Recursive dynamic mode decomposition of transient and post-transient wake flows

A novel data-driven modal decomposition of fluid flow is proposed, comprising key features of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The first mode is the normalized real or imaginary part of the DMD mode that minimizes the time-averaged residual. The $N$th mode is defined recursively in an analogous manner based on the residual of an expansion using the first $N-1$ modes. The resulting recursive DMD (RDMD) modes are orthogonal by construction, retain pure frequency content and aim at low residual. Recursive DMD is applied to transient cylinder wake data and is benchmarked against POD and optimized DMD (Chen et al., J. Nonlinear Sci., vol. 22, 2012, pp. 887–915) for the same snapshot sequence. Unlike POD modes, RDMD structures are shown to have purer frequency content while retaining a residual of comparable order to POD. In contrast to DMD, with exponentially growing or decaying oscillatory amplitudes, RDMD clearly identifies initial, maximum and final fluctuation levels. Intriguingly, RDMD outperforms both POD and DMD in the limit-cycle resolution from the same snapshots. Robustness of these observations is demonstrated for other parameters of the cylinder wake and for a more complex wake behind three rotating cylinders. Recursive DMD is proposed as an attractive alternative to POD and DMD for empirical Galerkin models, in particular for nonlinear transient dynamics.

Switching of a Double-Comb Microactuator by Time-Lag Modulation and Electrical-Damping Control

A switching and control scheme for a novel double-comb microactuator is proposed in this paper. The device is actuated by a time-lag modulation voltage and its transient behavior is controlled by the time lag and a resistor. Numerical simulation is applied to analyze the nonlinear transient dynamics of an example system. A transient optimization to reduce the settling time and overshoot of the time response to a time-lag modulation is carried out using the OCS performance index. The optimal control parameters are obtained including the optimal resistance and time lag to balance the performance tradeoff.