Statistical measures for proportional–integral–derivative control quality: Simulations and industrial data

Abstract

This article focuses on investigation of statistical approaches to the task of control performance assessment. Different statistical measures with Gaussian and non-Gaussian probabilistic distributions are taken into consideration. Analysis starts with the observations for simulated proportional–integral–derivative control error histograms followed by its statistical investigation using selected probabilistic distribution functions. Simulation experiments are followed by the analysis of control data originating from real industrial loops. Shadowing effect of long-tail control error histograms is identified, as it may significantly disable proper loop quality assessment. Results show that non-Gaussian approach with Cauchy or α-stable distributions seems to be reasonable assessment alternative in case of disturbances existing in industrial processes.