Prof. Kirsten Morris
Many control systems, such as flexible structures, are modelled by partial differential equations, and hence evolve on an infinite-dimensional state space. Infinite-dimensional systems also arise from delay-differential equation models and in smart materials. Also of interest is the control of physical systems that may be nonlinear but dissipate energy. I am interested in using this dissipativeness in controller design to obtain closed loop systems that are very robust with respect to modelling errors . These areas of research overlap. For instance, the mathematical description of some ``smart'' materials is infinite-dimensional as well as dissipative in a generalized sense. This is also true for structural vibrations. Furthermore, smart materials are being used to control acoustic/structure interactions.
1. Infinite-Dimensional Systems: For most infinite-dimensional systems, an approximation scheme must be used in controller design. The scheme must lead to a controller that behaves as predicted by simulations when implemented with the infinite-dimensional system. I am generally interested in determining conditions for when a scheme can be used in controller design. These schemes can then be used for designing controllers.
2. Energy-based controller design: This enables structures to be successfully controlled despite the presence of modelling errors such as uncertain damping. This approach is being used to control hysteretic materials. The controlled system is guaranteed to be stable under a wide variety of conditions. The analysis has been confirmed by experiment. Some of this work is in collaboration with various faculty members in the Faculty of Engineering.
There are projects available for qualified graduate students, in both of these areas. All accepted students will be provided with sufficient funding to cover tuition and living expenses. For more information, contact me.
Last Modified: Tuesday 19 January 2010
