Model-based control of solenoid actuators using flux channel reluctance models

Flatness-based state decomposition in magnetic flux-channel models for solenoid valve control

“…The approach is a reinterpretation of the flatness property equations (9) and (10). They are solved for the highest derivative, leading to (17) and (18). y,ẏ, ..., y (β1−1) ) Λ x2 (x 2 , y,ẏ, ..., y (β2−1) ) .…”

“…The input u or each state variable x 1 ...x n leads with (17) or (18) to the flat output y. Reversely, the flat output leads without integration to the input and the state variables (with (9) and (10)). Thus, each of those system parameters (the state variables and the input) carries the whole system's information.…”

“…A second drawback arises from eddy currents and field diffusion not properly represented in lumped parameter models. While finite element models are not suitable for optimizing control strategies due to computational burden, so-called fluxchannel models [13] [14] [15] [16] have been found to provide a good compromise between lumped parameter and finite element models [17]. There, it has also been shown that this type of model provide sufficient fidelity by using geometric dimensions and material properties without any tuning.…”

“…In this paper, the focus is put on a detailed derivation of the method, exemplified on a particular low order model. Simulation results can be found in [18] and [17], but are omitted here due to space limitation. The paper is structured as follows: In the next section, different modeling approaches for a solenoid valve are shown in comparison, emphasizing the flux-channel model which then is inverted in the next section.…”