Kailash Krishnaswamy Perry Y. Li Department of Mechanical Engineering, University of Minnesota, 111 Church St. SE, Minneapolis, MN 55455 e-mail: kk,pli@me.umn.edu On Using Unstable Electrohydraulic Valves for Control High bandwidth, high flow rate electrohydraulic valves typically have two or more stages. Most multi-stage valves are expensive, require meticulously clean fluid, and introduce higher order dynamics. On the other hand, single-stage spool valves are cheaper and more reliable. However, a majority of them are not suitable for high bandwidth, high flow rate applications due to limitations of the electromechanical/solenoid spool-stroking ac- tuators. In this paper, we investigate the feasibility of reducing this limitation by exploit- ing the transient flow forces in the valve so as to achieve spool dynamics that are intrin- sically open-loop unstable. While conventional valves are designed to be open-loop stable, the unstable valve design has to be stabilized via closed-loop feedback. Simulation case studies are conducted to examine the potential dynamic and energetic advantages that an unstable valve may offer. These studies indicate that unstable valves provide faster response than the stable counterparts when stroking forces are limited. Moreover, un- stable valves tend to require less positive power and energy to operate. DOI: 10.1115/1.1433801 Keywords: Flow Instability, Solenoid Actuator, Electrohydraulic Valves, Transient Forces, Unstable Flow Forces, Unstable Valves I Introduction High bandwidth, high flow rate electrohydraulic valves typi- cally have two or more stages, one of which is usually a nozzle flapper pilot valve. Although highly popular, multi-stage electro- hydraulic valves are more expensive than single-stage valves and a majority of them have the drawbacks that 1 they require me- ticulously clean fluid, as dirt deposition will cause the pilot valve to malfunction; 2 they increase the order of the dynamics of the system, thus potentially introducing undesirable time lags, and making control design more challenging. Single-stage, direct-acting control valves are valves in which the spools are directly stroked by an electromechanical or sole- noid actuator. They are less expensive and less sensitive to dirt. They are also easier to manufacture and have lower order dynam- ics than multistage valves. Proportional control valves are ex- amples of this type of valve. Unfortunately, most of the commer- cially available single-stage direct-acting valves are not suitable for high performance, high flow rate applications. It is because at high bandwidth and large flow rate, the force and power required of the electromechanical actuator to stroke the spool become very significant, thus limiting the performance of the single-stage valve. The discussion above indicates that single-stage direct-acting control valves may become more practical for high performance, high flow rate applications if it is possible to reduce the force and/or power demand on the electromechanical actuator that strokes the spool. With advances in control theory and technolo- gies, one idea is to design the valve spool so that they are open- loop unstable and to utilize the flow forces associated with the instability advantageously. Spool valves can be made unstable by appropriately manipulating the transient flow forces. The unstable valve will be stabilized subsequently via closed loop feedback. The idea is similar to the design of high performance ‘‘fly-by- wire’’ fighter aircrafts in which the aerodynamics are sometimes deliberately designed to be open-loop unstable so as to enhance their agility. Past studies on valve instability have been restricted to ensuring that instabilities do not occur 1–3. In this paper, we investigate whether a single-stage valve which is designed to be open-loop unstable offers any advantages in terms of performance improvements or requirements on the electromechanical/solenoid actuator. The rest of the paper is organized as follows. In Section II, we discuss how flow forces determine the stability of a four way directional spool valve. In section III we present two numerical simulation experiments to quantify the potential benefits of un- stable valves. Performance is quantified in terms of step re- sponses, and in terms of power and effort required to track sinu- soidal signals. Section IV contains discussion and some concluding remarks. II Flow Forces and Spool Stability A four way directional flow control valve is shown in Fig. 1. We assume that it is matched and critically centered. The displace- ment x v of the spool controls the flow into a hydraulic device connected to the two ports on the right. In addition to the stroking force u provided by the electromechanical/solenoid actuator, the spool of the valve experiences both pressure forces and flow in- duced forces or Bernoulli forces1. Since the same pressure acts on the opposing surfaces of the lands of equal areas, they have no net effect on the dynamics of the spool. Flow induced forces are of two types, 1 steady-state flow forces and 2 transient flow forces. Inviscid, incompressible flow is assumed in the fol- lowing derivations. Steady-state flow forces are the reaction forces on the spool due to the changes in the momenta of the fluid entering and leaving the valve chamber. Referring to Figs. 2a and 2b, as the spool meters flow into out of the valve chamber, the vena contracta in which the fluid enters leaves the chamber is at an angle  to the spool axis. The fluid however leaves enters perpendicular to the spool axis. Thus, fluid entering and leaving the valve chamber can have different lateral and axial momenta. This necessitates reac- tion forces on the spool in both lateral and axial directions. By locating the ports symmetrically on the circumference of the valve Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS,MEASUREMENT, AND CONTROL. Manuscript received by the Dynamic Systems and Control Division February 9, 2001. Associate Editor: N. Manring. Journal of Dynamic Systems, Measurement, and Control MARCH 2002, Vol. 124 Õ 183 Copyright © 2002 by ASME