Research On Zero Dynamics Of Nonlinear Differential Algebraic Systems

Differential algebraic systems are composed by differential equation systems and algebraic equation systems. At present, the geometric theory of nonlinear systems has hardly been applied to the control of differential algebraic systems. For more generality differential algebraic systems with nonlinear restraint, the concept and properties of the zero dynamics are obviously important but have not been studied so far, and there exists a class of differential algebraic systems with nonlinear restraint applied widely in the power systems models, so that the research on this class systems is of more actual significance.In this paper, firstly, the background and development of nonlinear differential algebraic systems are summarized in detail. Secondly, the basic concepts of nonlinear differential algebraic systems are drawn out corresponding to the classical theory of nonlinear systems. The typical problems for nonlinear systems are extended to nonlinear differential algebraic systems by means of the theory of differential geometry methods. To this end, the following two topics are to be studied, and some research results have been obtained.(1) The zero dynamics problem of control systems is considered. The zero dynamics theories and methods of the nonlinear systems are generalized to nonlinear differential algebraic systems. The concept of output zeroing submanifold and zero dynamics are proposed for a class of differential algebraic systems with nonlinear restraint. By means of M derivative methods, the properties of output zeroing submanifold are studied, and a zero dynamics algorithm on this system is given, some properties of this algorithm are discussed also. Finally, an example is provided to illustrate the zero dynamics algorithm given in this paper.(2) The application of zero dynamics of nonlinear systems is studied, including the zero dynamics of nonlinear systems and zero dynamics of nonlinear differential algebraic systems. In the power systems, to design the excitation control law of generator with zero dynamics design enables the system's internal dynamics, "the zero dynamics", stable, so that the whole systems are stable.