You are given a high-speed proportional solenoid valve. A voltage proportional to the desired position of the spool is applied to the coil. The resulting magnetic field produced by the current in the coil causes the armature to move. A push pin connected to the armature moves the spool. A linear voltage differential transformer (LVDT) that outputs a voltage proportional to displacement senses the spool’s position. This voltage can be used in a feedback path to implement closed-loop operation (Vaughan, 1996). Draw a functional block diagram of the valve, showing input and output positions, coil voltage, coil current, and spool force.