Nonlinear Programming Strategy for the dynamic spinning process optimization

The polyester fiber spinning process is extensive, and the involved dynamic models are complex and difficult to solve analytically. This paper presents the optimal control strategy of polyester fiber production. Based on a dynamic model of the spinning process, optimal objectives are determined to minimize production costs and meet production goals. We employ Radau collocation on finite elements to discretize the continuous dynamic model, which is transformed into finite-dimensional nonlinear programming (NLP) model. The developed strategy combines a multiple shot algorithm and half-score method to solve the obtained NLP model. We find the best initial values quickly and achieve the control objective under the constraints of the spinning process's mechanism equations. The objective function measures the difference between the actual production and the desired value, and the merit of the objective function directly affects the control variables. In this paper, single-objective and multi-objective control strategies are designed according to different production requirements. To make the objective function effectively reflect the product quality, its setting is inseparable from each state variable, and we explore the control effect for different objective functions. Finally, simulation results verify the feasibility and superiority of the orthogonal collocation on finite element and multiple shooting algorithms.