Well-Conditioned Observer Design for Model-Based Monitoring Systems

Model-based monitoring systems for machine diagnostics and control are receiving increased attention. These techniques can estimate process and machine variables from inexpensive, easy to install remote sensors based on state-space models of the machine structure between the machine variables of interest and the location of the remote sensors. Model-based monitors are most frquently based on state observer techniques. Unfortunately these observers can be ill-conditioned leading to poor peformance. The authors show in previous papers that the conditioning of the observer performance can be repesented by a single performance index, the condition number of the eigensystem of the state observer matrix, and that there exists an upper bound for the index in non-normal matrices and the bound can be determined by the structure and eigenvalues of the observer matrix. In this paper, a design methodology for synthesizing well-conditioned observers is proposed based on the upper bound of the performance index. This is in contrast to using classical pole placement techniques. From the fact that small upper bound guarantees the small value of the performance index, a well-conditioned matrix form is defined and block-by block design strategy for a well-conditioned observer matrix is presented. A complete design procedure for well-conditioned deterministic state observers is given for the single-output case, while for multi-output case only a sufficient condition is given. The design stategy is illustrated with an example that shows that a well-conditioned observer performs much better than an observer designed with traditional techniques.