Using Taguchi's method and orthogonal function approximation to design optimal manipulated trajectory in batch processes

A novel experimental scheme is proposed to integrate orthogonal function approximation with Taguchi's method (orthogonal array) for designing the optimal manipulated trajectory of a batch process. The orthogonal function approximation finds a set of orthonormal function,; as the basis to represent the batch trajectory. The optimal trajectory can be obtained if the location of the coefficients of the orthonormal functions is properly adjusted in the function space. The Taguchi approach is used to design and analyze the effect of each coefficient on reaching the optimal objective (quality) function. Because the coefficients are implicitly related to the objective function, they simply vary over two levels in a systematic way, and they would be moved into the optimal design condition. A search procedure for the optimal design coefficients is also proposed. As opposed to model-based design, the proposed method utilizes the simplicity of Taguchi methods to determine the potentially available knowledge of dynamic batch processes, For its potential applications, this combinational method is demonstrated through two simulation case studies.