(769b) Novel Approaches to Online Process Optimization Under Uncertainty

This presentation deals with real-time process optimization, where the objective is usually to minimize an economic cost. Steady-state real-time optimization (RTO) has been around for more than 25 years, but still it is not used much in practice. Some of the reasons and challenges for this are (in expected order of importance):

1. High cost of developing and updating the model structure (offline)
2. Inaccurate values of model parameters and disturbances (online)
3. Computational issues of solving numerical optimization problems

In a recent review paper on current practices of RTO [1], it was noted that the fundamental limiting factor of many traditional RTO implementation is the steady-state wait time associated with the online update of the model. In other words, one must wait for the process to reach steady-state before updating the model using "data reconciliation" (Challenge 2). In order to address this issue, we propose a novel approach to combine traditional steady-state and dynamic RTO, known as “Hybrid RTO” [2]. Here, we update the model using dynamic models and transient measurements as done in dynamic RTO but solve the optimization problem using the corresponding steady-state models as done in traditional RTO. By doing so, we show that we can achieve similar performance as dynamic RTO, but at computation times similar to steady-state RTO [2].

The Hybrid RTO approach would still require solving a numerical optimization problem online. In order to eliminate the need for online computation (challenge 3), we propose a feedback-based approach, where we show that optimal operation over different operating conditions can be achieved using conventional feedback control structures and simple logics [3,4]. The main idea here is to systematically control the active constraints tightly and for the remaining unconstrained degrees of freedom, we estimate and control the steady-state gradient from the cost to the inputs using a novel non-obvious gradient estimation method. This is achieved by linearizing a nonlinear dynamic model from the inputs to the cost, which is updated using transient measurements [5]. Using this novel gradient estimation approach, we provide a generalized framework for optimal operation without solving numerical optimization problems [3].

We finally present an integrated formulation of the different RTO approaches that can tackle all the three challenges listed above. With the recent developments of various approaches to online process optimization, different methods work in different timescales and can handle different kinds of uncertainty. We show that the different approaches are in fact complementary and not contradictory [6]. We propose to combine the different approaches in a hierarchical fashion with three layers that work in the fast, medium and slow time scale. Methods such as self-optimizing control provides fast reaction to the disturbances keeping the process in the near-optimal region. This is followed by model-based RTO approach such as the hybrid RTO approach that adjusts the setpoints to the optimizing control layer below in the medium time scale. Finally, data-based approaches such as extremum seeking control or modifier adaptation estimates the plant steady-state gradients directly from the cost measurements to account for model structural mismatch in the slow time scale.

References

1. Darby ML, Nikolaou M, Jones J, Nicholson D. RTO: An overview and assessment of current practice. Journal of Process Control. 2011 Jul 1;21(6):874-84.
2. Krishnamoorthy, D., Foss, B. and Skogestad, S., 2018. Steady-State Real-time Optimization using Transient Measurements. Computers and Chemical Engineering, Vol 115, pp.34-45.
3. Krishnamoorthy, D. and Skogestad, S., 2019. Online Process Optimization with Active Constraint Set Changes using Simple Control Structures. Ind. Eng. Res. Chem (submitted)
4. Reyes-LúaA, Zotică C, Das T, Krishnamoorthy D, Skogestad S. 2018. Changing between Active Constraint Regions for Optimal Operation: Classical Advanced Control versus Model Predictive Control. Computer Aided Chemical Engineering, Vol. 43, pp. 1015-1020.
5. Krishnamoorthy, D., Jahanshahi, E. and Skogestad, S., 2019. A Feedback Real Time Optimization Strategy using a Novel Steady-state Gradient Estimate and Transient Measurements. Ind. Eng. Res. Chem, Vol. 58 (1), pp. 207–216
6. Straus, J. Krishnamoorthy, D. and Skogestad, S., 2019. On combining self-optimizing control and extremum-seeking control - Applied to an ammonia reactor case study. Journal of Process Control (In-Press).