(40h) Distributed Estimation and Nonlinear Model Predictive Control of a Benzene Chlorination Process

Model predictive control (MPC) is a prevalent control strategy inherently tailored to accommodate optimal performance criteria and handle constraints, which are two major concerns of the control of processes in the chemical industry [1]. The philosophy underlying MPC design is to cast the control problem in the form of a repeated constrained dynamic optimization problem that computes a sequence of future manipulated inputs at each sampling time [2]. Consequently, the applicability of MPC hinges on the real-time solvability of the underlying optimization problem. This is a challenge when applying a centralized control architecture to industrial scale process systems that require solving a large-scale constrained nonlinear dynamic optimization in real-time [3]. An alternative approach to overcome the computational challenges of centralized model predictive control (CMPC) is to decompose the original optimization-based control problem into a number of smaller control problems. This idea results in a distributed model predictive control (DMPC) architecture comprised of local controllers with some level of cooperation and communication [4], [5].

The decomposition of the system, i.e. deciding on the number of subsystems and identifying how the manipulated inputs and output variables distribute among the network of subsystems is a key factor for DMPC implementation. From a network theory perspective, this problem can be posed as identifying weakly-connected subsystems whereby the variables of each subsystem are strongly connected. The impact of system decomposition on the closed-loop performance and the computational requirements of employing DMPC has been investigated by considering different levels of communication and cooperation between local controllers, levels of system uncertainty, dynamic optimization platforms, and operating points for the benchmark reactor-separator process network [6], [7]. The identified optimal distributed architecture by the community detection method has been then employed to address the DMPC problem for a class of real chemical process networks [8]. Such studies focused on the distributed control problem assuming full state information at each sampling time in order to isolate and investigate the effects of decomposition on the controller design problem itself. However, such an assumption cannot be generally invoked in many practical cases, so the use of a state estimation method is required.

Among the several available methods for state estimation, moving horizon estimation (MHE) has attracted a lot of attention since it can be formulated as a similar constrained dynamic optimization problem [9], [10]. The MHE provides an optimal state estimation compatible with the system measurements at the past sampling times [11]. However, solving such an optimization-based estimation problem at each sampling time remains computationally challenging when applying a centralized architecture to large-scale process networks [12]. Any delay in such computations will directly affect the closed-loop performance since the distributed controllers require the initial values of all state variables at each sampling time. Like DMPC, an alternative approach to overcome the computational challenges of centralized estimation is the system decomposition and a distributed moving horizon estimation (DMHE) structure consisting of local estimators with some level of cooperation and communication. Extending the optimal decomposition of process networks to the combined control and estimation problem is the subject of this work.

Specifically, we provide a framework to combine iterative DMPC and DMHE to address the output-feedback control problem for a benzene chlorination plant. Such a process consists of three tubular reactors and two flash separators. A series of two elementary reactions take place in the reactors to produce mono and dichlorobenzene where monochlorobenzene is the desired product [13]. The first flash column separates the unreacted benzene in the product stream and recycles it to the fresh feed stream to be reused in the reactors. For each tubular reactor, we have five nonlinear parabolic partial differential equations (PPDEs) to describe the spatiotemporal dynamics of temperature and the concentrations of benzene, chlorine, mono, and dichlorobenzene. Galerkin’s method is employed to derive low-dimensional reduced order models in the form of ordinary differential equations (ODEs) which can approximate the dominant dynamics of the governing PPDEs [14]. The resulting ODEs are added to the set of algebraic equations and ODEs that describe the temperature and concentrations in the flash separators and are used as the basis for the combined DMPC and DMHE design.

The maximum temperature in the tubular reactors and the monochlorobenzene concentration at the outlet streams of the reactors and separators are considered as the controlled outputs. We can only measure the temperature at the outlet streams of the reactors and inside the flash separators and the total concentration of chlorobenzene (monochlorobenzene + dichlorobenzene) at the outlet streams of the reactors and flash separators. By considering these measured outputs, we require estimating the temperature and concentrations of all components in the reactors and separators at each sampling time by DMHE. Then the estimated state variables are used by DMPC as the initial values of the predictive model. Since the sets of controlled and measured outputs are different in this case study, we obtain different optimal decompositions for the control and estimation problems by applying the community detection method. Both optimal decompositions result in two subsystems, recommending a distributed estimation/control structure of two local estimators/controllers, which can communicate over the network. The closed-loop performance and the average computation time are evaluated using the detailed simulations. We additionally compare the results with those of centralized and fully decentralized control synthesis. The proposed distributed output feedback control design based on the optimal decomposition which minimizes the interactions between the distributed local estimators and controllers, is shown to enable closed-loop performance close to that of the centralized, while reducing the computational effort significantly.

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