Nonlinear Control Of Underactuated Overhead Crane Systems

Overhead cranes,as a cargo transportation tool,are widely utilized in many industrial sites such as workshops,warehouses,and shipyards.Moreover,as a typical nonlinear underactuated system,overhear cranes possess fewer control in-puts than degrees of freedom,which initiates challenges in control design.Therefore,controlling overhead cranes is of both practical and theoretical importance due to their underactuated characteristics.As a consequence,control of overhead cranes has attracted much attention of many researchers from the control community and has become a hot research topic in the control community.The basic tasks of overhead crane systems include driving a cargo from the initial point to the desired point,suppressing and eliminating the cargo swing during the transportation process.With the rapid developments of communication,computer and control techniques,extensive research has been done on overhead cranes and some of existing methods have been used to control the practical overhead crane systems.However,there exist some problems and drawbacks for the existing methods.To this end,some insightful studies are carried out for the anti-swing and positioning control of overhead cranes in this dissertation.The main work of this dissertation is summarized as follows:1.A partially saturated nonlinear controller for underactuated overhead cranes is proposed based on passivity.The main contribution is that the total energy shaping method assigns a new storage function to the system,which is characterized by a desired damping matrix and especially quadratic in a new error vector of the coupling form.Consequently,a partially saturated nonlinear controller enforcing the coupled-dissipation inequality is derived to introduce additional damping terms to the sway angle,thus guaranteeing favorable transit performance.Owing to the elaborate structure of the coupled-dissipation term,the control system can achieve significant oscillation reduction over a wide range of cable lengths and transportation distances without readjusting the control gains.Besides the Lyapunov theory,La Salle's invariance principle is carried illustrating the corresponding stability.The proposed controller is evaluated through both simulation and experimental results that demonstrate the improved performance and robustness.2.A significant Lyapunov function candidate for control of underactuated 3-dimensional overhead cranes is developed,which yields a nonlinear coupling-based controller to introduce active damping to the payload sway.In Particular,a new coupleddissipation signal is designed to strengthen the internal coupling between the trolley movement and the payload sway,thus significantly enhancing the transit performance of the control system.The proposed controller is extended by a smooth saturated function to ensure a soft trolley start.Due to the improved passivity and the partial saturation,the proposed controller can provide sufficient damping over a range of different travel distances,system parameters as well as external disturbances.The asymptotic stability guaranteed by the Lyapunov theory and La Salle's invariance principle is presented.The satisfactory performance of the proposed controller,including robustness features of the closed-loop system,is validated by simulation and experimental results.3.To increase the damping of the control system,a partially saturated couplingbased controller for underactuated overhead cranes is presented.A new storage function characterized with a desired inertia matrix and potential energy function is constructed,which is especially quadratic in a composite state vector,and subsequently,a nonlinear controller is designed by enforcing the coupled-dissipation inequality.Particularly,a composite signal is fabricated to augment the internal coupling between the trolley movement and the payload sway,thus drastically increasing the damping of the control system.The proposed controller is simple and very robust to different/uncertain cable lengths.Besides,the hyperbolic tangent function is adopted so that the proposed controller guarantees a soft trolley motion.In the frame of the Lyapunov theory,La Salle's invariance principle is applied to illustrate the asymptotical stability.Simulation and experimental results are presented to verify the effectiveness of the control system.4.Handling loads with small swings is difficult for a 3-dimensional overhead crane due to its hard nonlinearity.Moreover,the nonlinear dynamics increases the complexity of the required feedback,thus making the closed-loop system sensitive to a variation in the cable length that negatively influences the damping feature.To address these problems,a significant storage function characterized by the desired damping isconstructed based on passivity.Consequently,a nonlinear controller is delivered by enforcing the coupled–dissipation inequality,thus drastically increasing the damping of the closed-loop system.In particular,new coupled–dissipation signals are fabricated to augment the coupling between the trolley movement and the payload sway.Due to its very simple structure that excludes the cable length,the proposed controller is robust to unknown cable lengths and easy to implement.In the frame of the Lyapunov theory,La Salle's invariance principle is applied to illustrate the corresponding stability.The effectiveness of the proposed control on improving the system performance is verified through simulation results.