Applied nonlinear control of complex systems

拟议的研究调查的重要问题的分析，预测和影响的非线性系统的行为。如果一个系统的行为在数学上用非线性方程来描述，那么这个系统就是非线性的。大多数物理系统都是非线性的（例如，电机或化学反应器）和非线性模型对于完全捕捉其复杂行为是必要的。 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基于模型的控制效率低下。非线性控制领域在过去的二十年中已经发展到直接考虑系统非线性来控制系统而不诉诸线性模型近似;结果是效率和性能的真实的改进。拟议的工作开发新的理论在非线性控制，这将提供数学上有充分依据的性能优势。在许多情况下，非线性系统有一个特殊的内在结构，可以自然地利用它们的控制。事实上，这种模型的线性近似破坏了有用的结构，否则可以用来改善其控制。将开发一种合适的理论来检测这种结构，然后应用适当的补偿。导出的结果在非线性控制领域具有根本的重要性，因此影响了广泛的控制过程。预期的结果可以应用于加拿大工业中使用控制系统的任何地方（例如，制造业中的运动控制或能源部门中的过程控制）。 理论方法由经验发现补充，研究目标包括为特定的工程应用开发非线性理论。这种方法导致更高的性能在应用中，并确保派生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测试台：自轴承电机和自主模型直升机。这两种应用都有商业化的潜力，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.