This paper outlines the vibration reduction of a spacecraft with flexible appendage subject to external disturbances. The hybrid dynamic model of the spacecraft is described by both partial differential equations and ordinary differential equations. A vibration control scheme consisting of two boundary control laws and a distributed control law is developed to restrain the spacecraft's vibration and track the desired attitude. An infinite-dimensional disturbance observer is introduced as a feedforward compensator to handle unknown external disturbances. Based on the semigroup theory, the extended LaSalle's invariance principle and Lyapunov analysis, the well-posedness and stabilities of the designed control system are both discussed. Simulation results are given for validating the effectiveness of the developed vibration control scheme.

This article focuses on the vibration reducing and angle tracking problems of a flexible unmanned spacecraft system subject to input nonlinearity, asymmetric output constraint, and system parameter uncertainties. Using the backstepping technique, a boundary control scheme is designed to suppress the vibration and regulate the angle of the spacecraft. A modified asymmetric barrier Lyapunov function is utilized to ensure that the output constraint is never transgressed. Considering the system robustness, neural networks are used to handle the system parameter uncertainties and compensate for the effect of input nonlinearity. With the proposed adaptive neural network control law, the stability of the closed-loop system is proved based on the Lyapunov analysis, and numerical simulations are carried out to show the validity of the developed control scheme.

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.

In this study, an adaptive boundary control is presented for vibration suppression of an axially moving belt system. First, the infinite‐dimensional model of the belt system including the dynamics of high acceleration/deceleration and distributed disturbance is derived by utilising the extended Hamilton's principle. Subsequently, by using Lyapunov's synthesis method and an adaptive technique, an adaptive boundary control is developed to suppress the belt's vibration and compensate for the system parametric uncertainties. With the proposed control, the stability of the closed‐loop system and the uniform boundedness of all closed‐loop signals are both ensured. Besides, the S‐curve acceleration/deceleration method is adopted to plan the belt's axial speed and the disturbance observer is used to mitigate the effects of unknown boundary disturbance. Finally, the control performance of the closed‐loop system is successfully demonstrated through simulations.

This article demonstrates the realization of angle tracking and deformation suppression by developing two boundary controllers for a flexible variable-length rotary crane arm with extraneous disturbances and asymmetric input–output constraints. The dynamic model description of this kind of crane arm system is several partial differential equations integrated into few ordinary differential equations. The S-curve acceleration and deceleration scheme is utilized to adjust the elongation rate of the arm. A kind of novel observer is put forward to tackle unknown extraneous disturbances. Auxiliary systems and barrier Lyapunov functions are introduced to meet the asymmetric input–output constraints. With the help of Lyapunov’s theory, the global exponential stability and uniform boundedness are analyzed. The numerical simulations are finally provided to illuminate its availability of the designed control schemes.