Input shaping for travelling wave generation

Travelling wave patterns observed in the movement of certain aquatic animals has motivated research in the modification of flow behavior, especially to deal with boundary layer separation in airplane wings. Research has shown that inducing travelling waves on the top surface of the wing can generate sufficient momentum to prevent boundary layer separation without increasing the drag. Due to this effect of propagating waves on the aerodynamics, generation of travelling waves on solid surfaces is being widely studied. Recently, methods such as two-mode excitation, active sink and impedance matching have shown promise in generation of uniform travelling waves in solids with the help of piezo electric actuators. Unfortunately, there are some challenges involved in the experimental application of these methods. Although these techniques have shown to be adequate in laboratory settings, they require laborious tuning procedures which do not guarantee desired trajectories and are followed in light of interference from unwanted modes and their transients. Some methods rely on selective mode excitation, which can cause interference from unwanted modes if the transient behavior of the system is not accounted for. Feed-forward input shaping control methods are proposed that augment the open-loop piezo actuation method (two-mode excitation) and provide a more robust method for generating uniform travelling waves. The input shaping control alters the reference signal such that the parasitic behavior of unnecessary modes is cancelled out. The combination of the mode suppression and selective mode excitation through input shaping is verified experimentally for generation of a smooth travelling waves in finite structures.