Study on a GMDH-PID Controller Design Method Based on LASSO

Abstract

This paper proposes a group method of data handling based PID (GMDH-PID) controller using the least absolute shrinkage and selection operator (LASSO) that is one of the sparse modeling methods. A database-driven PID (DD-PID) controller is one of the effective nonlinear PID controller design methods. However, some electrical control units in industrial systems cannot implement the algorithm because the DD-PID control scheme requires a large amount of memory capacity and high-performance processor. The GMDH-PID controller that approximately expresses the behavior of the DD-PID controller by combinations of simple nonlinear functions has been proposed to solve the above problem. Although the GMDH-PID method can reduce the amount of memory capacity and calculation costs, calculated coefficients in nonlinear functions may not stable due to the multicollinearity of input signals. In this research, instead of the least squares method, the LASSO is employed as a coefficient calculation method of the GMDH in which some coefficients can be calculated as zero in order to avoid the influence of the multicollinearity. The effectiveness of the proposed method is evaluated by simulation examples.