Application of Multivariable Model Predictive Control (4x4) for Dimethyl Ether Purification from Methanol

Multi-variable model predictive control (MMPC) was used to control the dimethyl ether (DME) purification process of methanol in the production of DME from synthesis gas. The use of MMPC aims to capture the phenomenon of the interaction between the variables in the process in order to improve the control performance. As the process comprises four input variables and four output variables, MMPC (4×4) is used in this study. The inter-variable interaction is shown in a 4×4 matrix, where each matrix element is a first-order plus dead-time (FOPDT) model. MMPC (4×4) was tested by changing the set point (SP) and disturbance rejection. The control performance indicators used are integral absolute error (IAE) and integral square error (ISE) and, as a comparison, the control performance of the single-input single-output (SISO) model predictive control (MPC). The results show that MMPC (4×4) is better than MPC in both IAE and ISE. In terms of SP change, MMPC (4×4) is able to significantly improve the control performance of MPC, by 78% (IAE) and 90% (ISE). Whereas in the disturbance rejection testing, the improvements in control performance were 58 % (IAE) and 81% (ISE).

DME; Methanol; Multi-variable; Predictive; Purification

Dimethyl Ether (DME) can be used as an alternative energy source. As a propellant, DME is less polluting, naturally degrades easily, has a high cetane number, and does not produce SOx, CO, and particulate emissions. DME has physical properties similar to those of liquefied petroleum gas (LPG); hence, DME can be used as a substitute for LPG in domestic applications. In addition to this, DME can be used in diesel engines. Because of its wide range of applications, it is important for the large-scale production of DME to be actualized (Marchiona et al., 2008; Solichin et al., 2011; Patil & Thipse, 2012).

It is very important to obtain and maintain operating conditions at their optimum level so that the desired product can be successfully obtained (Kusrini, 2018). This requires process control so that any disturbances that arise can be handled as well as possible. Likewise, in the production of DME from synthesis gas, proper process control is needed so that the expected product is achieved.

In general, DME is produced via methanol dehydration in a catalytic fixed-bed reactor, followed by a purification process. Wahid and Gunawan (2015) demonstrated the method for determining  the  control structure of the DME plant designed by  Solichin et al. (2011) with the use of a proportional-integral (PI) controller structure. Research on the purification process of this DME production plant was continued by Yanuardi (2015) using an advanced control system that employed single variable model predictive control (MPC). Both the PI control system and MPC system are able to attain zero offset when the SP tracking test and disturbance test are given, but the error value, which uses the integral absolute error (IAE) and integral square error (ISE) as the error calculation, given by these two controls system is still relatively high. This may be caused by the strong interaction between the process variables in the process system. It is possible to manage this problem with the use of a more advanced control system, namely multi-variable model predictive control (MMPC). The use of MMPC can also reduce the total amount of capital investment in the control system by reducing the amount of controller used (Wahid & Ahmad, 2007).

The MMPC (4×4) used in this study differs from that used by Wahid and Ahmad (2015, 2016) because here, only one MMPC is used. Wahid and Ahmad (2015, 2016), in contrast, used several MMPCs (2×2) in a multi-model MPC to control the purity of the product from a distillation column. However, the use of one MMPC to control four controlled variables (CVs) is expected to meet the DME purity target in a distillation column.

This study shows that each of the CVs and MVs in the DME and methanol separation process interact with each other. This is indicated by the lack of a zero value inside the MMPC (4×4). This study also shows that MMPC (4×4) is better than MPC with respect to both IAE and ISE. In terms of SP change, MMPC (4×4) significantly improves the control performance of MPC, by 78% (IAE) and 90% (ISE). Whereas in disturbance rejection testing, the improvements in control performance were 58% (IAE) and 81% (ISE). Thus, while MMPC not only serves as a more effective controller system, it is also more beneficial in terms of the number of controllers used, which will affect capital costs.

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