Fluid-structure interaction analysis on motion control of a self-propelled flexible plate near a rigid body utilizing PD control.

Inspired by a previous experimental study of fish swimming near a cylinder, we numerically investigate the swimming and station-holding behavior of a flexible plate ahead of a circular cylinder whose motion is controlled by a proportional-derivative (PD) controller. Specifically, the deformation of this two-dimensional plate is actuated by a periodically varying external force applied on the body surface, which mimics the fish muscle force to produce propulsive thrust. The actuation force amplitude is dynamically adjusted by a feedback controller to instruct the plate to swim the desired distance from an initial position to a target location and then hold the station there. Instead of directly using the instantaneous position signal, an average speed measured over one force actuation period is proposed with the inclusion of instantaneous position information to form the tracking error for the PD control. Our results show that the motion control of swimming and station holding has been achieved by this simple but effective feedback control without large overshoot when approaching the target at different flow conditions and actuation force formulas. Although the swimming distance remains the same, a plate whose initial position is closer to the cylinder requires less energy expenditure to swim to the target location and hold the station there. This is because the low-pressure zone near the trailing edge of the plate is reduced in size, which provides drag reduction, contributing to reduced swimming energy. A higher Reynolds number also leads to energy savings. Under the same control strategy, the swimming performance is more affected by the force-frequency while the phase shift of the actuation force has a less significant impact.