Optimal linear control laws always require the direct measurement of every state. However they are impractical, since it is difficult to measure all the state variables in many realistic systems. Then the problem is to reconstruct the unavailable states from the available outputs, using an observer.
In this paper, we design an observer, which is a state estimator with decaying error at a desired speed, by using the nonlinear transformation of A. M. Letov. The characteristic feature of the method is to introduce a performance index and determine the observer gain uniquely by minimizing it. Also it is unnecessary to give judicious assignment of eigenvalues, since the standpoint of the method is essentially different from that of eigenvalue assignment.
The proposed observer is applied to the reconstruction of the entire state variables for a single machine connected to an infinite bus, including induction motor load. Then the true responses are compared with those given by the observer and the method is found to be useful in power systems including the effects of dynamic characteristics of load.