# Model-Predictive Controller Solves Complex Problems

## Model-predictive control is the latest trend in multivariable control technology. Model-predictive controllers (MPCs) use mathematical models to predict the future behavior of the processes they control, then adjust their control efforts to produce the desired results. MPCs are designed to steer multiple process variables towards their respective setpoints while keeping both process input...

03/01/1998

Model-predictive control is the latest trend in multivariable control technology. Model-predictive controllers (MPCs) use mathematical models to predict the future behavior of the processes they control, then adjust their control efforts to produce the desired results. MPCs are designed to steer multiple process variables towards their respective setpoints while keeping both process inputs and outputs within specified ranges.

This is no easy task. MPCs must account for complex process dynamics, interactions among the process variables, and delays between the application of a control effort and its effect on the process variables. Although several MPCs are now available as commercial software packages, no single technique has yet emerged as the definitive solution to all of these problems.

The Foxboro Company (Foxboro, Mass.) has entered the fray with Connoisseur, an MPC software package developed by Predictive Control Ltd. (Foxboro's sister company in Northwich, U.K.). Connoisseur was designed to make model-predictive control not only practical, but accessible to anyone with basic process engineering knowledge.

This too is a monumental undertaking. The mathematics behind an MPC is much more complex than simple proportional, integral, and derivative calculations. Connoisseur uses a "linear time-series sampled-data model with a multi-input, multi-output structure" just to quantify the behavior of the process. Customizing the generic model for a particular process involves an "unbiased recursive least squares parameter identification" technique.

Then there's the problem of optimizing the process's setpoints. An MPC generally has a choice of where each process variable should be maintained within a range constrained by the physical limits of the process. Certain choices will yield better results than others, depending on the behavior of the process and the placement of the constraints. Connoisseur uses the process model and a linear programming algorithm to search for the setpoints that will minimize the overall cost of operation without violating any of the constraints.

Fortunately, most of those technical details are handled, more or less, automatically. Users need to know enough about their process to specify the order of its model, its settling time, and the sampling interval. Otherwise, Connoisseur walks users through the configuration procedures without the need for extensive control theory.

The first step is creating a model for the process from experimental input/output data. Users can exercise the process by bumping it manually or by applying a series of random perturbations automatically. The resulting measurements of the process variables tell Connoisseur all it needs to know about the behavior of the process. From there, Connoisseur can create the specific controller required to meet the user's performance goals.

Connoisseur can even update the process model automatically if subsequent measurements show that the input/output relationships have changed. This feature allows the controller to adapt to the long-term effects of uncontrollable influences such as equipment wear, fouling, or variations in ambient conditions.

The MPC that Connoisseur produces as a result of these operations may or may not be the ideal controller for any given process. Judging from what I've seen, however, a Connoisseur controller should be particularly effective for handling processes subject to long deadtime, unmeasured disturbances, or both. Foxboro also claims that Connoisseur is faster than competing MPC products and is more economical for smaller processes.

Connoisseur is currently available on DEC, HP, Sun, and Windows NT. The minimum configuration for a PC implementation is a Pentium processor running Windows NT 4.0 (or better), SVGA graphics capability, at least 64 MBytes of RAM and 2 GBytes of disk space, a network communications card, and a Postscript printer. The Connoisseur software (including a runtime license) lists for \$44,800 and is available through Foxboro.

 Author Information Consulting Editor, Vance J. VanDoren , Ph.D., P.E., is president of VanDoren Industries, West Lafayette, Ind.

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