Fast Direct Methods for Real-Time Optimization of Chemical Processes
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Abstract:
Abstract. Some specialized direct methods for real-time optimization of dynamic chemical processes are presented. The methods are based on a boundary value problem approach to the solution of large, multistage optimal control and design optimization problems for processes described by DAE models (Leineweber et al., 1997). This simultaneous solution strategy uses a piecewise parametrization of the control functions and a multiple shooting discretization of the DAEs, combined with a specifically tailored SQP technique (Plitt, 1981; Bock and Plitt, 1984; Bock et al., 1988; Leineweber, 1995). The existing general approach has now been adapted to the specific requirements of real-time optimization through the development of suitable strategies to minimize the on-line computational effort. In a typical realtime context, e.g., an on-line reoptimization after disturbances, the resulting new methods are much faster than off-line optimization strategies, because they exploit precalculated information about the undisturbed nominal solution in order to greatly accelerate the solution process. This kind of previous information is not available in the off-line case. The new on-line strategies have been implemented within the modular optimal control package MUSCOD-II (Leineweber, 1995; Leineweber et al., 1997). A comparative study of these techniques has been done for the reoptimization of a fed-batch fermentation process. The results indicate that in particular the use of precalculated exact Hessians in so-called HOTstarts has great potential for the on-line optimization of complex chemical processes-- here the total computational cost of the reoptimization was reduced by almost an order of magnitude compared to the off-line strategy. Clearly, such an acceleration may be of crucial importance in time-critical on-line applications.
