This paper presents a novel single-shooting algorithm for gradient-based solution of optimal control problems with vapor–liquid equilibrium constraints. Such optimal control problems are important in several engineering applications, for instance in control of distillation columns, in certain two-phase flow problems, and in operation of oil reservoirs. The single-shooting algorithm uses an adjoint method for the computation of gradients. Furthermore, the algorithm uses either a simultaneous or a nested approach for the numerical solution of the dynamic vapor–liquid equilibrium model equations. Two numerical examples illustrate that the simultaneous approach is faster than the nested approach and that the efficiency of the underlying thermodynamic computations is important for the overall performance of the single-shooting algorithm. We compare the performance of different optimization software as well as the performance of different compilers in a Linux operating system. These tests indicate that real-time nonlinear model predictive control of UV flash processes is computationally feasible.

本文提出了一种新颖的单次射击算法，用于基于梯度的具有气液平衡约束的最优控制问题的求解。这样的最佳控制问题在一些工程应用中很重要，例如在蒸馏塔的控制中，某些两相流问题中以及在油藏的操作中。单次射击算法使用伴随方法进行梯度计算。此外，该算法对动态气液平衡模型方程的数值解采用了同时或嵌套的方法。两个数值示例表明，同步方法比嵌套方法要快，并且底层热力学计算的效率对于单次射击算法的整体性能很重要。我们比较了Linux操作系统中不同优化软件的性能以及不同编译器的性能。这些测试表明，对UV闪光过程进行实时非线性模型预测控制在计算上是可行的。