document: Control of a coupled map lattice model for vortex shedding in the wake of a cylinder The flow behind a vibrating flexible cable at low Reynolds numbers can exhibit complex wake structures such as lace-like patterns , vortex dislocations and frequency cells . These structures have been observed in experiments and numerical simulations , and are predicted by a previously developed low-order coupled map lattice -LRB- CML -RRB- . The discrete -LRB- in time and space -RRB- CML models consist of a series of diffusively coupled circle map oscillators along the cable span . Motivated by a desire to modify the complex wake patterns behind flexible vibrating cables , we have studied the addition of control terms into the highly efficient CML models and explored the resulting dynamics . Proportional , adaptive proportional and discontinuous non-linear -LRB- DNL -RRB- control methods were used to derive the control laws . The first method employed occasional proportional feedback . The adaptive method used spatio-temporal feedback control . The DNL method used a discontinuous feedback linearization procedure , and the controller was designed for the resulting linearized system using eigenvalue assignment . These techniques were applied to a modeled vortex dislocation structure in the wake of a vibrating cable in uniform freestream flow . Parallel shedding patterns were achieved for a range of forcing frequency-forcing amplitude combinations studied to validate the control theory . The adaptive proportional and DNL methods were found to be more effective than the proportional control method due to the incorporation of a spatially varying feedback gain across the cylinder span . The DNL method was found to be the most efficient controller of the low-order CML model . The required control level across the cable span was correlated to the 1/1 lock-on behavior of the temporal circle map
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extractive_keyphrases: coupled map lattice vortex shedding wake proportional feedback coupled circle map oscillators temporal circle map vortex dislocation cylinder low reynolds numbers vortex dislocations vibrating flexible cable
abstractive_keyphrases: spatio-temporal feedback control 1/1 lock-on discontinuous nonlinear control