**Abstract**

Reactive distillation (RD), a process-intensified technique, involves the integration of reaction and separation in a single unit. High non-linearities associated with the reactive distillation process constrict the control degrees of freedom and set the key challenge in the design of a robust control system. In this chapter, reactive distillation diphenyl carbonate (RD-DPC) design is optimized, and a decentralized as well as centralized feedback control configuration is applied to carry out the control studies. To execute the control scheme, a dynamic model of RD-DPC process is developed using Aspen Dynamic and interfaced with MATLAB Simulink for online control implementation. A comparative multi-loop feedback controller control performance study is done for different transfer function models obtained by using analytical- and optimization-based process identification techniques. The controller parameters obtained from the simple internal model control (SIMC) tuning relations for decentralized controller and Tanttu & Lieslehto (TL) tuning relations for centralized controller are applied to (i) the linear transfer function model and (ii) non-linear plant model. Set-point tracking, load rejection studies and robust stability analysis are carried out to compare the performance of different models and to investigate the controller performance of the non-linear model.

**Keywords:** reactive distillation, diphenyl carbonate (DPC), decentralized controller, centralized controller, robustness, non-linear model

## **1. Introduction**

Polycarbonates, containing carbonate groups in their chemical structures, are an important group of thermoplastic polymers. Diphenyl carbonate (DPC), an acyclic carbonate ester, is a monomer in the production of polycarbonate polymers. The production of DPC is carried out by the transesterification reaction between dimethyl carbonate (DMC) and phenyl acetate (PA). The reactive distillation process, involving the integration of reaction and separation in one place, is usually associated with high non-linearities. The interaction of reaction and separation, responsible for the occurrence of multiple steady states, sets a challenge in designing a robust controller. Furthermore, the high non-linearity and dynamic interactions cannot be effectively controlled by single-input

single-output (SISO) controller and hence urges for multi-input multi-output (MIMO) controller.

In this work, RD–DPC process model is simulated using Aspen Dynamic V11. The transfer function model and controller development are performed using MATLAB 2019b Simulink Control system and custom proportional-integral-derivative (PID) coding. An online control environment is created by interfacing Aspen Dynamic with MATLAB Simulink via AM System block and similarly linking the centralized controller to MATLAB Simulink via S-function block.

This chapter reflects the designing of RD-DPC two-column indirect sequence and a control system for maintaining the molar purity of DPC and methyl acetate (MA) greater than 99%. The chapter also shows a comparative study between control performance of decentralized and centralized feedback controllers.

#### **2. RD-DPC multivariable process**

DPC is produced by reacting phenyl acetate (PA) and dimethyl carbonate (DMC) in a reactive distillation column. The involved reactions and the corresponding reaction rates are mentioned subsequently (Eqs. (1)–(3)). The reaction kinetic constants for the forward and backward reactions are taken from the work done by Cheng et al. [1]. There is a rectification and a reaction zone in the RD column, as shown in **Figure 1**. Column design specifications and additional parameters are reported in **Table 1**. Although high-purity DPC is obtained at the bottoms of the RD column, the purity of methyl acetate (MA) obtained at the distillate of the RD column is low. To obtain MA at the desired purity, we have to use another separation column, thus reactive distillation plus non-reactive distillation.

*C*3*H*6*O*<sup>3</sup> þ *C*8*H*8*O*<sup>2</sup> ⇌ *C*8*H*8*O*<sup>3</sup> þ *C*3*H*6*O*<sup>2</sup> *r*<sup>1</sup> ¼ *k <sup>f</sup>* <sup>1</sup>*CDMCCPA* � *kb*1*CMPCCMA* (1)

$$\rm C\_8H\_8O\_3 + C\_8H\_8O\_2 \rightleftharpoons C\_{13}H\_{10}O\_3 + C\_9H\_6O\_2 \ r\_2 = k\_{f2}C\_{\rm MPC}C\_{PA} - k\_{b2}C\_{\rm DPC}C\_{MA} \tag{2}$$

$$2\text{C}\_8\text{H}\_8\text{O}\_3 \rightleftharpoons \text{C}\_{13}\text{H}\_{10}\text{O}\_3 + \text{C}\_3\text{H}\_6\text{O}\_3 \text{ } r\_3 = k\_{f3}\text{C}\_{\text{MPC}}^2 - k\_{b3}\text{C}\_{\text{DPC}}\text{C}\_{\text{DMC}} \tag{3}$$

Aspen Plus/Dynamics is used to design and simulate the RD-DPC indirect sequence. The steady-state simulation results are shown in **Table 2**. In terms of the model validation, the required data are taken from the original case study [1, 2].

**Figure 1.** *The conventional RD-DPC process. [y(s) = Gp(s) u(s)].*

*Centralized and Decentralized Control System for Reactive Distillation Diphenyl Carbonate… DOI: http://dx.doi.org/10.5772/intechopen.101981*


#### **Table 1.**

*Design specifications and parameters.*

