On the Stability of Electromechanical Switching Devices

Electromagnetic relays and solenoid actuators are commonly used for their bistable behavior, which allows for switching between two states in electrical, pneumatic, or hydraulic circuits, among other applications. Although there has been extensive research on modeling, estimation, and control of these electromechanical systems, a gap remains in the analysis area. This paper addresses this gap by presenting an equilibrium and stability analysis to gain deeper insight into their bistability. This analysis leverages a hybrid dynamical model to obtain analytical expressions that relate the physical parameters to the switching conditions. These expressions are useful, e.g., for fundamental understanding, quick analyses, or design optimization. The results are discussed in depth and potential practical applications are explored. Finally, the analysis is validated with experimental results from a real device.