Estimation of the Dynamic Matrix and Noise Model for Model Predictive Control Using Closed-Loop Data

A dynamic matrix is a lower triangular matrix containing the step response coefficients of the deterministic input used in the model predictive control schemes such as the dynamic matrix controller. Subspace matrices (defined in subspace state-space identification methods) corresponding to the deterministic input and the stochastic input contain the impulse response coefficients of the deterministic and stochastic models, respectively. This paper proposes a new subspace identification based method for the estimation of the dynamic matrix of the deterministic input(s) directly from the closed-loop data. The noise model is simultaneously obtained from the closed-loop data in the impulse response form. The method is extendable to the case of measured disturbances. All of the results presented in this paper are applicable to the multivariate systems. Guidelines for the practical implementation of the algorithm are also presented in this paper. The proposed method is illustrated through MATLAB simulations and an application on a pilot-scale plant.