Nonlinear Control Systems Design by Transformation Method

Abstract

The analytical approaches to design of nonlinear control systems by the transformation of the nonlinear plant equations into quasilinear forms or into Jordan controlled form are considered. Shortly definitions of these forms and the mathematical expressions necessary for design of the control systems by these methods are submitted. These approaches can be applied if the plant’s nonlinearities are differentiable, the plant is controllable and the additional conditions are satisfied. Procedure of a control system design, i.e. definition of the equations of the control device, in both cases is completely analytical. Desirable quality of transients is provided with that, that corresponding values are given to roots of the characteristic equations of some matrixes by calculation of the nonlinear control. The proposed methods provide asymptotical stability of the equilibrium in a bounded domain of the state space or its global stability and also desirable performance of transients. Performance of the nonlinear plants equations in the quasilinear form has no any complexities, if the mentioned above conditions are satisfied. The transformation of these equations to the Jordan controlled form very much often is reduced to change of the state variables designations of the plants. The suggested methods can be applied to design of control systems by various nonlinear technical plants ship-building, machine-building, aviation, agricultural and many other manufactures. Examples of the control systems design by the proposed analytical methods are given.