Optimal Laypunov exponent parameters for stability analysis of batch reactors with Model Predictive Control

Abstract

Thermal runaways in exothermic batch reactions are a major economic, health and safety risk in industry. In literature most stability criteria for such behaviour are not reliable for nonlinear non-steady state systems. In this work, Lyapunov exponents are shown to predict the instability of highly nonlinear batch processes reliably and are hence incorporated in standard MPC schemes, leading to the intensication of such processes. The computational time is of major importance for systems controlled by MPC. The optimal tuning of the initial perturbation and the time frame reduces the computational time when embedded in MPC schemes for the control of complex batch reactions. The optimal tuning of the initial perturbation and time horizon, dening Lyapunov exponents, has not been carried out in literature so far and is here derived through sensitivity analyses. The computational time required for this control scheme is analysed for the intensication of complex reaction schemes.

Thermal stability criterion of complex reactions for batch processes

“…The concentration for o-nitrotoluene, given by the solid lines in Figure 7b, reaches the target concentration of 2.5 kmol m −3 within 7 hours, which is similar to the results obtained in Kähm and Vassiliadis (2018b), where Lyapunov exponents were used instead of criterion K.…”

“…Furthermore, the ratio of each nitrotoluene product obtained from the three different initial temperatures is equal in each case, as shown by the vertical dotted lines in Figure 7b. In Kähm and Vassiliadis (2018b) s for initial temperatures of 430 K, 440 K, and 450 K, respectively (Kähm and Vassiliadis, 2018b). Hence it is seen that the computational time required with MPC framework 1, as presented in this work, is reduced by at least 4-fold compared to the framework using Lyapunov exponents as the measure of thermal stability (Kähm and Vassiliadis, 2018b).…”

“…Finally, MPC framework 1 is applied to the industrial case study (Halder et al, 2008) presented in Section 3.2.3. The results are compared to the solutions obtained in Kähm and Vassiliadis (2018b), where a similar MPC framework with a different thermal stability criterion, given by Lyapunov exponents (Strozzi and Zaldívar, 1994), was employed. The same industrial process is simulated in both cases, enabling the comparison of computational time for both MPC frameworks.…”

“…This case study was considered in Kähm and Vassiliadis (2018b) with a different method to evaluate the system stability, given by Lyapunov exponents. The reactor parameters used in Kähm and Vassiliadis (2018b) are used in this work for the results to be comparable. The reactor parameters used for the nitration of toluene are given in Table 1.…”

Robust thermal stability for batch process intensification with model predictive control

“…Thermal stability criterion K results in less computational time than Lyapunov exponents. Furthermore, Lyapunov exponents require careful tuning to make them reliable for batch processes (Kähm and Vassiliadis, 2018b).…”