Algebraic Properties of Noncommensurate Systems

Noncommensura te systems are those in which either the input vector or the output vector contains elements with different physical units. Such systems are encountered in situations where different physical quantities must be combined to achieve a given goal. An example is the control of robot manipulators where position with units of distance and orientation with units of angle must be combined. Unless proper care is taken, control systems based on current optimization techniques may yield inaccurate and misleading results. This paper examines properties of noncommensurate systems and develops several algebraic properties and requirements on the physical units involved in the control methods for such systems.