(295e) State and Parameter Estimation in Dynamic Real?Time Optimization with Closed?Loop Prediction

Closed-loop dynamic real-time optimization (CL-DRTO)[1] is an extension of the traditional Dynamic Real-time Optimization [2] strategy that accounts for the plant closed-loop response when making economic decisions. This is accomplished by including the underlying model predictive control structure in the system model. Even though the computational load for computing the optimal trajectories increases, CL-DRTO implementations outperform the traditional static counterpart especially when the controller is detuned due to performance limitations, such as plant-model mismatch, inverse response, and dead time.

To date, plant feedback has been incorporated into the CL-DRTO model through an additive noise paradigm. Here, the difference between the model prediction and current system measurements is computed and this “bias” is added to the model outputs and kept constant during the prediction horizon. Despite being simple to implement and showing good results in several case studies, this feedback strategy may not be flexible enough for practical applications. For example, if the noise magnitude depends on the value of the deterministic plant disturbances, the noise effect on the model may increase proportionally with the disturbance value and an additive disturbance model may fail to represent this phenomenon.

In this work, we use different strategies for incorporating plant feedback into the CL-DRTO cycle, namely: estimating only the states, and a combined parameter and state estimation via Moving Horizon Estimation (MHE). On the one hand, these alternatives allow different ways of representing the model uncertainty, such as uncertainty in the CL-DRTO initial condition and/or parametric uncertainty that may affect the model nonlinearly. On the other hand, solving an MHE problem may be computationally expensive and, in the case where parameters are estimated, identifiability problems may arise.

Therefore, our work contributes to the CL-DRTO literature by investigating the benefits and practical challenges associated with these feedback strategies, when compared to the standard bias updating strategy, in two important chemical engineering case studies, a distillation column and a continuous stirred tank reactor (CSTR).

[1] Jamaludin, M.Z. and Swartz, C.L., 2017. Dynamic real‐time optimization with closed‐loop prediction. AIChE Journal, 63(9), pp.3896-3911.

[2] Kadam, J., Marquardt, W., Schlegel, M., Backx, T., Bosgra, O., Brouwer, P.J., Dünnebier, G., Van Hessem, D., Tiagounov, A. and De Wolf, S., 2003. Towards integrated dynamic real-time optimization and control of industrial processes. Proceedings foundations of computer-aided process operations (FOCAPO2003), pp.593-596.