Abstract
In model following control systems, it is assumed that zero points of a linear part are stable because zero points of a linear part of a controlled object become poles of a closed loop system. This situation is same also in case of nonlinear model following control systems, but it happens that boundedness of inner states of a closed loop is assured depending on nonlinear properties. A nonlinear system is stable when the convergent degree of a nonlinear part is stronger than the divergent degree of a linear part.
We will discuss nonlinear model following control systems in case of the above mentioned situation in this paper.
In case that unstable zeros are controllable and observable poles of a nonlinear closed loop system, a linear output feedback which stabilizes an unstable part of an object system exists implicitly. This operation is to take out a linear part from a nonlinear part and construct an output feedback. As this operation is a theoretical one, no operations are necessary in actualitly. This theoretical operation is possible when an inner product of a nonlinear function vector f(v) satisfies a inequality condition and a transfer function from f(v) to v in a closed loop system is positive real in the mean of weakness. Weakly positive real is not necessary to satisfy equality conditions but satisfies inequality conditions. These conditions relieve conventional positive real conditions, so the concept is useful for design of general linear systems.
We show a simulation of nonlinear model following control system which has the third order polynomial and two inputs and two outputs in order to assure the effectiveness of a design theory of this paper.
