Research On Trajectory Planning And Anti-swing Control For Underatuated Overhead And Gantry Crane Systems

Cranes play a very important role in industries,such as railway container center stations,harbors,offshore platforms,nuclear power plants,hydropower stations and so on.Flexible wire ropes are commonly adopted as hoisting mechanism.Some cranes lift payloads through rigid lifting guides or add rigid anti-swing mechanisms.Such guides or mechanisms are heavy and can only be adopted at low lifting heights.On the contrary,in most applications,cranes have no rigid lifting guide frame or rigid anti-swing mechanisms.They are typically underactuated and light-weight.They also can lift payloads higher.For such underactuated cranes,during the transportation process and at the time of reaching the desired position,the payload swings inevitably because of the inertia force and external disturbances.Currently,cranes are mainly operated by drivers in most applications.If the driver does not have sufficient experience,it is easy to result a large residual swing angle of the payload,which not only greatly reduces the efficiency of transportation,but also may cause safety accidents such as collision,tipping over,dropping the payload and so on.To improve the transportation efficiency and safety,lots of researchers have put forward many schemes to improve the accuracy of positioning of the trolley and to eliminate the residual swing of the payload.However,the existing schemes have the following drawbacks: 1)not enough rationality of adopting rigid beam assumption for crane dynamic modeling when designing anti-swing controllers;2)the existing trajectory planning methods of trolley does not give the relationship between the trolley’s motion and the payload’s swing,and it is a timeconsuming task to tune the optimal parameters of the existing methods;3)in most cases,it is difficult to obtain the full state feedback of the system fast and accurately,especially for doublependulum cranes,measuring the payload’s motion is the most difficult task.To tackle the aforementioned drawbacks,the dissertation aims to establish a novel dynamic model of the cranes and to design novel anti-swing control methods.The main contributions of the dissertation are as follows:(1)Combining Lagrange’s equations of the second kind and the assumed mode method,a novel dynamic model of overhead and gantry cranes including a two-axle trolley is established.The correctness of the novel model is validated by comparing it with the flexible beam-moving mass model and the traditional crane model named flexible beam single-axle trolley model.On the basis of the novel model,the effect of the trolley’s axle base on the dynamic responses of the flexible beam,the effect of the payload’s initial swing angle of the dynamic responses of the flexible beam,and the effect of the beam’s dynamic responses on the payload swing are studied.(2)A new trajectory planning method is proposed.Two desired swing trajectories of the payload are designed for short-distance and long-distance cases,respectively.The ideal trajectories of the trolley are derived,based on the desired swing trajectories and combined with the linear simplified dynamic model of the crane system.The initial states and final states are adopted to calculate the coefficient of the ideal trajectories of the trolley.By analyzing the characteristics of the payload’s desired swing trajectories and the trolley’s ideal trajectories,the relationships between the only tunable parameter of trolley’s ideal trajectories and the upper bounds of the absolute payload swing angle,absolute trolley acceleration and trolley speed can be obtained.(3)A pure neural network controller is proposed to control double-pendulum overhead crane systems,which does not require the crane system parameters,such as the mass of the trolley,the mass of the payload,the lengths of the cable and so on.The proposed controller contains only one neural network and the output of the neural network is used as the control input of the crane systems directly.If the range of variation of the crane system parameters is determined,one can design a conservative trajectory of the trolley,independent to the parameters of crane systems change,hence the residual swing of the payload can be always suppressed in an acceptable small range.The weights update law of the neural network is designed as well as the stability of the proposed controller is proved using Lyapunov stability theory.The weights of the neural network are updated real-time.In other words,no offline pre-trained process is needed.The biggest advantage of the proposed controller is that it can make the trolley to track its ideal trajectory perfectly with only the feedback signals of the trolley,that is,partial state feedback.(4)For double-pendulum overhead crane systems,it can be found and proved that with no external disturbances,if the system is stable,then the hook and the payload reach at their respective equilibrium points simultaneously.The payload swing is regarded as the external disturbance of the trolley-hook subsystem,so the original double-pendulum system(trolleyhook-payload system)can be reduced to a single-pendulum system(trolley-hook system)with unknown external disturbances,and then one can rewrite the dynamic model.Based on the new model,a sliding mode controller is designed to regulate the original double-pendulum crane.In this case,the sliding mode controller is a partial state feedback controller,because the feedback signals of the payload are unknown.This method can deal with the effects of non-zero initial states,unmodelled dynamics and unknown external disturbances.(5)An experimental platform that mimics a 2-dimensional overhead crane is constructed.The experimental platform is actuated by four servo motors and controlled by a PLC real-time control system.The states of the trolley and the payload are measured by encoders.Several experiments are conducted to validate the effectiveness of the swing trajectory planning method in suppressing the residual swing of the payload.To sum up,firstly,the rationality of adopting rigid beam assumption for crane dynamic modeling when designing anti-swing controllers is studied in the dissertation.Secondly,a new swing trajectory planning method is proposed,and the relationships between the only tunable parameter of trolley’s ideal trajectories and the upper bounds of the absolute payload swing angle,absolute trolley acceleration,and trolley speed is given.Thirdly,a pure neural network controller for tracking control and a new sliding mode controller for regulating control are proposed for double-pendulum cranes,both of them are based on partial state feedback.Finally,the effectiveness of the swing trajectory planning method in suppressing the residual swing of the payload is validated through experimental tests.