Trade-offs on fault estimation via proportional multiple-integral and multiple-resonant observers for discrete-time systems

Abstract

The authors develop a fault estimation strategy which is based on a novel proportional multiple-integral (PMI) and multiple-resonant observer. This observer is an extension of the well-known PMI observer and it is able to estimate from low to high-frequency fault signals. The proposed estimation strategy is applied to discrete-time systems which are affected by faults and stochastic noises. We present a multi-objective design strategy of the observer that fixes the trade-offs between practical engineering parameters regarding the noise attenuation and the ability to track each kind of fault dynamics considered by the augmented observer. They study the influence of the order of the observer on the steady-state and transient performance of the estimation of different types of faults. Finally, a numerical example is given to illustrate the effectiveness of the proposed observer, design and characterisation.