Model Algorithmic Control

When thermodynamics or physics relates secondary measurements to product quality, it is easy to use secondary measurements to infer the effects of process disturbances upon product quality. When such a relation does not exist, however, one needs a solid knowledge of process operation to infer product quality from secondary measurements. This knowledge can be codified as a process model relating secondary to primary measurements. These strategies are within the domain of model-based control Dynamic Matrix Control (DMC), Model Algorithmic Control (MAC), Internal Model Control (IMC), and Model Predictive Control (MPC—perhaps the broadest of model-based control strategies). 

Other recent developments in the field of adaptive control of interest to the processing industries include the use of pattern recognition in lieu of explicit models (Bristol (66)), parameter estimation with closed-loop operating data (67), model algorithmic control (68), and dynamic matrix control (69). It is clear that discrete-time adaptive control (vs. continuous time systems) offers many exciting possibilities for new theoretical and practical contributions to system identification and control. 

Model predictive control (MPC) has become widely known as dynamic matrix control (DMC) and model algorithmic control (MAC). A review of the origins of this class of techniques and their theoretical foundations is provided by Garcia et al. [10]. Many complex applications were reported at the recent IFAC Workshop [11]. 

Wright, S. J. Applying New Optimization Algorithms to Model Predictive Control. Chemical Process Control—V Proceedings. AIChE Symp Ser 316, 93 147-155 (1994). 

Sparacino, G. and Cobelli, C., Deconvolution of physiological and pharmacokinetic data comparison of algorithms on benchmark problems, in Modeling and Control in Biomedical Systems, Linkens, D.A. and Carson, E., Eds., Elsevier, Oxford, 1997, pp. 151-153. 

The details of the control strategy have received much less attention. The theoretical (159) and experimental (160) analyses of the transfer function for CZ growth are notable exceptions. Algorithms for model-based control are just being developed. 

One important class of nonlinear programming techniques is called quadratic programming (QP), where the objective function is quadratic and the constraints are linear. While the solution is iterative, it can be obtained quickly as in linear programming. This is the basis for the newest type of constrained multivariable control algorithms called model predictive control, which is heavily used in the refining industry. See the earlier subsection on model predictive control for more details. 

A second approach to the problem of difficult to obtain measurements is knowledge-based or model-based control. Knowledge-based systems attempt to use various types of knowledge of the biological process (rules etc.) to supplement traditional mathematical control approaches.16 Expert systems are one type of knowledge-based control. Model-based control systems use a model of the process as part of the control algorithm their reliability depends on the accuracy of the model. 

However, it is essential that the triage nurse be prepared to utilize an infectious disease triage model algorithm when triaging during an infectious disease disaster. Should such a situation occur, the algorithm to be used will likely be issued by the state or territorial department of health in concert with the U.S. Centers for Disease Control and Prevention. 

After several years of effort, constrained model predictive control (MFC), the de facto standard algorithm for advanced control in process industries, has finally succumbed to rigorous analysis. Yet successful practical implementations of MFC were already in place almost two decades before a rigorous stability proof for constrained... 

Closed-loop identification has been addressed extensively in a linear stochastic control setting (Astrom and Wittenmark, 1989). Good discussions of early results from a stochastic control viewpoint are presented by Box (1976) and Gustavsson et al (1977). Landau and Karimi (1997) provide an evaluation of recursive algorithms for closed-loop identification. Van den Hof and Schrama (1994), Gevers (1993), and Bayard and Mettler (1992) review research on new criteria for closed-loop identification of state space or input-output models for control purposes. 

Badgwell, T. A., A robust model predictive control algorithm for stable nonlinear plants. Preprints of ADCHEM 97, Banff, Canada (1997). 

This paper presents the application of a model based predictive control strategy for the primary stage of the freeze drying process, which has not been tackled until now. A model predictive control framework is provided to minimize the sublimation time. The problem is directly addressed for the non linear distributed parameters system that describes the dynamic of the process. The mathematical model takes in account the main phenomena, including the heat and mass transfer in both the dried and frozen layers, and the moving sublimation front. The obtained results show the efficiency of the control software developed (MPC CB) under Matlab. The MPC( CB based on a modified levenberg-marquardt algorithm allows to control a continuous process in the open or closed loop and to find the optimal constrained control. 

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