Simultaneous, multiplicative actuator and sensor fault estimation

This paper considers the joint state/parameter estimation problem which arises when reconstructing multiplicative, simultaneous sensor and actuator faults using observer based methods. Results published in [1] for this type of fault, using a linear diagnostic observer and adaptive updating rules for the fault estimation, are shown unable to separate the individual contributions of faults and system states to obtain asymptotically convergent solutions. Basic constraints, on the presence of at least one fault-free measurable output and on the observability of the fault-free subspace, result in output error convergence guaranteeing state error convergence and resolve the problem. It is also shown that the system and fault representation used can be reformed and, meeting the same constraints, allows the use of existing theory in additive, simultaneous fault estimation, here for example using sliding-mode and linear observers. This enables an extension to the estimation of more general multiplicative faults than those seen in [1] to include time-varying signals.