Abstract
It is important to consider design, location, selection of an actuator, as these problems influence control-performance very much. Concerning actuator design, Kalman's study based on minimam energy control problem is well known. It is also important to advance research based on the same idea in actuator location selection problem. However, this problem being different from general design problem has combinatrial property, and it is difficult to get a solution. If this property is dissolved, actuator selection, location problem can be dealt with on the same basis as a general design problem. Therefore, it is important to dissolve combinatrial property, before studying the problem based on minimam energy control problem. We considered this problem from various kinds of viewpoints. Main studies are development of optimal local solution algorithms, proposition of possibility of comparison (we call it comparability), relation between comparability and uniqueness of solution etc. The latter is especially noticeable, because combinatrial property is dissolved with a proposition of the comparability. Desiring a solution by using this strong point, we must investigate actuator comparability in more detail.
In this paper, to decide the comparability, we propose a comparability matrix, and consider comparability more concretely. At first, we clarify the definition of comparability. We have previously studied the relation between comparability and uniqueness of solution and explain the result briefly. Then we show the equivalant condition of comparability in scalar input system. But this condition could not be expanded to a multi input system directly. Therefore we consider the simultaneous diagonal condition of comparability matrix. Using this condition, we show some equivalant comparability conditions in a multi input system. These conditions express comparability more clearly, and therefore they contribute to designing an optimal comparability actuator.
