**A
centralized/decentralized control approach for the Multicolumn Countercurrent
Solvent Gradient Purification (MCSGP) process**

Maria M.
Papathanasiou^{a,d}, Muxin Sun^{a}, Fabian Steinebach^{b},
Thomas Müller-Späth^{c}, Massimo Morbidelli^{b}, Athanasios
Mantalaris^{a}, Efstratios N. Pistikopoulos^{d*}

^{a}Dept. of Chemical Engineering, Centre for Process
Systems Engineering (CPSE), Imperial College London SW7 2AZ, Lodnon, U.K

^{b} Institute for Chemical and Bioengineering, ETH
Zurich,

Wolfgang-Pauli-Str. 10/HCI F 129,
CH-8093 Zurich, Switzerland
^{c }*ChromaCon
AG, Technoparkstr. 1, CH-8005 Zurich, Switzerland*
^{d}*Artie McFerrin Department of
Chemical Engineering, Texas A&M University, College Station TX 77843*
**stratos@tamu.edu*

** **

**Keywords: **periodic processes,
multi-parametric, control, stability

Industrial applications, such as separation processes and pressure swing adsorption systems (PSA) are characterized by cyclic operation profiles and they often involve tight constraints on product purity. In order to maintain the process under optimal operation, advanced computational tools need to be developed. The latter include optimization strategies and optimal control policies that are designed to meet the process constraints. During the past few years, several research groups have been focusing on the development of such tools, aiming to tackle issues related to system periodicity and nonlinearity [1-6].

In this work we present a centralized/decentralized control approach based on the principles of the Multicolumn Countercurrent Solvent Gradient Purification (MCSGP) process. MCSGP is an industrial, semi-continuous chromatographic separation process used for the purification of various biomolecules [7]. The system is described by a highly nonlinear Partial Differential and Algebraic Equation (PDAE) model that operates under a cyclic profile. Following our previously presented work [8, 9] we demonstrate a seamless procedure for the development of advanced decentralized multi-parametric control strategies for the system at hand.

The examined system shifts periodically between two distinct configurations (Figure 1). Figure 1a illustrates the continuous operation mode, where the two columns operate connected to each other. This is usually followed by batch operation as shown in Figure 1b. For further details regarding the complete system operation the reader is referred to Krättli, et al. [10]. In this study we develop independent control strategies for each column that are then linked during the interconnected operation, tracking the integral of the outlet concentrations. In particular, the outlet of column A is treated as a disturbance by the controller operating on column B during continuous operation (Figure 1a).

**Figure
****1**
Chromatographic system based on the principles of MCSGP for (a) continuous and
(b) batch operation mode, considering the modifier concentration as input, the
integral of the three outlet concentrations as outputs and the feed composition
as measured disturbance.

The periodic operation profile and the disturbances occurring from the feed stream render the preservation of the optimal operating conditions a challenging task. Therefore, to ensure optimal operation throughout the process cycle, the controller stability needs to be guaranteed. Following the framework presented by Pistikopoulos, et al. [8] the controller development is based on the derivation of a linear state space model that describes the system dynamics. The optimal periodic steady state and input strategy for the tracked process intervals are calculated off-line, minimizing the cost function of the optimization problem [11]. The online control scheme can then be applied by driving the system to the pre-computed optimal periodic steady state by using multi-parametric Model Predictive Control (mp-MPC) (Pistikopoulos, 2009). To prove the stability of the cyclic process we introduce a transformed system as suggested by to Huang, et al. [12].

The designed controllers are then tested in-silico, in a ‘closed-loop' fashion, using the original process model [8]. Due to the system dynamics a repetitive output time delay is observed that corresponds to the time that the components require to reach the column exit [13]. This can be either pre-computed or related to the output and/or control horizon during the design of the control policies. Here we examine both cases and we demonstrate the evolution of the time delay with respect to both the output and the control horizon. It can be observed that both strategies are equally effective, however the second case allows greater freedom in the controller design as the setpoints are tracked independently from the time delay. The suggested strategy can efficiently track the desired outputs and retain the process under optimal operating conditions. The designed controllers guarantee stable, cyclic operation and the system time delay is successfully eliminated.

**Acknowledgements **

Financial support from the European Commission (OPTICO/G.A. No.280813) is gratefully acknowledged.

**References**

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