Model predictive control moving horizon

FIG. 8-44 The moving horizon approach of model predictive control. 

Extended Kalman filtering has been a popular method used in the literature to solve the dynamic data reconciliation problem (Muske and Edgar, 1998). As an alternative, the nonlinear dynamic data reconciliation problem with a weighted least squares objective function can be expressed as a moving horizon problem (Liebman et al., 1992), similar to that used for model predictive control discussed earlier. 

FIG. 8-43 The moving horizon approach of model predictive control. (Seborg, Edgar, and Melliehamp, Process Dynamics and Control, 2d ed., Wiley, New York, 2004.)... 

Model Predictive Control, also referred as moving or receding horizon control, has become an attractive control strategy especially for linear but also for nonlinear systems subject to input, state or output constraints [4]. MPC determines the control action based... 

MPC (The Model Predictive Control) uses predictive control methods with a dynamic model (linear or non-linear) to compute control signal trajectory that minimize quality indicator for a given time horizon. In each step of the algorithm, the control vector in consecutive moments is computed x(fe),x(fe+1),..., x k + Ns — 1) (k - actual time, Ns - control horizon). In each discrete time step k first control vector x(fe) from optimized control trajectory is used—then, when the prediction and control time horizon are moved one step forward, the whole procedure is repeated. 

The MPC control problem illustrated in Eqs. (8-66) to (8-71) contains a variety of design parameters model horizon N, prediction horizon p, control horizon m, weighting factors Wj, move suppression factor 6, the constraint limits Bj, Q, and Dj, and the sampling period At. Some of these parameters can be used to tune the MPC strategy, notably the move suppression faclor 6, but details remain largely proprietary. One commercial controller, Honeywell s RMPCT (Robust Multivariable Predictive Control Technology), provides default tuning parameters based on the dynamic process model and the model uncertainty. 

A key feature of MPC is that future process behavior is predicted using a dynamic model and the available measurements. The controller outputs are calculated so as to minimize the difference between the predicted process response and the desired response. At each sampling instant the control calculations are repeated and the predictions updated based on current measurements, which is a moving horizon approach. Garcia et al. (1989), Richalet (1993), and Qin and Badgwell (1997) have provided surveys of the MPC approach. 

A second proposition relies on the idea that the on-line optimization problem is unconstrained after a certain time step in the finite moving horizon. Where in the finite horizon that happens is determined by examining whether the state has entered a certain invariant set (Mayne, 1997). Once that happens, then closed-form expressions can be used for the objective function from that time point the end of the optimization horizon, p. The idea is particularly useful for MFC with nonlinear models, for which the computational load of the on-line optimization is substantial. A related idea was presented by Rawlings and Muske (1993), where the on-line optimization problem has a finite control horizon length, m, and infinite prediction horizon length, p, but the objective function is truncated, because the result of the optimization is known after a certain time point. 

Once the solution of the dynamic optimisation problem is foimd (with 8 collocation points for state variables, and considering the control variable as piecewise constant within 1 element with a length of 0.06 h hich is the prediction horizon), the computed optimal input within the first sampling period is applied both to the actual plant and to the model. The whole procedure is repeated with the moving horizon strategy in each sampling instant. 

The AFM algorithm can be easily incorporated into an MFC scheme, where in each time step k a rigorous nonlinear optimization problem is formulated. The objective is to calculate the optimal values of the manipulated variables v over a control horizon M, so that the error between the RBF model predictions and the desired set-point over a prediction horizon N is minimized. As soon as the optimization problem is solved, the first control move (k) is implemented, and then the RBF model is updated using the AFM algorithm. The procedure is shown in figure 2. Assuming one controlled variable, the optimization problem can be described by the following set of equations ... 

The MPC strategy can be summarized as follows. A dynamic process model (usually linear) is used to predict the expected behavior of the controlled output variable over a finite horizon into the future. On-line measurement of the output is used to make corrections to this predicted output trajectory, and hence provide a feedback correction. The moves of the manipulated variable required in the near future are computed to bring the predicted output as close to the desired target as possible without violating the constraints. The procedure is repeated each time a new output measurement becomes available. 

In the recent years Simulated Moving Bed (SMB) technology has become more and more attractive for complex separation tasks. To ensure the compliance with product specifications, a robust control is required. In this work a new optimization bas adaptive control strategy for the SMB is proposed A linearized reduced order model, which accounts for the periodic nature of the SMB process is used for online optimization and control purposes. Concentration measurements at the raffinate and extract outlets are used as the feedback information together with a periodic Kalman filter to remove model errors and to handle disturbances. The state estimate from the periodic Kalman filter is then used for the prediction of the outlet concentrations over a pre-defined time horizon. Predicted outlet concentrations constitute the basis for the calculation of the optimal input adjustments, which maximize the productivity and minimize the desorbent consumption subject to constraints on product purities. 

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