Improvement of optimal high-gain PI-Observer design

In this paper, an optimal design approach for high-gain Proportional-Integral-Observer (PI-Observer), which is proposed by the authors, is improved and illustrated in details. PI-Observer, which can also be used as a type of high-gain observer, is successfully applied to estimate unknown inputs of systems. It is known that reasonable estimations of unknown inputs can only be derived assuming perfect knowledge about the model or using high gains in case of uncertain knowledge of the model or the inputs. In the latter case which is considered in this paper, extremely large gains can cause serious problems regarding measurements noise and unmodeled dynamics. In this contribution, an optimization approach to solve the conflict between the quality of the estimation and the sensitivity to the uncertainties is developed for a general class of systems. An elastic beam example is given to illustrate the advantages of the proposed approach.