Well-Conditioned Observer Design for Observer-Based Monitoring Systems

Observer-based monitoring systems for machine diagnostics and control are receiving increased attention. These observer 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. Unfortunately, these observers can be ill-conditioned and this leads to poor performance. The authors have previously shown that observer performance can be represented 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. The methodology is based on the fact that a small upper bound guarantees small values of the performance index. A well-conditioned matrix form is defined and a block-by block design strategy to produce a well-conditioned observer matrix is presented. A complete design procedure for well-conditioned deterministic state observers is given for the single-output case. The design strategy is illustrated with an example that shows that the proposed well-conditioned observer performs much better than an observer designed with traditional pole placement techniques.