**Magnetic
Analysis by a Flux-Centered Approach, Part 1:, Joseph Seale 2003**

**Choosing Flux
Linkage As An Independent Variable**

In most analyses of
solenoid dynamics, the three primary or __state__ variables are armature __position__,
armature __velocity__, and electric __current__.
The choice of these three determines that values of a number of dependent
variables: momentum, inductance, flux linkage, etc.
Other choices for the three state variables are possible, leading to
different dependent variables. This
paper argues that it is advantageous to pick __position__, __velocity__,
and __flux__ linkage as the state variables, making electric current a
dependent variable. From a
measurement standpoint, flux is less accessible than current, but the solenoid
governing equations are greatly simplified.
More important, thinking in terms of flux rather than current leads to a
different approach to engineering. This
thinking is evident in the Magnesense papers and in the patents that relate to
sensorless measurement and state space control.

**Magnetic
Analysis by a Flux-Centered Approach, Part 2:, Joseph Seale 2004**

**Basic Equations
for Solenoids with Ideal Ferromagnetic Conductors**

The content of this paper can be gleaned from physics and engineering texts, but this paper puts it together in one place. From fundamental physics it derives the basic equations for solenoids, ignoring magnetic saturation, hysteresis, and eddy currents. Anyone wishing to examine these effects of non-ideal iron properties needs to have mastered the basics of this paper.

**B
vs H Narrative, Joseph Seale 2003**

This paper presents Magnesense research into the non-ideal iron properties of the cores used in the valve rocker solenoid. While the results are particular, they are representative of the important realm of engine valve solenoids constructed from transformer lamination material. Departures of real behavior from the idealized behavior of the “Part 2: Basic Equations…” paper are quantified, indicating the kinds of first-order correction formulas in actual use in Magnesense real-time control software.

**Taming the
Electromagnetic Solenoid: Building a System that Achieves a Soft Landing,**

**presented Gary
Bergstrom at the
SAE TOPTEC Conference, 9/12/2000:**

In applying servo control to the motion of a solenoid, one starts with a basic control loop for driving the solenoid, then layers on feedback corrections. The drive control loop can regulate the winding current, the voltage, or the flux linkage. A choice that leads to a nearly stable system is preferable to one that is going to require a great deal of additional compensation. How do these three choices rank? Current control is the least stable solution and may be plagued by voltage overload problems, but it has the advantage of immunity to current runaway if the solenoid enters magnetic saturation. Voltage control leads to more stable dynamics but runs into trouble with magnetic saturation: the current spikes up rapidly. Flux linkage control means control of the time integral of inductive voltage. Applied voltage must be corrected for resistive voltage loss in order to compute inductive voltage, after which a time integration is needed. This effort pays off, however, as it is shown that the flux-controlled electromechanical system is relatively stable and less vulnerable to saturation problems.

**Magnesense
LLC Gorham,ME (207) 839-8637**

**©2009
Joseph Seale **