(289c) Decentralized Multi-Agent Control of MWD in RAFT Polymerization CSTR Networks

A wide range of factors determine the physical properties of polymers such as average molecular weights (AMW), molecular weight distribution (MWD), copolymer composition distribution, copolymer sequence length distribution, level of branching, content of gel and crosslinking.[1]. Control of these properties is important in industrial polymerization processes because a polymer's end-use properties are strongly dependent on them. Often in practice, a single AMW (e.g. weight AMW or number AMW) is controlled to yield the target polymer properties such as tensile strength and impact strength. Additionally, the breadth of polymer MWD is roughly measured by the ratio of weight AMW to number AMW (i.e., polydispersity). However, in certain situations the control of a single AMW together with the polydispersity is insufficient and it is necessary to control the polymer MWD at individual chain lengths. This study focuses on controlling the MWD on the application of a Reversible Addition Fragmentation Chain Transfer (RAFT) Polymerization system in a network of CSTRs. The aim is to be able to control the overall MWD in the network. Since the overall MWD is obtained by the contribution of all reactors in the network, in certain cases multimodal distributions can be obtained. In this work, a discretization method, namely Kumar and Ramkrishna (KR) method [2], is used for estimating the MWD at certain chain lengths (pivots) using the corresponding population balance equations (PBEs). In the KR method, the range of possible polymer chain lengths are divided into discrete intervals and each interval represents the chain lengths from ni to (ni+1 -1). A network of i interconnected isothermal CSTRs is modeled by specifying the material balance for each individual reactor i in the network, where i = 1..I. The interconnection flow rates, monomer, initiator and chain stopper feed concentrations are used as manipulated variables. The system is operated with constant volume. The reactor flow inputs include the reactor feed and the interconnection flows from the neighboring reactors. Outflow rates from each reactor include the interaction outflows to neighboring reactors as well as the drain. The simulator for the RAFT polymerization reactor network is built in C language and the multi-agent control architecture is built in the software suite (M)odeling, (A)nalysis, (D)iagnosis and (C)ontrol using (A)gent (B)ased (S)ystems (MADCABS). MADCABS is an adaptive hierarchical multilayered multi-agent supervision and control framework for managing nonlinear and distributed manufacturing processes. Various data reconciliation, monitoring and product grade control methods are implemented in a multi-agent framework, enabling flexible, modular and robust supervision of distributed processes. The ultimate objective is to create dynamic process supervision environment that can adapt itself and its actions in response to variations in operating conditions, set point and grade changes faults, disturbances and configuration changes. One novelty of the proposed research is the development of self-organizing decentralized multi-agent structures for the supervision tasks by designing auction-based mechanisms to give adaptation and self-organization capabilities, analyzing the performance of these mechanisms on the process and drive the system towards desired behavior. Earlier work by our group developed a centralized multi-agent approach to control the overall MWD of RAFT polymerization in a CSTR network [3]. In that study, the overall MWD was approximated by two parameters: The instantaneous AMW of the polymer produced from the network and the overall polydispersity of the product (higher polydispersity represents a wider distribution). In the centralized approach local controller agents implements conventional feedback controllers (PI) on manipulated variables of their CSTR's (monomer feed concentration, initiator concentration etc.) to control the AMW and the polydispersity. The global planner agent has access to instantaneous AMW and the polydispersities for each individual reactor. By looking at the operating conditions of individual reactors and the overall target to be met, the global planner agent decides on the set points for the individual reactors and updates them as necessary. The design approach taken in the decentralized control architecture is not managed by a central unit, instead local agents decide on their local targets in line with the global objective. This approach makes every local agent a local planner, increasing the robustness and the flexibility of the system. Since the framework is decentralized, the failure of one local agent in meeting its objective does not collapse the whole system. The agent-based system adapts to changing process conditions and modifies its strategy on-the-fly, if a more feasible solution appears or the solution being executed becomes unreachable. The system is in that sense, self-organizing and flexible to disturbances and failures of local units by creating alternative solutions dynamically. An auctioning mechanism is designed on the RAFT polymerization CSTR networks to control the overall MWD in the system. The algorithm uses the number of chains (Ni) at each interval to drive the shape of the MWD to the desired one. The MWD distributions in each CSTR contribute to the overall MWD. The objective is to control the overall MWD in a CSTR. The objective is to minimize the difference between the target and the current values for each pivot point in the overall MWD by changing the local pivot points in each CSTR. This is achieved by controlling the initiator and monomer concentrations in the feed flow, outflow rates and interconnection flow rates. The challenge is that it is almost impossible to treat every pivot point as an objective and match each of them with its target value. Instead our approach is to look at the general characteristics of MWD distributions and come up with a solution approach that fits our auctioning mechanism. One property of the MWD distributions is that the adjacent pivot points are correlated with each other. It is uncommon to observe sudden spikes or drops in the distribution as the adjacent pivot points represent concentrations of similar chain lengths. Instead, single or multiple peaks or valleys are more common shapes being observed. To take advantage of this property, it is assumed that the objective MWD could be achieved by the combination of multiple MWDs and each CSTR contributing to one of those distributions. In Figure 1, the bold line represents the overall MWD and contains two peaks. Individual MWDs for four CSTRs are also shown two of which are mostly contributing to the first peak and the other two contributing to the second peak. When the overall MWD in the network needs to be changed, a deconvolution agent analyzes the desired overall distribution and deconvoultes the distribution to a number of sub-distributions. The deconvolution agent uses a peak fitting algorithm for time-series signals. Its objective is to determine whether the signal can be represented as the sum of underlying peaks shapes. The auction organizer agent starts an auction for the each sub-distribution identified by the deconvolution agent. The auctions are to decide which CSTRs should contribute to which peak to move the overall MWDs towards the objective. The caps for each auction are determined by the area under the corresponding curve. So the number of CSTRs that should contribute to each peak that is proportional to the area under each curve. The logic used for calculating the bids of each local controller agent is slightly different than the one used for the autocatalytic case and takes into account the following factors: ? Distance between the units MWD's peak and the peak it is bidding, ? Distance between neighboring units MWD's peak and the peak it is bidding. The local controller agents have access to a number of manipulated variables and knowledge about the effect of each manipulated variable on the MWD for that reactor. The local controller agents will shift their MWDs according to their local objective MWDs by changing the relevant manipulated variables identified by their knowledge base. In the first stage, every local controller agent updates their interconnection flows and feed flows to shift their peaks towards the targeted peak. Once this stage is completed the shape of the overall distribution looks similar to the targeted overall distribution. However there will be still errors between the current and target values of the pivot points. In the second stage, these errors are minimized by fine tuning the locations of the MWDs for each unit by making small shifts. Basically the errors will be the areas between the current overall MWD distribution and the target overall MWD distribution curves.