An Application of a Relative Gain Array and Singular Value Decomposition for the Synthesis of Control Systems for Multivariable Processes

In this paper, a control system for a multivariable object is developed using the example of a distillation column using singular value decomposition and relative gain array. A model was built in the simulation package for the plant. On the basis of numerical experiments with the simulation model of the object, time series was obtained to identify the parameters of the transfer function matrix. With the help of singular value decomposition, the direction of the largest and smallest amplification was determined by the input and output vectors of variables. The singular value decomposition made it possible to answer the question of the expediency of the chosen composition of input and output vectors of variables. For the selected vectors, relative gain array matrix was calculated, which was used to select a decentralized control system. The calculation of the relative gain array, and the visualization of the singular value decomposition were performed in the MatLab mathematical modeling environment. Based on the results of applying the methods, the structure of the control system of the multivariable control object was proposed and the quality indices of regulation was determined.