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

摘要

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.