A boundary control approach is used to control a two-link rigid-flexible wing in this article. Its design is based on the principle of bionics to improve the mobility and the flexibility of aircraft. First, a series of partial differential equations (PDEs) and ordinary differential equations (ODEs) are derived through the Hamilton's principle. These PDEs and ODEs describe the governing equations and the boundary conditions of the system, respectively. Then, a control strategy is developed to achieve the objectives including restraining the vibrations in bending and twisting deflections of the flexible link of the wing and achieving the desired angular position of the wing. By using Lyapunov's direct method, the wing system is proven to be stable. The numerical simulations are carried out with the finite difference method to prove the effectiveness of designed boundary controllers.

This paper addresses a flexible micro aerial vehicle (MAV) under spatiotemporally varying disturbances, which is composed of a rigid body and two flexible wings. Based on Hamilton's principle, a distributed parameter system coupling in bending and twisting, is modeled. Two iterative learning control (ILC) schemes are designed to suppress the vibrations in bending and twisting, reject the distributed disturbances and regulate the displacement of the rigid body to track a prescribed constant trajectory. At the basis of composite energy function, the boundedness and the learning convergence are proved for the closed-loop MAV system. Simulation results are provided to illustrate the effectiveness of the proposed ILC laws.

This paper examines the boundary disturbance observer-based control for a vibrating single-link flexible manipulator system possessing external disturbances. Two new boundary anti-disturbance control strategies are presented to eliminate vibration, track disturbance, and determine angle position for the flexible manipulator system. Achieving rigorous analysis with no model reduction, the derived control can ensure the angle positioning and bounded stability in the controlled system. By appropriately designing parameters, the resulting simulation results can demonstrate the control performance.

This brief considers the control design problem for a flexible robotic manipulator. Our control strategies are to: 1) move the manipulator to the certain desired angle; 2) suppress the vibration at the neighborhood of the desired angle; and 3) handle the backlash nonlinearity existing in the practical system. Based on the infinite-dimensional dynamic model, a boundary controller with input backlash is designed to achieve the control aims. An output feedback method is adopted to represent a controller to handle the feedback signals that are not able to be measured directly. The effectiveness of the designed controllers and the stability of the system are demonstrated by theoretical analysis, numerical simulations, and physical experiments.

This paper focuses on adaptive robust vibration control for flexible riser systems affected by input nonlinearities and unknown external disturbances. An auxiliary system is constructed and adjusted to develop a boundary adaptive robust control for restraining the vibrational offset and eliminating the effect of input nonlinearities. Besides, an adaptive law of boundary disturbance upper-bound is constructed together with the vibration control strategy to estimate the magnitude of unknown boundary disturbance. Further, the convergence of states and stability of the system are ensured with the developed control scheme. By choosing the proper control parameters, the control performance is verified with the obtained simulation results.

The vibration offsets reduction is studied for an industrial axially moving accelerated string subjected to the external disturbances and input saturation. A boundary control strategy is put forward to reduce the vibration offsets and an auxiliary term is introduced to handle the restriction of the input saturation. In addition, both infinite-dimensional observer and finite-dimensional observer are, respectively, designed to track unknown disturbances. Under the developed control strategy, the existence, uniqueness, and convergence of the solution of the closed-loop string system are discussed without resorting to model reduction methods. By choosing the proper control parameters, the simulations are given to verify the performance of the developed control strategy.