Truncation error correction by designing input-adjustment-output coefficients for dynamic matrix control based on cubic spline function

The truncation error is an important problem in the dynamic matrix control (DMC) algorithm. Generally, the dynamic information of a plant for the traditional DMC algorithm is determined by the step response. However, the step response of the plant is limited in practice, which leads to the truncation error of the modeling horizon in the feedback correction of DMC algorithm. A truncation error correction method based on cubic spline function is proposed for DMC algorithm, which is realized by designing coefficients and tracking the dynamic response of the system. In the feedback correction of DMC algorithm, the relationship between the correction parameter and the correction difference is constructed by the fitting of cubic spline functions on the intervals. A truncation error correction procedure is presented to calculate the correction parameters by inputting of the correction difference into the relationship. Then, the control increment and predicted model output are computed based on the correction parameters and updated shift matrix. Finally, numerical experiments demonstrate that the control performance of the proposed DMC algorithm has been much improved compared to that of traditional DMC algorithm.