A New Observer for Nonlinear Systems With Application to Power Systems

In this paper, a new observer is presented for discrete-time nonlinear dynamical systems. The designed observer is a modified version of the recently developed regularized least square (RLS) observer. It leads to an estimator with almost zero or very small overshoot while keeping the settling time of the estimation error very short, a case which cannot be satisfied by the well-known observers available in the literature. The predicted estimate of the developed estimator is calculated from a weighted average of a set of predicted estimate of a set of points to be generated around the filtered estimate of the state vector at a given sampling instant of time. Through this approach, we get a highly accurate result of the predicted state vector, which intuitively leads to highly accurate filtered estimates of the states. The developed estimator can deal with highly nonlinear systems, does not need any state transformation, has no restrictions on the output measurement model, leads to a unique solution, and last but not least avoids the computation of the Jacobian matrices. The convergence of the proposed observer is analyzed, and the results show its superior performance when compared with the RLS observer. Moreover, a modified version of the developed observer is proposed to reduce the computational time while maintaining its main features. Illustrative examples of highly nonlinear power systems are presented to show the effectiveness of the proposed approach and its superiority when compared with other well-known observers.