Controlling of Multichannel Objects with Non-Square Transfer Function

The control of multichannel objects is an independent section of cybernetics. Traditionally, objects are considered in which the number of inputs coincides with the number of outputs, but there are separate publications devoted to cases when the number of inputs does not coincide with the number of outputs. Even for this purpose, special terminology has been invented. If traditionally the mathematical model of an object is a square matrix transfer function, then in this case the term “non-square matrix transfer function” is used. This term is unsuccessful, as shown in this article, since it combines problems that are simplified in comparison with traditional ones, and problems that are, strictly speaking, unsolvable. This article demonstrates that an additional number of object inputs is not only not a problem, but also offers additional opportunities, while an excess number of outputs is an insurmountable problem: one can only abandon the problem of controlling redundant outputs. This situation should not be confused with the situation of the presence of additional outputs of sensors of the controlled variable or intermediate values, which also serve to simplify the solution of the problem and not to complicate it. If output signals are understood as independent output values that should be independently controlled, then the number of outputs should never exceed the number of inputs, although this situation can easily be confused with some other similar situations. This article also shows an example of how additional signals, sometimes mistakenly called additional outputs, can be used, and gives recommendations for various situations.