Abstract
In the current study, a hierarchy of control-oriented Galerkin models is proposed targeting least-dimensional representations at different operating conditions. These models are employed for passive as well as active actuation. In passive control, a linearised model is shown to reproduce a wake stabilization experiment of Strykowski & Sreenivasan (1990). In particular, the effect and optimal position of control wires are accurately predicted. In active closed-loop control, focus is also placed on experiment. Here, control design requires a model which has on the hand a sufficiently broad dynamic range and is on the other hand low-dimensional enough for online computation. POD Galerkin models have a desirable mathematical structure and dimension for an online capable control design but tend to be over-optimised for the reference conditions. The resulting limited dynamic bandwidth is associated with the underlying expansion modes which change their shape at different operating conditions. To increase that model bandwidth, a novel continuous mode interpolation technique is proposed. The mode interpolation smoothly connects not only different operating conditions, but also stability and POD modes and even flows at different boundary conditions. In addition, the extrapolation of modes outside the design conditions is illustrated. The interpolated modes enable ‘least-order’ Galerkin models keeping the dimension from a single operating condition but resolving several states. These models are well suited for control design. The mode interpolation technique is demonstrated for three benchmark problems, the flow around circular cylinder, a NACA airfoil and an Ahmed body.
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Morzyński, M., Stankiewicz, W., Noack, B.R., King, R., Thiele, F., Tadmor, G. (2007). Continuous Mode Interpolation for Control-Oriented Models of Fluid Flow. In: King, R. (eds) Active Flow Control. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 95. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71439-2_16
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