A Hybrid Approach for Efficient Robust Design of Dynamic Systems
A Hybrid Approach for Efficient Robust Design of Dynamic Systems
复制标题
动态系统高效鲁棒设计的混合方法
作者：
M. Mönnigmann;W. Marquardt;C. Bischof;Thomas Beelitz;B. Lang;P. Willems
提出了一种新的动态系统参数鲁棒设计方法。这种方法可以应用于参数不确定的系统模型，因为这些参数的值不是精确已知的，而只是在一定的范围内。这种新的方法保证在这些范围内找到对每个参数组合稳定的最优稳态。我们的方法结合了约束优化问题的标准求解器的使用和非线性系统的严格解。优化问题的约束是基于参数空间法矢的概念，它度量试探性最优到最近的已知临界点的距离，即可能失去稳定性的点。这些法向量是使用非线性动力学的方法得到的。在优化后，使用严格的求解器来保证在最优值附近不存在临界点，或者检测这样的点。在后一种情况下，恢复优化，同时考虑新发现的临界点。这个优化和验证过程被重复，直到严格的非线性求解器能够保证最优解的附近没有临界点，因此最优解在参数上是鲁棒的。与现有的设计方法不同，我们的方法可以自动化，不依赖设计工程师的经验。一个简单的发酵罐模型被用来说明在典型的设计过程中出现的概念和活动顺序。
We propose a novel approach for the parametrically robust design of dynamic systems. The approach can be applied to system models with parameters that are uncertain in the sense that values for these parameters are not known precisely, but only within certain bounds. The novel approach is guaranteed to find an optimal steady state that is stable for each parameter combination within these bounds. Our approach combines the use of a standard solver for constrained optimization problems with the rigorous solution of nonlinear systems. The constraints for the optimization problems are based on the concept of parameter space normal vectors that measure the distance of a tentative optimum to the nearest known critical point, i.e., a point where stability may be lost. Such normal vectors are derived using methods from nonlinear dynamics. After the optimization, the rigorous solver is used to provide a guarantee that no critical points exist in the vicinity of the optimum, or to detect such points. In the latter case, the optimization is resumed, taking the newly found critical points into account. This optimize-and-verify procedure is repeated until the rigorous nonlinear solver can guarantee that the vicinity of the optimum is free from critical points and therefore the optimum is parametrically robust. In contrast to existing design methodologies, our approach can be automated and does not rely on the experience of the designing engineer. A simple model of a fermenter is used to illustrate the concepts and the order of activities arising in a typical design process.