B. Linearization Module
A subsystem diagram of the linearization module is shown in Figure IV.B.1. A limiting function receives the calculated net input force from the linear compensator and does two things. First, the limiting function ensures that the pulling force that each solenoid exerts is always positive. Second, to assure that the payload is always under tension, the limiting function ensures that a minimum tension force exerted by any one solenoid is always 2 Newtons.
Figure 2: Graph of force from left solenoid
Figure 3: Graph of force from right solenoid
The design approach is, as I said before, a version of feedback linearization. The linearization module is a nonlinear transformation from the total force to be exerted on the payload to the currents to be supplied to each solenoid using the VCCS. This transformation inverts the solenoids' dynamic process. To this end, the linearization module uses the solenoid current equation.
Another limiting function constrains the range of d to 0 < d < D. This limiting function protects against erroneous readings. If the payload were to go outside of this travel length, it would clang against the sides of the solenoids.
The solenoid current is limited to 4 Amperes to protect the electronic circuit. Additional fuses protect the solenoids from overcurrent. These fuses are slow blow and rated for 3 A. Note that this ceiling on the solenoid current will make the control system more stable. The maximum input force will decrease, which decreases the travel overshoot. The drawback of this ceiling is longer rise time.