Discrete-Time Well-Conditioned State Observer Design and Evaluation

Abstract

Abstract Model-based monitoring systems based on state observer theory often have poor performance with respect to accuracy, bandwidth, reliability (false alarms), and robustness. Previous work has investigated quantitatively the above limitations of the continuous-time observers from the machine monitoring viewpoint. The authors have shown that the limitations can be represented by a single performance index, kP2(P) (condition number of the eigensystem P in terms of L2 norm). Based on the performance index, the authors developed a design methodology for the well-conditioned observer and illustrated the estimation performance compared to a pole-placement methodology. This paper extends the work to discrete-time systems. A performance index is determined to represent the limitations of discrete-time state observers and a design procedure is described for the well-conditioned observers. The estimation performance of the well-conditioned observers is demonstrated on a DC spindle system designed and built for this purpose. The results show that the robustness of the estimate is similar to that obtained with a well-known Kalman filter technique. Additional simulation-based examples show that the transient as well as steady-state error robustness to perturbations is better than or equal to Kalman filter performance depending on the nature of the modeling error. Because of this robustness, the well-conditioned observer for discrete-time systems is an important technique for the development of improved machine monitoring systems.