Identification of Dynamic Matrix and Noise Model Using Closed-loop Data

Abstract

Model predictive controllers (MPC) have found many successful applications in process industries for about three decades. One of the key aspects of MPC is the prediction of the future process response and minimization of the output deviation from the setpoint by manipulating the inputs. A model for the process is required to make these predictions based on past data. Hence an MPC design starts with first identifying a nominal model for the process. One of the industrially successful predictive control schemes is the dynamic matrix control or DMC, which explicitly uses a lower triangular matrix called ‘dynamic matrix’ containing the step response coefficients corresponding to the deterministic input(s) to the process [1, 2]. Many other MPC formulations also use the dynamic matrix in one way or the other [92, 5, 93]. For constructing the dynamic matrix, in the case of DMC, a step response model for the process is first obtained from the open-loop data. The step response coefficients are then arranged in a specific lower triangular form in the dynamic matrix, as will be discussed in detail in Chapter 6. However, for safety reasons and other practical limitations, open-loop operation of the process may not always be possible, or in some cases there may be a hidden feedback in the system. Estimation of the dynamic matrix from closed-loop data is desirable in such cases. It has been shown [94] that if the model is used for model-based control design then the favorable experimental conditions are actually under closed-loop conditions.