An Optimal Identification of the Input-Output Disturbances in Linear Dynamic Systems by the Use of the Exact Observation of the State

A new methodology for the identification of the values of unknown disturbance signals acting in the input and output measurements of the dynamic linear system is presented. For the solution of this problem, the new idea of the use of two different state observers, which are coworking simultaneously in parallel, was elaborated. Special integral type observers are operating on the same finite time window of the width T and both can reconstruct the exact value of the vector state x(T) on the basis of input-output measurements in this interval [0, T]. If in the input-output signals the disturbances are absent (measurements of I/O signals are perfect) then both observers (although they are different) reconstruct the exact and the same state x(T). However, if in the measurement signals the disturbances are present then these observers will reconstruct the different values of the final states x1(T)=x(T)+e1(T) and x2(T)=x(T)+e2(T). It is because they have different norms and hence they generate different errors in both estimated states. Because of the disturbances, the real state x(T) is unknown, but it is easy to calculate the state difference: x1(T)-x2(T)=e1(T)-e2(T). It occurs that, based on this difference, the values of all the disturbances acting during the control process can be identified. In the paper, the theory of the exact state observation and application of such observers in online mode is recalled. The new methodology for disturbances identification is presented.