Applied nonlinear control of complex systems

拟议的研究调查了分析、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可以用非线性方程进行数学描述，那么它就是非线性的。大多数物理系统是非线性的(例如，电机或化学反应器)，为了完全捕捉它们的复杂行为，需要建立非线性模型。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，这种近似可能会导致失去洞察力和基于模型的低效控制。在过去的二十年里，非线性控制领域已经发展起来，直接考虑系统的非线性来控制系统，而不是求助于线性模型近似，结果是在效率和性能方面得到了真正的改善。所提出的工作发展了非线性控制的新理论，这将提供数学上的良好的性能好处。在许多情况下，非线性系统具有一种特殊的内在结构，这种结构可以自然地用于控制。事实上，这种模型的线性近似破坏了有用的结构，否则这些结构可以用来改善它们的控制。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。所得结果在非线性控制领域具有重要意义，因此对被控过程具有广泛的影响。预期成果可应用于加拿大工业中任何使用控制系统的地方(例如，制造业的运动控制或能源部门的过程控制)。理论方法得到经验发现的补充，研究目标包括为特定的工程应用开发非线性理论。该方法在实际应用中具有较高的性能，保证了推导出的理论具有一定的实用价值。应用工作的重点是申请者实验室正在开发的两个测试台：自承式马达和自动直升机模型。这两种应用都有商业化的潜力，并引起了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.