Synthesis of a Multichannel Controller for Plant with Two Input and Two Output Channels Using Polynomial Matrix Fraction

Abstract

To achieve the required level of control by the system, in some cases, the use of multi-channel controllers is required. One of the actual problems is to find the parameters of the controller. In this paper, we demonstrate the possibility of synthesizing controllers for a model of a multi-channel plant and take as an example a linear model of an unstable plant with two input and two output channels. The plant description is used in the form of a matrix transfer function, which shows the interaction in the multi-channel control system and the relationship between the channels. The plant was chosen taking into account the simplicity and illustrativeness of the applied algorithm for the synthesis of the automatic control system. The problem was that it was necessary to achieve certain quality indicators of the output vector process when controlling two input actions. To solve this problem, the method of polynomial-matrix decomposition was used. The system is presented in four variants of the plant and the controller numerator and denominator polynomial matrices decomposition. This is necessary for the formation of a more flexible approach to the synthesis of controllers, associated with the convenience of calculating the characteristic matrix of a closed system. Taking into account the degree of the selected plant, the PI controller is selected as the controller.