Analysis of alternative controller structures for modeling and controlling a multi-channel water plant

The task of controlling multi-channel objects, that is, objects with many inputs and many outputs, MIMO, can be the most effectively solved by a multi-channel controller that has the same number of inputs and outputs as the controlled object has. We consider only multichannel controllers that have the same number of inputs and outputs. Traditionally, in the matrix of such a controller, each element is a scalar PID controller, that is, a controller containing proportional, integrating and derivative channels. In this case, an n × n object requires n<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> scalar PID controllers, each with three channels. The calculation of such a controller requires the calculation of 3n<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> parameters.