Design, Control, and Analysis of Nonlinear Circuits with Tunnel Diode with Piecewise Affine Dynamics

抄録

A classic example of dynamic systems with nonlinearities is considered, using an electrical circuit including the tunnel diode, that features several equilibria points due to a piecewise positive and negative damping. These system-properties allow us to investigate the possible limit cycles, and the formal analysis of the closed-loop dynamics of such. In this paper, an experimental setup of nonlinear circuits is designed, followed by the system modeling and identification of the diodes' characteristics. An integral-state-feedback control is designed and evaluated for demonstrating the appearance of the limit cycles depending on the reference level. A piecewise affine (PWA) system formulation is also provided for allowing the use of formal verification tools for hybrid dynamic systems. An available tool, PWLTool, is applied in line with trajectory prediction from the numerical simulation of the identified closed-loop system.