Conversion of CGA models to Jordan controlled form for design significantly nonlinear control systems

Abstract

Tasks, opportunities and prospects of converting the significantly nonlinear mathematical models, obtained for technical objects by the method of fragmentary, multiplicative-isolating approximation, to the Jordan controlled form are investigated. The equations of nonlinear objects in the Jordan controlled form and the algorithm of the analytical solution of the designing problem of the stabilizing control law on the basis of this model are considered. It is shown that the mathematical models of many significantly nonlinear objects can be obtained in the fragmentary form, but not in the analytical one. It is also shown that the method of Cut-Glue approximation allows us to provide these models with analytical properties. This gives a possibility for the analytical design of the nonlinear control laws with the property of “analytical adaptation” on the basis of the CGA models. The effectiveness of this approach is illustrated by the example of the analytical design of the nonlinear control system for the object with the fragmentary and considerably changing static characteristic on the base of the Jordan controlled form.