6 th International Conference on Fluid Power Transmission and Control (ICFP 2005). March 2005. Flux Observer for Spool Displacement Sensing in Self-Sensing Push-Pull Solenoids Perry Y. Li and Qinghui Yuan Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455 USA, {pli,qhyuan}@me.umn.edu Abstract Spool position feedback in an electrohydraulic valve typically requires a spool displacement sensing device such as a LVDT. Self-sensing is the methodology to obtain spool displacement information directly from the solenoid spool actuators, thus obviating the additional cost and footprint of a LVDT or another displacement sensing device. A self-sensing scheme that uses only the measurement of electrical signals to the pair of push-pull solenoids was first proposed in [1]. It uses the position dependence of electrical inductance in the solenoids to infer the spool displacement. The scheme in [1] relies on a flux observer and several infinite dimensional filters that require explicit resets, and is prone to singularity. The present paper proposes a modified scheme in which the flux observer (and hence the self-sensing) problem is cast in a linear time varying system setting so that standard linear observer design techniques can be brought to bear. Keywords Self-sensing, observer, push-pull solenoids, spool displacement feedback. electrohydraulic valves 1 Introduction Spool position feedback is often needed or at least desirable for high performance nonlinear control of electrohydraulic systems. Spool position feedback is especially important in our own research of “unstable valves” where the unstable steady [3] and unstable unsteady [2] flow forces are deliberately utilized to improve the spool agility. This is to reduce the force and power requirements for the solenoid actuators to achieve high flow, high performance in single stage direct acting proportional valves. Since the ``unstable” valves are designed to be open-loop unstable, they need to be stabilized via closed-loop feedback. This makes the need for spool feedback even more critical in the new unstable valve designs than conventional valves which are designed to be open-loop stable. To reduce the cost of the additional spool displacement sensing device, a self-sensing scheme was proposed in [1] to obtain spool displacement information by measuring the voltage and current in the solenoids in the push-pull configuration. It uses the position dependence property of the solenoid actuators to determine the spool position. The key element in this scheme is the magnetic flux observer. Unfortunately, because the flux observer in [1] relies on solving the initial flux on a finite moving horizon and utilizes several time delayed (hence infinite dimensional) filters, it is rather complicated and is susceptible to singularity. In this paper, we present a reformulation of the problem into the standard observer design formulation, so that many time varying linear design methodologies can be applied. The resulting observer and spool displacement estimator are easier to implement and less prone to singularity. 2 System Models Fig. 1: Push-pull solenoid configuration. Consider the push-pull solenoid actuator spool in Fig. 1. We assume that the solenoid inductances are given by [1] [4] [5]: x d x L + = 1 1 1 ) ( β (1)