Modelling of an electro-hydraulic servo-system

Many theoretical models have been developed to simulate the performance of hydraulic Control components and systems, but all are limited by the assumptions involved and uncertain factors associated with practical hydraulic systems. Authors warn that seal compressibility, inertia of oil in lines, mounting compliance, structural damping, friction and cavitation may each be significant in appropriate circumstances,and even the bulk modulus of hydraulic oil is difficult to predict for practical systems. Manufacturers may reject theoretically predictable designs because they are prone to wear or expensive to make. For instance sharp edged orifices are replaced by the short tube type and oil passages consist of drilled holes intersecting at angles with frequent changes in section. The prospect of obtaining a comprehensive mathematical model applicable to manufactured components is therefore remote due to the uncertainties and complexities involved but the designer will require models and methods of solution sufficient for his purposes which are to obtain a reasonable prediction of performance at the design stage. 'Design' may mean the design of a hydraulic circuit component, such a pump or relief valve, or may involve matching standard components to form a system. Ideally the designer requires a model of each system component which can be assembled with all other component models to form a comprehensive system model which can be solved mathematically. If linear models are possible an exact final solution may be feasible but when non-linearities are present, a digital simulation of the model giving a time response to defined inputs may be the only practical method of solution and, inevitably, the designer is involved with the problems of computation. Computers are now commonplace in design offices, Small computer installations offer a hands ,-on facility which is flexible and versatile whilst large installations offer enormous capacity and capability but are often remotely located with inflexible management procedures ill-suited to the trial and error design techniques often required for component design optimisation. As such,a small computer may offer the most efficient means of solving these design problems. This thesis is concerned with methods of modelling hydraulic components and systems with particular emphasis placed on the use of a small computer installation for digital simulation of models, and for other tasks related to laboratory testing of actual systems. The basic aims are to obtain physical and mathematical models of an existing electro-hydraulic two-stage servo-valve, to use a small computer to predict open and closed-loop responses, to obtain actual system responses for comparison with those predicted, and to examine non-linearities encountered. The thesis is set out in the order in which the work was done. Initially similar work was studied and extended after which the servo-valve was measured and tests were conducted to ascertain physical constants required for the system equations. A linear model was then simulated and actual system responses were obtained for comparison with the first linear model. After this the linear model was slightly modified and other more advanced non-linear models developed. NOTATION Symbols are defined when they are introduced and a comprehensive table of symbols appears in section A3.1 in Appendix 3. Commonly used servo-valve variables are defined on figure (2-4) in chapter 2.