Robust Optimal Design of Unstable Valves

This paper is concerned with the application of robust control design concepts for the physical geometric design of electrohydraulic valves. Limitations of solenoid actuators have prevented single stage electrohydraulic valves which are simpler and more cost effective from being utilized in high flow rate and high bandwidth applications. Fluid flow force induced instability has been proposed as a means to alleviate the demand on the solenoid actuators. Previous research has demonstrated that simple changes in the valve geometry can be used to manipulate both the transient flow force as well as the steady flow force for this purpose. This paper considers the dimensional design of such ldquounstablerdquo valves to minimize the net steady flow force. The robust optimal design method, in which the design must be robust to uncertainties such as variations in operating pressure ranges and dynamic viscosity, etc., is proposed. By representing the original problem as a linear fractional transformation interconnection, the robust design problem is formulated into one of synthesizing an optimal controller for an appropriate static plant with a structured uncertainty. An algorithm for solving this design synthesis problem is proposed. A case study is conducted to compare the nominal optimal (without considering uncertainty) and the robust optimal designs. It is shown that viscosity effect is exclusively utilized in the nominal optimal design, whereas both the viscosity effect and the nonorifice flux effect are needed in the robust optimal design. The robust optimal design imposes smaller steady flow force on the spool than the nominal optimal design under perturbed situations. Based on the robust design method, an actual prototype design of the unstable valve has been developed.