Biblio

A general approach to the synthesis of the conditionally unstable fuzzy controller is introduced in this paper. This approach allows tuning the output signal of the system for both fast and smooth transient. Fuzzy logic allows combining the properties of several strategies of system tuning dependent on the state of the system. The utilization of instability allows achieving faster transient when the error of the system output is beyond the predefined value. Later the system roots are smoothly moved to the left-hand side of the complex s-plane due to the change of the membership function values. The results of the proposed approaches are compared with the results obtained using traditional methods of controller synthesis.

The problem of analytical synthesis of the reduced order state observer for the bilinear dynamic system with scalar input and vector output has been considered. Formulas for calculation of the matrix coefficients of the nonlinear observer with estimation error asymptotically approaching zero have been obtained. Two modifications of observer dynamic equation have been proposed: the first one requires differentiation of an output signal and the second one does not. Based on the matrix canonization technology, the solvability conditions for the synthesis problem and analytical expressions for an acceptable set of solutions have been received. A precise step-by-step algorithm for calculating the observer coefficients has been offered. An example of the practical use of the developed algorithm has been given.