Model predictive control prediction horizon

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

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. 

In MPC a dynamic model is used to predict the future output over the prediction horizon based on a set of control changes. The desired output is generated as a set-point that may vary as a function of time the prediction error is the difference between the setpoint trajectory and the model prediction. A model predictive controller is based on minimizing a quadratic objective function over a specific time horizon based on the sum of the square of the prediction errors plus a penalty... 

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. 

Model predictive control, as put forward in Section 9.4.1, is commonly known in its linear form as receding horizon model predictive control and has been used primarily in the control... 

Figure 9.2 Shrinking horizon model predictive control (SHMPC)...

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.)... 

The Model Predictive Control has been characterized by a wide success in industrial applications. It requires a model of the process (and, eventually, an estimate of the disturbances), the measurement on a given time horizon of both the input (i.e., the control action u) and the output (i.e., the controlled variable y) of the controlled process, the desired output (ydes), and a prediction of the process input and output on the same time horizon. 

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. 

The controller receives the on-line composition measurement of the product outlets (extract and raffinate) as feedback data from the plant. These measurements are filtered through a periodic Kalman filter and used together with the simplified SMB model results to estimate the state of the system and to remove the possible moidel errors. The formulation of RMPC is based on the assumption that possible errors or disturbances are likely to repeat and will have a periodic effect on the output, which is the most likely correlation between disturbances and output in a SMB unit. The estimated future concentration profile in the SMB is used to optimize the future behaviour of the plant over a predefined prediction horizon. The controller implements the calculated optimal plant input by changing the external flow rates in order to control the internal flow rates, which are the manipulated variables. Time lags, e.g. between online concentration measurements and optimizer or between optimizer and SMB plant, are insignificant relative to the process dynamics and sampling time for the planned scheme. 

Hence, there is a close link between the model- and modifier-adaptation methods in that the parameterization and the update procedure are both intended to match the KKT conditions. Essentially, modifier-adaptation schemes use a model-predictive control with a one-step prediction horizon. Such a short horizon is justified because the system is static. However, since the updated modifiers are valid only locally, modifier-adaptation schemes require some amount of filtering/regularization (either in the modifiers or in the inputs) to avoid too aggressive corrections that may destabilize the system. 

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... 

The second level is the advanced and predictive control. These are two different control schemes that work at the same level. Information is transmitted horizontally and vertically in this (and upper) level. More elaborated control strategies as selective control, ratio control, feedforward control are implemented. In this second level implicit as well as explicit (heuristic and first principles based) models are used to generate the action. The action is the set point (goal) to achieve at the lowest level. Prediction horizon is (in the case of model predictive control) of tens of movements. 

This work presents the on-line level control of a batch reactor. The on-line strategy is required to accommodate the reaction rate disturbances which arise due to catalyst dosing uncertainties (catalyst mass and feeding time). It is concluded that the implemented shrinking horizon on-line optimization strategy is able to calculate the optimal temperature profile without causing swelling or sub-optimal operation. Additionally, it is concluded that, for this process, a closed-loop formulation of the model predictive controller is needed where an output feedback controller ensures the level is controlled within the discretization intervals. 

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. 

During the last two decades, model-predictive control (MPC) (Allgower et ah, 1999, Mayne, 2000 and Rao and Rawlings, 2000) has increasingly been applied to the control of processes with interacting dynamics. The basic idea of MPC is to employ a plant model that predicts the reaction of the plant to the past and future inputs, and to optimize a number of future inputs such that the predicted outputs follow the desired trajectory over a certain period of time (called the prediction horizon). This process is iterated, only the next input is applied to the plant, and new inputs are computed for a prediction horizon that is shifted one step into the future, taking new measurements into account. Thus, the behavior of the real process and disturbances are taken into account. 

In the classical concept of predictive control, the trajectory (or set-point) of the process is assumed to be known. Control is implemented in a discrete-time fashion with a fixed sampling rate, i.e. measurements are assumed to be available at a certain frequency and the control inputs are changed accordingly. The inputs are piecewise constant over the sampling intervals. The prediction horizon Hp represents the number of time intervals over which the future process behavior will be predicted using the model and the assumed future inputs, and over which the performance of the process is optimized (Fig. 9.1). Only those inputs located in the control horizon H, are considered as optimization variables, whereas the remaining variables between Hr+1 and Hp are set equal to the input variables in the time interval Hr. The result of the optimization step is a sequence of input vectors. The first input vector is applied immediately to the plant. The control and the prediction horizon are then shifted one interval forward in time and the optimization run is repeated, taking into account new data on the process state and, eventually, newly estimated process parameters. The full process state is usually not measurable, so state estimation techniques must be used. Most model-predictive controllers employed in industry use input-output models of the process rather than a state-based approach. 

As discussed above, the task of the controller is to optimize the performance of the process over a certain horizon in the future, the prediction horizon. Specifications of product purities, equipment limitations and the dynamic process model (a full hybrid model of the process, including the switching of the ports and a general rate model of all columns) appear as constraints. The control algorithm solves the following nonlinear optimization problem online ... 

The desired purity for the experiment reported below was set to 55.0% and the controller was started at the 60th period. As in the simulation study, a diagonal matrix R = 0.02 I (3,3) was chosen for regularization. The control horizon was set to Hr = 1 and the prediction horizon was Hv = 60 periods. Figure 9.10 shows the evolution of both the product purity and the controlled variables. In the open-loop mode, where the operating point was calculated based on the initial model, the product purity constraint was violated at periods 48 and 54. After one cycle, the controller drove the purity above 55.0% and kept it there. The controller first reduces the desorbent consumption. This action seems to contradict the intuitive idea that more desorbent injection should enhance separation. However, in the presence of a reaction, this is not true, as shown by this experiment. The controlled variables converge towards a steady state, but they still change from period to period, due to the non-ideality of the plant. 

The essential step in the LQG benchmark is the calculation of various control laws for different values of A and prediction (P) and control (M) horizons (P = M). This is a case study for a special type of MPC (unconstrained, no feedforward) and a special parameter set (M = P) to find the optimal value of the cost function and an optimal controller parameter set. Using the same information (plant and disturbance model, covariance matrices of noise and disturbances), studies can be conducted for any t3q>e of MPC and the influence of any parameter can be examined. These studies... 

Model predictive control, 238 control horizon, 239 prediction horizon, 239 tuning parameters, 242... 

In the present work, we focus on the operational planning and control of integrated production/distribution systems under product demand uncertainty. For the purposes of our study and the time scales of interest, a discrete time difference model is developed. The model is applicable to networks of arbitrary structure. To treat demand uncertainty within the deterministic supply chain network model, a receding horizon, model predictive control approach is suggested. The two-level control algorithm relies on a... 

A two-layered control strategy was described for supply chain management purposes. The strategy combines feedback controllers to account for the fast dynamics at the inventory nodes, while utilising the power of a fiilly-centralised optimisation-based model predictive controller to achieve an optimal operating policy for the supply chain network over a selected time horizon. 

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