Detection and elimination of insignificant interacting subsystems in MIMO closed-loop systems using the least mean square-based partial correlation algorithm

Abstract

Closed-loop identification of multi-input multi-output (MIMO) systems in large-scale plants has significant difficulties due to subsystem interactions. This complexity is attributed to several input‒output variables, interactions such as recycling to improve or save material and energy, and disturbances such as heating or cooling within the plant. One of the fundamental problems in closed-loop identification is the input perturbation of the interacting subsystems to capture the dynamics of the system for producing an informative dataset and consequently obtaining an accurate model. However, perturbing all the interacting subsystems in the plant increases the applied excitation signals, which makes the identification a nontrivial task. Thus, a precise and quantitative procedure to evaluate the significance and contribution of such interacting subsystems before applying these excitation signals is required to simplify the identification task. Conventional partial correlation analysis is one of the implemented techniques to measure the significance of these interacting subsystems. However, this technique is based on least square estimation. Thus, incorrect estimation of the model errors is produced due to the correlations amongst the process inputs and unmeasured disturbances. Accordingly, this paper describes the implementation of a developed least mean square-based partial correlation algorithm for detecting and eliminating insignificant interacting subsystems of MIMO closed-loop systems. The developed algorithm can discriminate the interacting subsystems that substantially influence the plant interaction from those that do not by minimizing the model regression errors produced due to the process input correlation, unmeasured disturbances, and colored noise. The effectiveness of the proposed method is demonstrated through a case study.