controllers using describing function

In nonlinear systems, limit cycles may exsist in some's parameters and may cause some unexpected damage. This paper proposes a design method of a reset controller for the Reset control of limit cycles. We consider a plant consisting of a linear system with a nonlinear feedback element and show a condition of the parameter for which limit cycles exists, using describing functions of the nonlinear element and the reset controller. The adjustable parameter of the reset controller is determined by the intersection of the inverse Nyquist locus of the linear system and the existence region of the limit cycles on the complex plain. We apply the proposed design method of the reset controller to the van der Pol equation and show its effectiveness.