A spool valve is a single degree of freedom system that has coupled ‘meter in’ and ‘meter out’. Decoupling of meter in from meter out provides for more controllability and potential for energy saving in overrunning load cases when compared with a conventional spool valve controlled hydraulic system. A four-valve configuration controlling a hydraulic cylinder is emphasized in this paper. The four-valve configuration can operate in several two-valve discrete modes because each of the four valves is controlled separately from the others. Five distinct (or discrete) metering modes that exist in the literature are initially studied: Powered Extension, High Side Regeneration Extension, Low Side Regeneration Extension, Powered Retraction, and Low Side Regeneration retraction. Each of these modes has different force and speed capabilities and the operating mode should consequently be selected based on the load and the commanded speed. Proper switching between these modes is crucial for efficient and productive performance. The problem of switching between these five modes is treated as an optimal control problem of a switched dynamic system. General theory for the optimal control problem is derived and then applied to the hydraulic system of interest. The results are then interpreted and explained by looking into the force-speed capability of modes, and a closed form solution for the quasi static case is presented. 

Keywords: hydraulics, independent metering valves, metering modes, mode capability curve, mode switching