A Recursive Proper Orthogonal Decomposition Algorithm for Flow Control Problems

3 A RECURSIVE PROPER ORTHOGONAL DECOMPOSITION ALGORITHM FOR FLOW CONTROL PROBLEMS 

The POD method is an efficient tool for extracting the most dominant features of a dynamical system. It has been used in several flow control problems to develop 

Equation (19.5) is the RePOD algorithm, which is the main contribution in this section. 

The recursion is performed on new flow data using gradient techniques, which are then followed by the determination of control input. The RePOD method can also be used in isolation to compute the modal basis, potentially resulting in substantial savings in computational resources and time. The algorithm was applied to two classes of problems [15]. In the first, the problem of heat conduction through a one-dimensional rod with a sinusoidal heat perturbation source located inside the rod was considered. The objective is to reduce the temperature 

In a first-order reduced model of Eq. (19.8), since An is negative, the system becomes stable if the perturbation term is eliminated by the control term. Hence, the control law chosen was 

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Sahoo, D., S. Park, D. Wee, A. M. Annaswamy, and A. F. Ghoniem. 2002. A recursive proper orthogonal decomposition algorithm for flow control problems. Adaptive Control Laboratory, MIT. Technical Report 0208. 

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