A semilinear distributed parameter approach for solenoid valve control including saturation effects

In this paper a semilinear parabolic PDE for the control of solenoid valves is presented. The distributed parameter model of the cylinder becomes nonlinear by the inclusion of saturation effects due to the material´s B/H-curve. A flatness based solution of the semilinear PDE is shown as well as a convergence proof of its series solution. By numerical simulation results the adaptability of the approach is demonstrated, and differences between the linear and the nonlinear case are discussed. The major contribution of this paper is the inclusion of saturation effects into the magnetic field governing linear diffusion equation, and the development of a flatness based solution for the resulting semilinear PDE as an extension of previous works [1] and [2].