Global Analysis of an RC-Filter for a Switched Hydraulic Drive

In switched hydraulic systems control is done by fast on-off valves which are operated at high frequencies. Such operation is likely to excite unwanted oscillatory response in the multi-modal combined hydro-mechanical system. This paper presents a detailed analysis for a system comprising a hydraulic cylinder, which is connected to the on-off valves by a long transmission line and a hydraulic RC-filter placed right after the valves. The problem of an optimal tuning of this filter for quite different system configurations is treated in a comprehensive way to allow a full global understanding of the system and filter parameter influences on the main oscillation effects. To this end a proper nondimensionalization of the linearized system equations in frequency domain is derived leading to only two nondimensional plant parameters and two filter parameters. The qualitative properties of a transmission line allow giving an upper limit of useful filter resistances. In addition to this limit condition a two criteria optimization problem is defined for filter dimensioning purposes. The first criterion is the deviation of the system from the ideal response as given by an incompressible, inviscid, zero density fluid in a sub-critical frequency domain. The second criterion evaluates how much the actual amplitude exceeds the critically damped cylinder frequency response in the resonance frequency range and beyond. The respective Pareto-fronts are the best achievable filter performances for a certain plant parameter situation. An atlas of these fronts for a variety of plant parameters provides a compact insight into the possible system responses under optimal filter tunings.