On the Stability of Electromechanical Switching Devices

Abstract

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.

Figures (10)

• Figure 1: Diagram of a single-coil c-core reluctance actuator.
• Figure 2: Hybrid automaton modeling the hybrid dynamics of a switching actuator. If the model equations do not include saturation, $\phi_\mathrm{sat}=\infty$.
• Figure 3: Basic model. Curves $f_v(x)=0$ and $f_\phi(x,u)=0$ in the $z$-$\phi$ plane for different values of $u$. As the absolute value of $u$ increases, the hyperbolas $f_\phi(x,u)=0$ move farther away from $f_\phi(x,0)=0$. Values outside the domain of the functions are shown in light gray.
• Figure 4: Basic model under continuous operation. Bifurcation diagram of equilibria in terms of $u$. Position (top) and magnetic flux (bottom). Stable/unstable equilibria are plotted with solid/dashed lines.
• Figure 5: Model with magnetic saturation. Curves $f_v(x)=0$ and $f_\phi(x,u)=0$ in the $z$-$\phi$ plane for different values of $u$. As the absolute value of $u$ increases, the curves $f_\phi(x,u)=0$ move farther away from $f_\phi(x,0)=0$. Values outside the domain of the functions are shown in light gray.