Applied nonlinear control of complex systems

提出的研究探讨了分析、预测和影响非线性系统行为的重要问题。如果一个系统的行为是用非线性方程在数学上描述的，那么这个系统就是非线性的。大多数物理系统是非线性的（例如，电机或化学反应器），非线性模型是必要的，以充分捕捉其复杂的行为。控制非线性系统的常用方法依赖于数学上方便的线性模型近似。然而，这种近似可能导致失去洞察力和低效的基于模型的控制。在过去的二十年里，非线性控制领域得到了发展，直接考虑系统非线性来控制系统，而不诉诸线性模型近似；其结果是效率和性能的真正改进。提出的工作发展了非线性控制的新理论，将提供数学上良好的性能效益。在许多情况下，非线性系统具有一种特殊的内在结构，可以很自然地利用这种结构进行控制。事实上，这种模型的线性近似破坏了有用的结构，而这些结构本来可以用来改善它们的控制。将发展一种合适的理论来检测这种结构，然后应用适当的补偿。所得到的结果在非线性控制领域具有重要意义，因此影响了广泛的被控过程。预期的结果可以应用于加拿大任何使用控制系统的工业（例如，制造业的运动控制或能源部门的过程控制）。理论方法与实证发现相辅相成，研究目标包括发展具体工程应用的非线性理论。这种方法可以提高应用程序的性能，并确保推导出的理论具有实际意义。申请工作的重点是申请人实验室正在开发的两个试验台：一个自轴承电机和一个自主模型直升机。这两种应用程序都有商业化的潜力，并引起工业合作伙伴的兴趣。

The proposed research investigates the important problems of analyzing, predicting, and influencing the behaviour of nonlinear systems. A system is said nonlinear if its behaviour is described mathematically by nonlinear equations. Most physical systems are nonlinear (e.g., electric machines or chemical reactors) and nonlinear models are necessary to fully capture their complex behaviour. A common approach to controlling nonlinear systems relies on a mathematically convenient linear model approximation. However, this approximation can lead to lost insight and inefficient model-based control. The field of Nonlinear Control has been developed over the last two decades to directly account for system nonlinearity to control the system without resorting to linear model approximation; the result is real improvement in efficiency and performance. The proposed work develops new theory in Nonlinear Control which will provide mathematically well-founded performance benefits. In many cases, nonlinear systems have a special intrinsic structure which can be naturally exploited in their control. In fact, linear approximations of such models destroy useful structure which could otherwise be used to improve their control. A suitable theory will be developed to detect such structures and then apply appropriate compensation. The derived results have fundamental importance in the field of Nonlinear Control and therefore impact a wide range of controlled processes. The anticipated outcomes can be applied in Canadian industry wherever control systems are used (e.g., motion control in manufacturing or process control in the energy sector). The theoretical approach is complemented by empirical discovery and the research goals include developing nonlinear theory for specific engineering applications. This approach leads to higher performance in the application and ensures the derived theory has practical relevance. The focus of the applied work is on two test stands under development in the applicant's lab: a self-bearing motor and an autonomous model helicopter. Both applications have potential for commercialization and generating interest from industrial partners.