Models, residual design and limits to fault detection for a complex multi-tank hydraulic control system

System modelling, fault detection and control are considered for a general hydraulic n-tank system. A subsystem of n - 2 tanks is situated in a remote, and possibly hazardous, environment and only control and measurements of the outer tanks are possible. The non-linearities in the system model are not particularly smooth. Given a set of non-linear differential equations, several transformations and smooth approximate input-output maps are derived to aid the establishment of equilibrium points and the design of controllers, observers and residuals for fault detection. A non-linear, high-gain, observer-based residual design is considered and developed for which error stability and detectability are examined. This design and a design based on a polynomial model are used to examine residual effectiveness as system complexity increases. For each design four systems are considered with n = 3, 6, 12, 24. Evidence shows that, for both designs, and for each fault position selected, the effectiveness of an observer-based residual is limited by system complexity. The limit is shown to be expressed in terms of a limiting line relating measurement error to n. The transformations, mappings, and the methodology involved are applicable to other hydraulic systems of similar non-linear structure.