Synthesis of robust control systems based on the unification of modelling and design

提供给设计工程师的标称模型中包含的不确定性主要取决于建模方法和数据可靠性。因此，为了正确处理不确定性，有必要考虑建模过程。从这个意义上说，在设计鲁棒控制系统时，建模和设计是密不可分的。这是本项目的主要观点。我们主要关注的是鲁棒镇定问题，这是鲁棒控制最基本的问题。基于经典的Nevanlinna-Pick插值理论，给出了系统存在鲁棒镇定的充要条件。在本项目中，针对SISO系统的这一结果在两个方向上被推广到MIMO情况。一种是基于压缩算子的调和函数理论，另一种是基于“方向内插理论”。在这两种方法中，都得到了所有鲁棒稳定器的完全参数化。然而，该参数化法中模型不确定性的量化问题仍有待解决，我们还推导出了一种同时适用于单输入单输出和多输入多输出的鲁棒无差拍控制的设计方法。在该方法中，引入了一个与闭环系统灵敏度密切相关的鲁棒性指标。在无差拍响应约束下，对该鲁棒性指标进行了优化。最后，我们得到了一种有效的信号产生方法。实际上，这一结果证实了最小相位系统的有效性。虽然现在这个问题似乎比我们在项目开始时假设的要困难得多，所获得的结果也不多，但可以说为未来的发展提供了基础。

The uncertainty included in the nominal model given to the design engineer crucially depends on the method of modelling and the data reliability. Therefore, to handle the uncertainty properly, it is necessary to take into account the process of modelling. In this sense, modelling and design are inseparably connected in the design of robust control systems. This is the principal viewpoint of this project.Our primary concern has been on the robust stabilization which is the most fundamental issue of robust control. We derived a necessary and sufficient condition for the existence of robust stabilizer based on classical Nevanlinna-Pick interpolation theory. In this project, this result for SISO systems has been extended to MIMO cases in the two directions. One is based on the harmonic function theory of contraction operators and the other is based on the "directional interpolation theory". In both approaches, a complete parametrization of all robust stabilizers is obtained. However, the problem of quantification of the model uncertainty in this parametrization remains to be solved.We also derived a method of designing robust deadbeat control both for SISO cases and MIMO cases. In this method, a robustness index is introduced that is closely related to the sensitivity of the closed-loop system. Under the constraint of deadbeat response, this robustness index is optimized. The resulting system exhibits superior performance with respect to parameter variation.Finally, we derive an effective method of generating signals for identification. Actually, this result establishes the effectiveness of minimum phase systems.Though the problem now seems to be much more difficult than we assumed at the start of this project and the results obtained are not much, it can be said that the basis for future developement is obtained.