Repetitive Control Process for Periodic Disturbance Cancellation Using Data Classification With a Fuzzy Regression Approach

Abstract

The utilization of a repetitive controller to cancel periodic disturbance or noise in mechanical systems has become increasingly important for industrial applications. In this study, a repetitive control process was developed using a data classification method, with a fuzzy regression approach and basis function, to reduce tracking errors in feedback controllers. First, a system model using the basis function is illustrated to compute the matched basis functions and their associated coefficients. A real case example of improving the focus of an electron beam subjected to periodic fluctuations has been described for verification and error analysis. Next, model algorithms containing pure and fuzzy regression are introduced into a repetitive feedback control system to reduce tracking errors caused by a periodic disturbance. System output data are categorized using fuzzy inference rules as similar data forming a single group are typically more reliable than the entire output data. The fuzzy theorem approach adopts a Gaussian membership function for system output variables owing to uncertainties that arise from modeling errors, environmental noise, etc. It is determined that the repetitive control process based on data classification with a fuzzy regression approach is more effective than using a pure regression approach. Increasing the number of data classifications initially improves accuracy; however, this decreases when the number of data classifications continues to increase. The optimal root-mean-square output tracking error convergence value was determined as 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-14.09</sup> when the system output data was classified into four categories, demonstrating the satisfactory reduction of a periodic disturbance. Similar results were obtained using the pure regression algorithm, where the lowest averaged verification error was 2.71% for the linear basis function model, with data classified into four categories, and this corresponded to an average prediction error of 3.86%.