Control model predictive

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. 

MPC is traditionally formulated directly in the discrete-time domain, i.e., for sampled data systems. In detail, it is assumed that the system s input is computed (and the system s output is measured) only at discrete time steps tk = kAt, where k is an integer variable, and At is the sampling time. Hereafter, for the sake of compactness, the discrete-time variable is denoted simply by the integer k. 

The basic idea of MPC is to compute, at each time step, k, a prediction of the control action values in Ns time steps, u(k + i k) (i = 1. Ns), where the notation i j stands for the value computed at step i on the basis of the information available up to step j. Then, by using the process model and the predicted control action, an estimate of the process output in the same Ns time steps y (k + i k) (i = 1. Ns) is computed. The predicted value at time k + 1 is applied to the process. 

The prediction of the control input is computed via an optimization method that minimizes a suitably defined objective function, usually composed by two terms the first one is related to the deviation of the predicted output from the reference trajectory (i.e., the tracking error), while the second term takes into account control input changes. Hence, the optimization problem has the form 

In this framework, constraints on the decision variables can be directly taken into account, i.e., the optimization problem is (5.2) subject to 

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C. R. Cutier and R. B. Hawkins, "AppHcation of a Large Model Predictive Controller to a Hydrocracker Second Stage Reactor," Proceedings of... 

Use a decouphng control system d. Use a multivariable control scheme (e.g., model predictive control)... 

Introduction The model-based contfol strategy that has been most widely applied in the process industries is model predictive control (MFC). It is a general method that is especially well-suited for difficult multiinput, multioutput (MIMO) control problems where there are significant interactions between the manipulated inputs and the controlled outputs. Unlike other model-based control strategies, MFC can easily accommodate inequahty constraints on input and output variables such as upper and lower limits or rate-of-change limits. 

Basic Features of MFC Model predictive control strategies have a number of distinguishing features ... 

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

Garcia, C., and Prett, D., Advances in industrial model-predictive control. In Chemical Process Control, CPC-III. (Morari, M. and McAvpy, T. J., eds.). CACHE-Elsevier, New York, 1986. 

Lee, M., and Park, S., A new scheme combining neural feedforward control with model predictive control. AIChE J., 38, 193 (1992). 

Michael Nikolaou, Model Predictive Controllers A Critical Synthesis of Theory and Industrial... 

Off-line analysis, controller design, and optimization are now performed in the area of dynamics. The largest dynamic simulation has been about 100,000 differential algebraic equations (DAEs) for analysis of control systems. Simulations formulated with process models having over 10,000 DAEs are considered frequently. Also, detailed training simulators have models with over 10,000 DAEs. On-line model predictive control (MPC) and nonlinear MPC using first-principle models are seeing a number of industrial applications, particularly in polymeric reactions and processes. At this point, systems with over 100 DAEs have been implemented for on-line dynamic optimization and control. 

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... 

We now develop a mathematical statement for model predictive control with a quadratic objective function for each sampling instant k and linear process model in Equation 16.1 ... 

EXAMPLE 16.3 MODEL PREDICTIVE CONTROL OF A CHEMICAL REACTOR... 

For this example, the controller design was carried out using the MATLAB Model Predictive Control toolbox, which includes a QP solver. Three cases were considered in the preceding problem statement. 

Comparison of the system behavior using three different model predictive controllers (a) minimum variance, (b) input constraint, (c) input penalty. 

Diagram showing the combination of real-time optimization and model predictive control in a computer control system. 

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. 

Backx, T. O. Bosgra and W. Marguardt. Integration of Model Predictive Control and Optimization of Processes. ADCHEM Proceedings, pp. 249-259, Pisa, Italy (2000). Baker, T. E. An Integrated Approach to Planning and Scheduling. In Foundations of Computer Aided Process Operations (FOCAPO), D. W. T. Rippin J. C. Hale and J. F. Davis, eds. CACHE Corporation, Austin, TX (1993), pp. 237-252. 

Camacho, E. F. and C. Bordons. Model Predictive Control. Springer-Verlag, New York (1999). 

Qin, J. and T. A. Badgwell. An Overview of Industrial Model Predictive Control Technology. In Chemical Process Control V, AlChE Symp Ser 316, 93 232-256 (1997). 

Lee J. H. and B. Cooley. Recent Advances in Model Predictive Control and Other Related Areas. Chemical Process Control—V Proceedings, AIChE Symp Ser 316,93 201-216 (1997). 

Morari, M. J. H. Lee and C. E. Garcia. Model Predictive Control. Prentice-Hall, Englewood Cliffs, NJ (in press). 

Patwardhan, A. A., Rawlings, J. B., and Edgar, T. F., Model predictive control of nonlinear processes in the presence of constraints, presented at annual AIChE Meeting, Washington, D.C. (1988). 

Model predictive control is concerned with continuous feedback of information with the objective of reducing the variability of product quality by changing the set points (narrowing the range) in a plant control loop." By nsing model predictive control, projections on batch quality can be made and midstream corrections made to keep a batch within the target limits of the process. 

Due to the complexity of bioprocesses, and the lack of direct in-process measurements of critical process variables, much work is being done on development of soft sensors and model predictive control of such systems. Soft sensors have long been used to estimate biomass concentration in fed-batch cultivations. The soft sensors can be integrated into automated control structures to control the biomass growth in the fermentation. 

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