Optimal control problems polymerization

The books by T. Kailath [Unear Systems, 1980, Prentice-Hall) and H. Kwakernaak and R. Sivan Linear Optimal Control Systems, 1972, Wiley) can be consulted for detailed information. A recent paper by MacGregor, et al. ( State Estimation For Polymerization Reactors, 1986IFAC Symposium, Bournemouth, U.K.) discusses some of the problems of applying state estimators to chemical engineering systems. 

The really interesting issues in control of polymerization are not in the control of the operating conditions (flow, temperature, etc.). These loops are controlled in much the same way as would be done in any other chemical process. The real interest is in the control of polymer properties (monomer conversion, MW, particle size, copolymer composition, etc.). The next sections will review a number of control studies, each using a different approach to deal with the control problems specific to polymer property control (lack of sensors, one-sided control, nonlinearities, etc.). This will be followed by a discussion of an alternative approach to polymerization reactor control, statistical process control, and a discussion of the optimization of operating trajectories. 

It can cope with process variability and redefine the optimal operating conditions online. Nevertheless, the control of the PSD in emulsion polymerization by means of closed-loop strategies is a challenging problem [1]. Difficulties associated with the online measurement of the PSD can limit operational options and make the control problem a formidable task. In addition, the nonhnear behaviour of the process causes conventional control strategies to fail in ensuring a consistent product quality. 

The final aqueous detritylation is a complicated step that requires careful process optimization, such as control of pH, oligo and salt concentrations etc. 49 After detritylation, the oligonucleotide is precipitated quantitatively from the acidic DMT cation containing solution under optimized conditions. This step can be labor intensive at the large scale, and may be inconvenient for the high-throughput small-scale synthesis. One way to circumvent the problem is to use on column detritylation, where the RP and detritylation steps are combined in one chromatographic operation. Since the acid can leach the silica based columns, this is more useful on polymeric supports. 

After solving the optimization problem, the user obtains the optimum operation policy (u°P ) and the optimum reference values for state variables (x°p ) and end-use properties (yopt). These values can be used for implementation of open-loop operation of the polymerization reactors and for closed-loop control purposes, as discussed in the following section. 

One final point about closed-loop process control. Economic considerations dictate that to derive optimum benefits, processes must invariably be operated in the vicinity of constraints. A good control system must drive the process toward these constraints without actually violating them. In a polymerization reactor, the initiator feed rate may be manipulated to control monomer conversion or MW however, at times when the heat of polymerization exceeds the heat transfer capacity of the kettle, the initiator feed rate must be constrained in the interest of thermal stability. In some instances, there may be constraints on the controlled variables as well. Identification of constraints for optimized operation is an important consideration in control systems design. Operation in the vicinity of constraints poses problems because the process behavior in this region becomes increasingly nonlinear. 

Often, batch polymerization control is a matter of specifying an open-loop policy for the introduction of various materials. Due to the fact that there is no steady state around which to regulate, and to the fact that by the time a problem is detected, the batch may have progressed beyond the point of possible corrective action, it is often useful to track the behavior of a polymerization from batch to batch, and re-optimize the current batch based on the experience gained in preceding batches. An example is shown in Figure 5.10. Here a mathematical model is used to specify the optimal initiator... 

Mathematical theory and state-of-the-art numerical methods possess a great ability in computing optimal solutions for process control in chemical engineering which is until today not exhausted compared to other fields. The investigation of the optimal temperature control of a semi-batdi polymerization reactor being still a comparatively simple problem, might show some... 

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