State estimator and its application for systems with disturbances

Based on the implicit observer techniques, a new expression of the state is obtained by the first order filters of the input, output and disturbance. For the minimum phase dynamical systems with arbitrary relative degrees (with respect to the relation between disturbance-output), the higher order filters of the disturbance is estimated by using the VSS equivalent control method. Then, by some new techniques, the lower order filter of the disturbance is estimated. Eventually, the disturbance is also estimated. Thus, the state vector is asymptotically expressed by the first order filters of the input and output and the estimate of the first order filters of the disturbance. The estimated state and the disturbance are applied to a controller to place a desired pole and to cancel the disturbance. Examples and simulation results are presented to show the effectiveness of the proposed algorithms.