Well-Conditioned Observer Design for Two-Output Systems

Abstract

It was shown that the robustness of deterministic observers with respect to modeling errors, measurement bias and round-off errors can be represented by a single performance index, χ2(P), the condition number of the observer eigenvector matrix. In this paper, based on the performance index, a robust observer design method is proposed for two-output systems where the observer gain can not be determined uniquely with respect to the desired observer poles. Utilizing the pole/zero locations of the observer dynamics, a step-by-step design procedure of the well-conditioned observer is developed. In addition, a new scaling method is developed with employing the eigenvector matrix as a scaling matrix. The proposed method is evaluated and compared with the Kalman filter technique in a spindle-drive simulation example where the load speed needs to be estimated based on the measured signals.