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Optimal and robust design of unstable valve

Our research is concerned with the design of a cost effective single stage direct acting electrohydraulic valves for high flow rate and high bandwidth applications by utilizing the instability caused by flow induced forces. In our past research, we have demonstrated simple change in valve geometry can be used to manipulate both transient flow force as well as steady flow force for this purpose. In this paper, with the goal of minimizing the steady flow forces range, we present two optimal design methods over the space of these design parameters: (1) the nominal optimal design method, in which no uncertainty is taken into account; (2) the robust optimal design method, in which the design must be robust enough to model uncertainty and perturbations. By representing the original problem as a LFT interconnection, the robust design problem can be formulated into synthesizing an optimal controller for an appropriate static plant with a structured uncertainty. An algorithm is then presented to transform the LFT into an appropriate robust control problem and synthesize the controller. The case study shows that unlike the nominal optimal solutions where viscosity effect is exclusively utilized, the robust optimal solutions tend to take advantage of both viscosity effect and non-orifice flux effect, and in return provide the better performance over nominal optimal solutions.