Unified modeling and analysis of a proportional valve

Developments in nonlinear control theory have made it possible to design controllers for systems having non-smooth nonlinearities in their dynamics. Hydraulic systems that use inexpensive proportional valves are examples of such systems, where nonlinearities arise due to valve geometry and spool imperfections. Without a proper valve model, however, nonlinear analysis and control of these hydraulic systems is not possible. e developed nonlinear equations for a generic proportional valve model and have used them to obtain simplified flow rate expressions under generally accepted assumptions. These equations relate a set of geometric spool properties and physical model parameters to the flow rate through the valve ports. The development focuses on obtaining a single set of flow rate equations applicable to critical center, overlapped, and underlapped proportional valves. These unified model equations are useful for simulation and nonlinear controller design. We have also demonstrated that the errors incurred when using the unified valve model are dependent on the damping coefficient alone and are less than 10% in the frequency range within which most valves are used.