Proportional valve control calculation. Part 1.
Part 1. Proportional control of double acting hydraulic cylinder.
See also:
Part 2. Proportional control in the regeneration mode
Online calculator for cylinder proportional control.

Fig.1. Double acting cylinder control.
The goal of this calculation is a definition of a cylinder velocity at any percent of the operating control signal at the valve’s solenoid (voltage or amperage).
For calculations we need to know: cylinder and valve parameters (take them from manufacturer catalog), values of forces at the cylinder rod (load), and pressure drop at the return line (can be assumed as zero if unknown).
Summary:
1.1. Hydraulic cylinder extension calculation.
1.1.1. Spool lands ratio.
1.1.2. Pressure drops at the spool lands
1.1.3. Balance of forces at the cylinder.
1.1.4. System pressure calculation.
1.1.5. Flow through spool lands: max. and at current voltage.
1.2. Hydraulic cylinder retraction calculation.
1.3. Full stroke time calculation.