Control of Linear Multichannel Objects with Numerical Optimization

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 deeply rooted, ideas and approaches that we would like to analyze. This analysis is presented through typical examples and with the use of usually inexpensive software, which can also be obtained for free in a demo version. Using this software is easy with the help of intuitive buttons and options. Thus, solving problems in the design of a regulator for multichannel systems becomes accessible to anyone who has a mathematical model of the object. The principles of control of two-channel objects are considered, i.e., objects of size 2 × 2, which by induction can be extended to objects of size 3 × 3 and, possibly, even more. At the beginning, a solution to the problem of controlling a two-channel object of size 2 × 2 is proposed using a PID regulator of the same size or its simplest modifications. Then the problem with 3 × 3 objects is solved. There are two main factors that influence the result: the presence or absence of dominance of the absolute value of the diagonal elements of the object’s transfer function matrix over the remaining elements; the selected optimization objective function. In the case of dominance, the control task is significantly simplified. In its absence, in some cases it can be ensured by changing the numbering of the channels. Recommendations for forming the objective function are given. For the first time, the use of a fractional degree in the objective function is proposed, and the effectiveness of this approach is justified and shown. For the first time, an additional modification of the test signals during optimization is proposed, and the effectiveness of this modification is shown. It is also shown how the control quality of some channels can be improved at the expense of some deterioration in the control quality of other channels.