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373225 Assessing the Reliability of SOC Real-Time Optimization Methodologies

Increased industrial competition and the need for decreased energy consumption spent by production processes require the optimization of plant operations at optimum. The Real Time Optimization (RTO) technology is one of the best known and widely used techniques to improve profit and decrease the energy consumption of a process production. However, there is not a general consensus about the benefits of implementing this technology to increase the profit of process plants (Darby, Nikolaou, Jones, & Nicholson, 2011).

The classical way to design a RTO layer uses a first principles steady state model to describe the plant behavior and to optimize an economical objective function subject to this set of constraints. At each RTO iteration, some key model parameters are updated to reduce plant-model mismatch, using information provided by the plant measurements at actual operating points (Miletic and Marlin, 1998). The optimal economic set points, obtained by the RTO layer, are sent to Model Predictive Control (MPC) layer, which is responsible to keep the process under control at this target. A drawback related to this optimization approach is the low frequency of set point updates by the RTO layer. Since the RTO algorithm is performed under steady state conditions, the plant operates, in presence of disturbances, under suboptimum conditions until the detection of the next steady state. This has a clear disadvantage over other RTO methodologies, such as Economic MPC or Dynamic Real Time Optimization.

Considering this disadvantage, it is important that the control layer is more tightly coordinated with the RTO layer. In particular, the control layer must be robust regarding common disturbances affecting the plant profit. In other words the control layer should “obtain acceptable profit loss with constants set point values”. That is the definition of self-optimizing control (SOC, Skogestad, 2000). The main idea behind the SOC is to choose a set of controlled variables that have set points values insensitive to disturbances, for instance, state variables that keep at active constraints despite presence of disturbances.

Several studies have developed methods to find optimal linear combinations of measured variables, which for artificial controlled variables that are insensitive to disturbances. These include the Exact Local method developed by Halvorsen and coworkers (2003), and the Null Space method by Alstad and Skogestad (2007), which uses the optimum output sensitivities to disturbances to find a matrix of measurements combinations. In this case, the artificial controlled variables present zero loss respect to the analyzed disturbances. Alstad and coworkers (2009) extended the Null space method, using extra measurements to reduce the loss assigned to measurement noise.

In this setting, the SOC methodology can be an alternative to reduce the low frequency of set points update in the classic RTO implementation (Jäschke and Skogestad, 2011). However, the practical implementation requires the solution of some challenges. The first one relates to the need to compute new solutions for large-scale nonlinear optimization problems for each disturbance analyzed, in order to compute the optimal sensibilities matrix necessary to the measurements combinations methods. An alternative for this problem could be to use the solver sIPOPT (Pirnay, López-Negrete and Biegler, 2012) to compute sensitivities with low computational cost, but this does not handle active set changes directly.

Another problem related to active set change is that it implies the need to modify the set of measured variables that must be controlled. For this reason, in the present work an algorithm is proposed to implement the SOC methodology in an MPC control, considering the choice of active constraints and linear combination of measured variables as controlled variables. The transformation matrix is updated in each RTO cycle, as are the manipulated set points and the MPC tuning. This is demonstrated on a detailed simulation of a multi-column distillation process. The results show better economic performance of the MPC with SOC compared with the classic MPC, and less change in the manipulated variables, thus indicating that it can be a good alternative to address the low frequency problem of the RTO algorithm.

**REFERENCES**

Alstad, V., & Skogestad, S. (2007). Null Space Method for Selecting Optimal Measurement Combinations as Controlled Variables. *Industrial & Engineering Chemistry Research*, *46*(3), 846–853. doi:10.1021/ie060285+

Alstad, V., Skogestad, S., & Hori, E. S. (2009). Optimal measurement combinations as controlled variables. *Journal of Process Control*, *19*(1), 138–148. doi:10.1016/j.jprocont.2008.01.002

Darby, M. L., Nikolaou, M., Jones, J., & Nicholson, D. (2011). RTO: An overview and assessment of current practice. *Journal of Process Control*, *21*(6), 874–884. doi:10.1016/j.jprocont.2011.03.009

Halvorsen, I. J., Skogestad, S., Morud, J. C., & Alstad, V. (2003). Optimal Selection of Controlled Variables †. *Industrial & Engineering Chemistry Research*, *42*(14), 3273–3284. doi:10.1021/ie020833t

Jäschke, J., & Skogestad, S. (2011). NCO tracking and self-optimizing control in the context of real-time optimization. *Journal of Process Control*, *21*(10), 1407–1416. doi:10.1016/j.jprocont.2011.07.001

Miletic, I. P., & Marlin, T. E. (1998). On-line Statistical Results Analysis in Real-Time Operations Optimization. *Industrial & Engineering Chemistry Research*, *37*(9), 3670–3684. doi:10.1021/ie9707376

Pirnay, H., López-Negrete, R., & Biegler, L. T. (2012). Optimal sensitivity based on IPOPT. *Mathematical Programming Computation*, *4*(4), 307–331. doi:10.1007/s12532-012-0043-2

Skogestad, S. (2000). Plantwide control: the search for the self-optimizing control structure. *Journal of Process Control*, *10*(5), 487–507. doi:10.1016/S0959-1524(00)00023-8

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