Real-Time Optimization for Large Scale Nonlinear Processes
Real-Time Optimization for Large Scale Nonlinear Processes
复制标题
DOI：
10.11588/heidok.00001659
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
M. Diehl
中科院分区：
文献类型：
--
作者：
M. Diehl
提出了一种有效的数值方法，用于实时求解非线性模型预测控制（NMPC）中的最优控制问题。该方法的实际适用性证明在实验应用中的试点工厂蒸馏塔，涉及实时优化的大规模微分代数过程模型，采样时间只有几秒钟。该解决方案的方法是基于直接多次射击法，它允许联合收割机使用先进的，完全自适应DAE解算器的优势，同时战略。实时方法的特点是由一个初始值嵌入策略，有效地利用解决方案的信息，在随后的优化问题。在实时迭代方案中，将解迭代与过程开发相结合允许将采样时间减少到最小，但保持了优化问题的完全非线性处理的所有优点。它示出了如何在每个实时迭代的计算可以分为一个准备阶段和一个相当短的反馈阶段，这避免了一个采样时间的延迟，是目前在所有以前的NMPC计划。实现了一种最小二乘积分的Gauss-Newton算法，该算法能以很小的计算代价计算出一个很好的Hessian近似，并从理论上研究了该算法的收缩性质，在较弱的条件下证明了实时迭代的收缩性.关于最优解的最优性损失的界限被建立。在一个实验验证的概念研究中，开发的数值方法被应用到位于斯图加特大学的Institut für Systemdynamik und Regelungstechnik的中试蒸馏塔的NMPC。一个合适的系统模型，这是刚性的，包括200多个状态变量，系统参数拟合实验数据。扩展卡尔曼滤波器（EKF）的一个变种的状态估计。采用实时优化算法，在实际条件下可实现采样时间小于20 s，反馈延迟小于400 ms。该方案显示出良好的闭环性能，特别是对大干扰。
Efficient numerical methods for the real-time solution of optimal control problems arising in nonlinear model predictive control (NMPC) are presented. The practical applicability of the methods is demonstrated in an experimental application to a pilot plant distillation column, involving the real-time optimization of a large scale differential algebraic process model, with sampling times of only a few seconds. The solution approach is based on the direct multiple shooting method, which allows to combine the use of advanced, fully adaptive DAE solvers with the advantages of a simultaneous strategy. The real-time approach is characterized by an initial value embedding strategy, that efficiently exploits solution information in subsequent optimization problems. Dovetailing of the solution iterations with the process development in a real-time iteration scheme allows to reduce sampling times to a minimum, but maintains all advantages of a fully nonlinear treatment of the optimization problems. It is shown how the computations in each real-time iteration can be divided into a preparation phase and a considerably shorter feedback phase, which avoids the delay of one sampling time that is present in all previous NMPC schemes. A Gauss-Newton approach for least squares integrals is realized which allows to compute an excellent Hessian approximation at negligible computational costs.The contraction properties of the algorithm are investigated theoretically, and contractivity of the real-time iterates is shown under mild conditions. Bounds on the loss of optimality with respect to the optimal solution are established. In an experimental proof-of-concept study the developed numerical methods are applied to the NMPC of a pilot plant distillation column situated at the Institut für Systemdynamik und Regelungstechnik at the University of Stuttgart. A suitable system model is developed, which is stiff and comprises more than 200 state variables, and the system parameters are fitted to experimental data. A variant of the Extended Kalman Filter (EKF) is developed for state estimation. Using the real-time optimization algorithm, sampling times of less than 20 seconds and feedback delays below 400 milliseconds could be realized under practical conditions. The scheme shows good closed-loop performance, especially for large disturbances.