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Evaluating some Gain Scheduling Strategies in Diagnosis of a Tank System

In model-based diagnosis the problem of finding all the relations that can be used to detect and isolate different faults, is solved for linear systems, with e.g. ``The Minimal Polynomial Basis Method''. However, for nonlinear systems the situation is much more complicated. Here an approach will be taken using the linear method above together with gain scheduling. Linear residual generators are designed at a number of stationary points. The approach is based on using a nominal selector matrix, using null-space redesign dependent on the scheduling variable, and using a proposed optimization method. Two different gain scheduling strategies are applied to form the residual generators between design points, namely nearest neighbour approximation and linear interpolation. The approach is applied to a simple nonlinear system consisting of two coupled water tanks. The simulations show that the performance of the residual generators are good under steady state conditions. It is also shown that linear interpolation has better performance than nearest neighbour approximation, especially during transients.

Marcus Klein


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