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

Abstract

In this paper, a model inversion approach is presented that can be used particularly in cases, where the links between subsystems are hard or even impossible to express within the framework of differential flatness. To overcome this problem, i.e. to establish a link between the desired physical output and the flat output, properties inherent to flat systems are utilized. The method is called flatness-based state decomposition and is applied to a magnetic flux-channel model, within an electromagnetic-mechanical solenoid valve model. This approach shows excellent performance in simulation and has been integrated in the well-established flatness-based optimization scheme for feedforward trajectory generation.

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

“…It is referred to [1] or [2] for a detailed description of the trajectory planning procedure and how the distributed parameter model is incorporated in a feed-forward control scheme for solenoid actuators. The adaptability of the nonlinear PDE (3), and its series solution (9) with the coefficients calculated by (8) has been tested by numerical simulation. Therefore, as a desired flat output y(t) the compact support function…”

“…A comprehensive discussion of the influence of the Gevrey class α to the convergence of the series can be found in [11]- [15]. Theorem 1: The series approach (9) with coefficients calculated by (8) and flat output a 0 (t) = y(t) (10) of Gevrey class 1 + δ < α ≤ 2, δ > 0 converges to a solution of (3) with initial condition (4), boundary conditions (5)-(6), and has a radius of convergence R greater than min 4 3 2 γ σ…”

“…For instance, the eddy currents, and limited field diffusion velocity of the magnetic inductance have a decisive impact on the achievable switching time as well as the losses, caused by the applied control strategy. The consideration of eddy currents in a lumped parameter model is usually handled by integration of a resistor and a stray inductance in an equivalent circuit diagram [6], or in a more sophisticated way by so called flux channels [7], [8]. The drawback with these lumped parameter models is, however, besides a possibly unduely simplification, the requirement for measurement data for identifying the model parameters.…”