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Asymmetric Input–Output Constraint Control of a Flexible Variable-Length Rotary Crane Arm

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.