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The article is devoted to the control of multichannel objects by the method of numerical optimization. In this area, there are several not entirely accurate, but ingrained ideas and approaches that it is time to sort out in detail. For clarity, typical examples are considered that anyone can check using inexpensive software, which, moreover, can be obtained free of charge in a demo version. Programming in this software is easy with the use of intuitive buttons and options. Thus, solving the problems of designing a regulator for multichannel systems becomes available to anyone who has a mathematical model of the object. The theses are based on the theory and confirmed by examples. The principles of controlling two-channel objects are proposed, i.e. objects of dimension 2×2, which by induction can be extended to objects of dimension 3×3 and, possibly, further. At the beginning, the solution to the problem of controlling a two-channel object of dimension 2x2 using a PID controller of the same size or its simplest modifications. Next, the problem of 3×3 objects is solved. There are two main factors for the result: the presence or absence of dominance of the absolute value of the diagonal elements of the transfer function matrix of the object over the re-maining elements, as well as the selected optimization objective function. In the case of dominance, the control problem is greatly simplified; in its absence, it can be ensured in some cases by changing the channel numbering. Recommendations are given for the formation of the objective function. For the first time, the use of a fractional power in the objective function is proposed, the effectiveness of this approach is substantiated and shown. For the first time, an additional modification of test signals during optimization is proposed, the effectiveness of this modification is shown. It is also shown how the quality of control of some channels can be improved at the expense of some deterioration in the quality of control of other channels.