Applied nonlinear control of complex systems

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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.