Non-Iterative Data-Driven Tuning of Model-Free Control Based on an Ultra-Local Model

In this paper, we present a data-driven tuning method for model-free control based on an ultra-local model (MFC-ULM), which is also called intelligent proportional-integral-derivative control. In industries, the control design must be easy, and it is important that the control law can be applied to nonlinear systems. The MFC-ULM has most of these features. However, in practice, trial-and-error tuning of MFC-ULM design parameters is necessary. To address this problem, we adopt a data-driven tuning approach. In the proposed method, the MFC-ULM design parameters can be tuned from single-experiment data without requiring system identification, and optimal parameters for the MFC-ULM are obtained using the least-squares method. Additionally, we adopt
$L_{2}$
-norm regularization to avoid overlearning. The effectiveness of this method was examined using simulations of two nonlinear systems. The results revealed that the MFC-ULM design parameters can be obtained directly without knowing the characteristics of the controlled object.