(642c) Gray-Box Modeling of an Integrated Plant with Incomplete Dynamic Information

Competitive market environment has driven many chemical plants to adopt complex and integrated processes with material recycle loops. These recycle streams recover valuable material and provide economic benefits. At the same time, however, they introduce process interactions and multiple time-scale phenomena, which pose challenges to identification, modeling, and control. First, integrated plant shows a combination of both fast dynamics from individual processes as well as slow changes arising from the recycle loop interaction. These slow-scale dynamics often last very long time compared to the residence time of individual units and complicate the system identification experiment. Many identification literatures often assume that model identification experiment can be performed over a long period of time, such as more than three days [1], [2]. Nonetheless, in many practical situations the experiment may be limited to much shorter time. In this case, the obtained model may be unable to capture the slow dynamics of the system accurately. Secondly, this multiple time-scale system tends to be very ill-conditioned, if the recycle ratio is high. There are some input and output directions that show very high gains, while others have very small gains. Therefore, the identified model may not describe this low gain direction very accurately, because the outputs are hardly excited along these directions during the plant experiment. Unfortunately, these small gain directions can severely compromise the robustness of a model-based controller. This is because any small error along the low-gain directions can be amplified when the model is inverted and cause the manipulated variables to move aggressively.

Oftentimes in practice, a steady-state description of the plant is available, such as from material balances, thermodynamic equations, flowsheet simulator, etc. Nonetheless, performing plant-wide optimization based on the steady-state model may not provide as much benefit as the dynamic optimization as shown in many works (such as in [3], [4]). Motivated by this, we propose to derive a dynamic model of an integrated plant that is suitable for the plant-wide optimization. In particular, we are interested in practical cases where identification experiment is limited to much shorter period of time than the plant's largest time constant, but prior knowledge about the plant's steady state gains is available. Our approach suggested that an identification experiment is first performed on the integrated plant up to an allowable period of time, which is likely to be less than 50 hours. With appropriate experimental design and data preprocessing, a dynamic model that captures initial transient dynamics of an integrated plant can be obtained. However, because the experiment is relatively short, the dominant pole (or the longest time constant) of the system will not be captured by the model, making it unreliable for the long range prediction. Therefore, our approach is to parameterize the identified model as a step response model truncated at the time when the prediction accuracy starts to degrade. Then the residual dynamics are approximated as low-order system and augmented to the step response model, while ensuring that the settling gains of the model match up with the steady-state gain from the prior knowledge.

In this presentation, the proposed method is demonstrated on integrated plant examples, including a reactor-distillation-recycle system. The results show that an MPC using the augmented model has better performance than the one using an original identified model from the short experiment. In addition, we provide a guideline to prevent the model errors in the low-gain directions of such an ill-conditioned system from degrading the performance in the MPC optimization.

References

[1] R. Amirthalingam and J. H. Lee, Subspace identification based inferential control applied to a continuous pulp digester, J Process Contr, 9: 397-406, 1999.

[2] B. C. Juricek, D. E. Seborg, and W. E. Larimore, Identification of the Tennessee Eastman challenge process with subspace method.

[3] J. Z. Lu, Challenging control problems and emerging technologies in enterprise optimization, In Proc. 6th IFAC symposium on Dynamic and Control of Process Systems, pp. 23-24, 2001.

[4] T. Tosukhowong, J. M. Lee, J. H. Lee, and J. Lu, An introduction to a dynamic plant-wide optimization strategy for an integrated plant, Comput. Chem. Engng., 29(1):199-208, 2004.