System and methodology and adaptive, linear model predictive...

Details System and methodology and adaptive, linear model predictive... System and methodology and adaptive, linear model predictive...

2000-04-06

2004-11-30

Teska, Kevin J. (Department: 2123)

Data processing: structural design, modeling, simulation, and em

Simulating nonelectrical device or system

Chemical

C700S029000, C700S038000

Reexamination Certificate

active

06826521

ABSTRACT:

FIELD OF THE INVENTION
This invention relates to the control of a multivariable, time-varying, industrial process that exhibits either linear or nonlinear response characteristics and more particularly the on-line execution of an adaptive, linear model predictive controller derived from a rigorous, nonlinear model of such processes.
DESCRIPTION OF THE PRIOR ART
There are many multivariable, time-varying, industrial processes that exhibit either linear or nonlinear response characteristics. Several examples of such processes are a distillation column, a separator train, a catalytic cracking unit, a chemical reactor, and a utility boiler. Control of these processes using traditional multivariable control techniques with fixed model representations is difficult because of the variable process conditions that result from either process nonlinearities, measured or unmeasured disturbances, feedstock changes, or operator-induced changes.
The standard practice for advanced industrial process control in processes of the type described above is to use linear, multivariable, model predictive controller (MPC) software. See for example, the Setpoint, Inc. product literature dated 1993 entitled “SMC-Idcom: A State-of-the-Art Multivariable Predictive Controller”; the DMC Corp. product literature dated 1994 entitled “DMC™: Technology Overview”; the Honeywell Inc. product literature dated 1995 entitled “RMPCT Concepts Reference”; and Garcia, C. E. and Morshedi, A. M. (1986), “Quadratic Programming Solution of Dynamic Matrix Control (QDMC)”, Chem. Eng. Commun. 46: 73-87. The typical MPC software allows for model scheduling (i.e. changing the model gains and/or dynamics) to improve control performance when operating on a nonlinear and/or time-varying process. The controller uses new models that are generally calculated in an off-line mode, or may be calculated by an adaptive algorithm that uses recent operating data.
If the models are calculated off-line, then the controller requires additional on-line logic to determine which set of model parameters should be used at the current time. This logic is often difficult to develop since it may depend on numerous operating variables. For large problems there may be a significant number of different models required in order to improve performance. Furthermore, there is a possibility that invoking a particular set of model parameters for certain operating points will eventually lead to unstable operation. Thus, the off-line model identification task is extremely time-consuming and expensive and its implementation on-line is not proven robust over wide operating ranges. Therefore, in most applications a simplified set of models is defined (e.g. high feed rate and low feed rate models; or winter and summer operation models).
The control performance using a simplified set of models is not much better than what can be achieved using a single model. In fact, controllers developed using this methodology do not usually remain on-line for processes demonstrating a high degree of non-linearity.
Adaptive model identification is another way to modify linear models to capture current operating conditions. This procedure uses recent operating data to automatically adjust the models on-line. One of the biggest problems of this approach is inherent from the dual control principle, which essentially states that the uncertainty in model identification increases as the control performance improves (i.e. as the control uncertainty decreases). Thus, it is always much more difficult to obtain accurate new models when the controller is running since the input signals are correlated and the output signals have small deviations. In fact, the identification process often fails because of the loss of persistent excitation in the input signals. See Astrom, K. J. and Wittenmark, B. (1995) “Adaptive Control”, Addison-Wesley Publishing Company, Inc., pp. 69-70 and 473-477, for a detailed discussion of this problem. This inherent mathematical problem limits the success of adaptive, linear model identification. Current algorithms use various methods to turn off or heavily filter the parameter changes in the adaptive identification. Otherwise, poor models could be selected because of the high model uncertainty and ultimately the control performance would suffer.
There are some types of industrial processes that cause additional problems for empirical model identification methods. For example, a batch process could operate with multiple product runs during which the model gains change by orders of magnitude (e.g. polyethylene, polypropylene processing), yet the batches may not reach equilibrium. Linear, empirical methods cannot obtain accurate models for such processes since the necessary operational data is not available.
Model identification problems also occur for processes that do not allow plant testing near dangerous or unstable operating conditions (e.g. catalytic cracking, reactors). Controllers for such processes try to prevent violation of constraint limits that could lead to unstable behavior, however the benefits often increase by operating closer to the limits. Therefore to improve performance and maximize benefits, the controller needs to have multiple models available for all the operating regions. This is not possible with linear, empirical methods. A rigorous, nonlinear process simulation model could, however, provide these multiple models for the controller.
The same type of model identification problems can occur for non-dangerous processes that have product specification limits (e.g. distillation columns). The plant manager does not want to generate off-spec product, so the testing must be conducted such that the purity remains within acceptable limits. However, greater benefits are typically obtained by operating closer to these limits. Thus, the empirical methods cannot generate accurate models for operating points that are close to or beyond the limits. High-purity separation processes present the most significant modeling problems as very nonlinear behavior may occur over the different operating regions.
Another disadvantage of empirical MPC identification methods occurs when the controller is used together with real-time optimization (RTO) since the models are not consistent. RTO generally uses a more rigorous, nonlinear model while MPC is either using a fixed linear model obtained from plant testing, or an adaptive, linear model obtained from on-line data. In either case, the MPC models are not derived from the RTO model (nor vice versa), so this inconsistency often leads to significant performance degradation. See for example the article by Y. Z. Friedman entitled “What's wrong with unit closed loop optimization?” which appeared in the October 1995 issue of Hydrocarbon Processing at pp. 107-116.
Another means of treating nonlinear, time-varying processes is to use robust control methods. The idea behind robust control is to use a single process model, but to tune the controller by accounting for modeling uncertainties. The control design is tested against a range of expected operating conditions and is retuned until the performance is fairly consistent (or robust) over all conditions. The robust tuning method reduces the sensitivity of the controller to model error. Honeywell has applied this technique to its RMPCT (Robust Multivariable Predictive Control Technology) product as described in the product literature referenced above.
However, there are some drawbacks to using robust control techniques. In particular, by restricting the controller to a single linear model, robust tuning often results in slow, sluggish control performance over the typical operating range because it attempts to improve the worst-case performance. Thus, the robust tuning often degrades performance during periods of small modeling error. This occurs because the expected range of modeling uncertainties is often too large for a single model and single set of tuning parameters. It is possible to vary the tuning, but this becomes a difficult on-line implementation task. The re

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