Predictive control

Even with the advanced PID control, regulation is never perfect. The system needs a difference between Cl and CO to react and with a small gain this difference can be large, so at least temporarily the control is partial. Moreover, an attempt to compensate for this, for example by increasing A3 in Eq. (5), may lead to instabilities, oscillations, etc. 

A simple way to circumvent the problem and improve the control is to use predictive control, often called feed forward. The idea is to use a control signal, CCff, which in some way reflects the expected time-course of CC that is needed to keep CO close to CL In technical systems this control is frequently called model predictive control (MPC [12]), because CCff is typically derived from a mathematical model. In biological systems, the feed forward is mostly delivered by nerve signals, more rarely by hormones. 

All exocrine and endocrine glands have a considerable nerve supply. Well known is Pavlov s conditioned reflex [13], where the digestive juices can be secreted via, for example, a sound. But also for many relatively fast reacting hormones - including insulin - the neural feed forward control plays a considerable role. 

Another familiar example is the control of muscle movements [7, 14]. On top of complex sensory feedback systems in muscles and spinal cord, the cerebellum and basal ganglia deliver a feed forward signal that takes the person s reaction time into consideration and presets the muscles to a situation some 50-100 ms ahead. The PID control can then make small corrections. The precision of the movements can 

Rawlings, IEEE Control Systems Magazine, 20(3) 38, 2000). Camacho and Bordons, Model Predictive Control, 23 ed., Springer-Verlag, New York, 

Maciejowski, Predictive Control with Constraints, Prentice-Hall, Upper Saddle River, N.J., 2002. Seborg, Edgar, and Mellichamp, Process Dynamics and Control, 2d ed., Wiley, New York, 2004, Chap. 20. 

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

A key feature of MPC is that future process behavior is predicted by using a dynamic model and 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. In typical industrial applications, the set point and target values for the MPC calculations are updated by using online optimization based on a steady-state model of the process. 

The current widespread interest in MPC techniques was initiated by pioneering research performed by two industrial groups in the 1970s. Shell Oil (Houston, Tex.) reported its Dynamic Matrix Control (DMC) approach in 1979, while a similar technique, marketed as IDCOM, was published by a small French company ADERSA in 1978. Since then, there have been thousands of applications of these and related MPC techniques in oil refineries and petrochemical plants around the world. Thus, MPC has had a substantial impact and is currently the method of choice for difficult multivariable control problems in these industries. However, relatively few applications have been reported in other process industries, even though MPC is a very general approach that is not limited to a particular industry. 

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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)... 

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. 

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. 

Application of Wiener type predictive controller to the continuous solution polymerization reactor... 

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. 

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). 

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