Bassam Bamieh

Abstract: Control systems with large arrays of sensors and actuators are increasingly common in several applications such as fluid low control, process control, smart structures, and arrays of Micro-Electro-Mechanical (MEMS) devices. These are systems where distributed arrays of sensors and actuators interact with media described by partial differential equations. We address the important issues of controller design, controller architecture and the communication requirements between sensors and actuators in such arrays.

We consider a special (but common) class of such systems which posses spatio-temporal invariant dynamics, and show that optimal controllers inherit this invariance property.  We show how one can use multidimensional transform techniques to constructively design quadratically optimal (i.e. H2 or H-infinity) distributed controllers by solving parameterized families of Ricatti equations. It turns out that such optimal controllers have an inherent degree of localization or semi-decentralization. The implications for controlled actuator/sensor arrays will be discussed. We illustrate these concepts with an example of controlling arrays of capacitively actuated micro-cantilevers.

Abstract: The problem of describing transition and turbulence in wall bounded shear flows such as pipes, channels and boundary layers is an important and old problem in Hydrodynamic Stability. This type of turbulence is responsible for a significant portion of the drag on marine and aeronautical vehicles. Recently, a new theory of transition has emerged that appears to be in much better agreement with experiments than classical hydrodynamic stability. We review this theory and show the surprising parallels it has with the central notions of robust control theory. We show how tools like robust stability analysis, input-output norms and singular value plots describe transition and turbulent flow structures with surprising fidelity. It thus appears that in the technologically important case of wall bounded shear flows, transition is not so much a problem of linear or nonlinear instability, but rather of robustness to ambient uncertainty. This characterization of turbulence in terms of system theoretic norms and stability margins allows for a nice framework for its control. We will show how skin friction drag reduction problems can be recast as:

1. they apply to general nonlinear systems with disturbances;
2. we obtain explicit (often non-conservative) bounds on the maximal allowable transmission interval that guarantee stability; and
3. we show that this approach is valid for a wide range of network protocols. This provides a flexible framework for design of NQCS, NCS and/or QCS that is amenable to various extensions and modifications, such as a treatment of dropouts and stochastic protocols, combined controller/protocol design, and so on.