Design and application of a sparse GMDH‐PID controller

Summary The database‐driven PID (DD‐PID) controller is an effective nonlinear PID controller design method; however, some electrical control units in industrial systems cannot implement its algorithm because the DD‐PID control scheme requires a large memory capacity and a high‐performance processor. In this article, to solve this problem, a group method of data handling PID (GMDH‐PID) controller is proposed that approximately expresses the behavior of the DD‐PID controller by combinations of simple nonlinear functions. Although this method can reduce the amount of memory capacity and computing power required, the coefficients in each nonlinear function calculated by the least squares method (LSM) may not be stable because of the multicollinearity of the input signals. In this study, instead of LSM, the least absolute shrinkage and selection operator, which is a sparse modeling method, was 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 multicollinearity. The effectiveness of the proposed method was evaluated by simulation and experimental testing.