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This study presents a repetitive control method based on a multi-stage particle swarm optimization (PSO) algorithm with variable intervals to enhance the tracking performance of Takagi–Sugeno (T–S) fuzzy systems. First, a T–S fuzzy model is used to describe a nonlinear system. A modified repetitive control structure with two repetitive loops guarantees the tracking accuracy of periodic signals. Taking advantage of the two-dimensional (2D) property with continuous control and discrete learning, a continuous-discrete 2D model is presented to describe the nonlinear repetitive control system. Next, a multi-stage PSO algorithm with variable intervals searches for the best parameter combination in the linear matrix inequality-based stability condition to regulate the control and learning actions, which avoids a suboptimal solution and guarantees high control accuracy. Finally, an application to control the speed of synchronous motor with a permanent magnet demonstrates the validity of the method, and comparisons with related methods show its superiority. [ABSTRACT FROM AUTHOR]

Plate shape recognition in the roller quenching process provides effective feedback signals for plate shape control. Its accuracy directly affects the control effect. Most studies have obtained the high recognition accuracy of the plate shape defects by neural networks or parameter identification methods, but cannot provide a sufficiently detailed feedback signal with controllable accuracy for plate shape control, limiting the further improvement of the control effect. For these problems, a plate shape recognition method for roller quenching process is proposed. Firstly, the roller quenching process and the representation of the plate shape are introduced, and the structure of the plate shape recognition method is designed. Secondly, the Gaussian function is used to describe the plate shape defects, and the physical significance of each parameter in the Gaussian function is analyzed. Based on the Gaussian function, a plate shape fitting method with iterative structure and controllable fitting accuracy is designed to extract the detailed information about each defect. Thirdly, according to the actual production experience, the expert rules are designed for plate shape classification and to evaluate the quality. Finally, the method is verified by industrial production data. The results verify the correctness and effectiveness of our method, indicating that the method can provide important guidance for the improvement of plate shape quality and lays an important foundation for plate shape control. • An plate shape fitting framework is proposed with controllable fitting accuracy. • Higher classification accuracy is obtained by integrating the expert rules. • The algorithm process is simple and easy to implement in the industrial field. [ABSTRACT FROM AUTHOR]