Discrete-Time Well-Conditioned State Observer Design and Evaluation

Model-based monitoring systems based on state observer theory often have poor performance with respect to accuracy, bandwidth, reliability (false alarms), and robustness. The above limitations are closely related to the ill-conditioning factors such as transient characteristics due to unknown initial values and round-off errors, and steady-state accuracy due to plant perturbations and sensor bias. In this paper, by minimizing the effects of the ill-conditioning factors, a well-conditioned observer is proposed for the discrete-time systems. A performance index is determined to represent the quantitative effects of the ill-conditioning factors and two design methods are described for the well-conditioned observers. The estimation performance of the well-conditioned observers is verified in simulations where transient as well as steady-state error robustness to perturbations is shown to be better than or equal to Kalman filter performance depending on the nature of modeling errors. The estimation performance is also demonstrated on an experimental setup designed and built for this purpose.