Generalized characterization of tracking systems and linear multivariable plants

Abstract

In order to design tracking systems incorporating linear multivariable plants with more controlled outputs than manipulated inputs, it is shown that a more'general tracking concept than set-point tracking is necessary. The inclusion of inequalities in tracking conditions facilitates the characterization of tracking systems and linear multivariable plants. It is shown that the possibility of undertracking (i.e. tracking with non-negative errors) is characterized by the separation theorem of convex analysis, that linear multivariable plants can be classified into Class I and Class II plants based upon their steady-state transfer-function matrices, and that, in the case of Class I plants, undertracking is possible for any set-point commands. Furthermore, the necessary and/or sufficient conditions for Class I plants are given. Finally, it is shown that, in the case of Class 1 plants, undertracking is also possible for any set-point commands and any constant disturbances.