PDE Modeling and Tracking Control for the Flexible Tail of an Autonomous Robotic Fish

This article studies a single boundary regulator for the flexible tail of an autonomous robotic fish to implement complex oscillating body motions. The dynamic model of the flexible tail is derived by Hamilton’s principle, and conforms to the partial nonuniform Euler–Bernoulli beam with the uneven parameters. Then, a boundary control at the body–tail junction is proposed to manipulate the oscillation of the flexible tail, which is given in the form as a torque. The exponential stability of the error system is deduced by the integral Lyapunov synthesis. For further considering the boundary disturbance at the same point with control and the distributed disturbance, a disturbance observer is proposed. By appropriately choosing the designed parameters, the uniformly ultimate boundedness with disturbances is proved and the tracking error converges to a small neighborhood of 0. Finally, some simulations are presented to illustrate the effectiveness of the proposed control.