On the numerical solution of steady-state equations of digital hydraulic valve-actuator system

Digital valve system uses plurality of simple on/off valves instead of proportional or servo valves in the implementation of high performance and energy efficient valve controlled hydraulic actuators. Typical digital valve system consists of 20 valves each having two states, which yields the over one million possible control combinations. A potential way to control this kind of system is the model based control utilizing the steady-state model of the system. The solution of the steady-state system equations must be made numerically because no analytical solution exists. This paper analyses the steady-state system equations, develops the condition for existence and uniqueness of the solution, and studies different iteration algorithms. The new results of the paper are: 1) system equations can be transformed into scalar form, 2) the solution exist and is unique if a simple necessary and sufficient condition holds, and 3) Ridders’ method is fast and robust method for this problem.