In certain areas of science and technology, physical quantities of different natures are combined in a variety of involved mathematical processes that obscure the interaction of these physical units and sometimes lead to unreliable results. Noncommensurate systems are those in which either the input vector or the output vector contains elements with different physical units. 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 article examines properties of noncommensurate systems and develops several algebraic properties and requirements for the physical units involved in the control methods for such systems.
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