Research On Automatic Control Of An Underactuated Nonlinear Overhead Crane System

Underactuated systems are systems that have fewer independent control inputs than degrees of freedom to be controlled. Because fewer actuators are utilized, the mechanical design and manufacture of underactuated systems become more simplified than that of the full-actuated systems. Moreover, the cost as well as the system weight could be reduced. Thanks to these benefits, a lot of practical systems are designed to be underactuated, such as aircrafts, underwater vehicles, satellites, flexible robots and so on. Besides, a full-actuated system would become underactuated due to actuator failure. Although the underactuated nature brings much convenience to system design and manufacture, it creates a great challenge for the control of these systems. For these reasons, underactuated systems have become a research focus in the field of control theory and technology.An overhead crane is a typical nonlinear underactuated system with strong states coupling. Due to such merits as high flexibility and less energy consumption, it is widely used for industrial production, port transportation, and so on. To improve the efficiency and the safety of the crane system, there is a great need for an effective control approach. Specifically, two control objectives should be achieved in the transportation task: on one hand, the trolley is required to arrive at the desired position within a short time to increase transferring efficiency; on the other hand, the payload swing should be suppressed within a given domain for safety concern. Unfortunately, the overhead crane is an underactuated system and there exist some uncertain disturbances such as frictions, thus it is usually difficult, if not completely impossible, to reach the aforementioned two control objectives simultaneously. For years, some researchers have made great efforts to address the control problem of the overhead crane system. Although many novel control methods have been proposed, for instance, input shaping, optimal control, intelligent control, and so on, there are some deficiencies hindering them in applications.This dissertation makes a further study on the control techniques of the overhead crane systems. Specifically, two energy-based adaptive strategies are proposed for the transportation, and a switching-based braking control method is employed to ensure the safety of the transportation in case of an unexpected emergency. With the aid of some stability analysis tools including Lyapunov's Method, Barbalat's Lemma and LaSalle's Invariant Theorem, it proves that the stability of the closed-loop system can be ensured by the proposed control methods. Besides, a simulation testbed and a prototype testbed are constructed to demonstrate the superior performance of the proposed control techniques. In general, the work in this dissertation can be summarized as follows:(1) Modeling of a 3D overhead crane system. The dynamic model of a 3D overhead crane system is established with utilizing Lagrange's equation. Because the model pays much attention on such nonlinear disturbances existing in the environment as mechanical frictions (including coulomb friction, linear friction and Stribeck effect) and air resistance, it can describe the dynamics of the practical system well and accurately. This dynamic model is a precondition for the construction of the simulation testbed, and it is also a foundation for system analysis and model-based controllers design which will be discussed in the following parts.(2) Design and construction of the simulation and prototype testbed. Simulations and experiments are important means for performance evaluation in engineering science. Based on the dynamic model of a 3D overhead crane system, a simulation testbed is designed and developed using Matlab/Simulink, which can simulate the variations of the system states accurately. Furthermore, it can be easily used to test various control algorithms, as well as observe and analyze the simulation results. In the simulation testbed, a mask matrix is utilized to keep some states constant. According to the working principle and the components of a commercial overhead crane, a prototype testbed of a 3D overhead crane is constructed. Using the simulation testbed and the prototype testbed, various tests are carried out in a comparison way, and the test results show the correctness of the dynamic model and the validity of the simulation platform. Furthermore, the controller modules of the two testbeds are both developed via Matlab/Simulink, hence a control algorithm can be transported from one testbed to the other freely. (3) Energy-based adaptive controller design. To position the trolley rapidly and suppress the payload swing in the transportation, an energy-based adaptive controller is designed for the overhead crane system. The controller can estimate the unknown parameters including the mass of the payload and the length of the rope on line. In addition, an improved adaptive controller is proposed and it can reduce the swing of the payload effectively. Utilizing Lyapunov's Theory and LaSalle's Theorem, it is proved that both the position error of the trolley and the swing angle of the payload converge to zero asymptotically. Simulation and experiment results show that the designed adaptive controllers achieve a superior performance for the overhead crane system.(4) An adaptive control strategy based on motion planning of the trolley. To increase the flexibility of the controller design for an overhead crane, a novel two-step control approach is presented for the positioning of the trolley and the reduction of the payload swing. In the first step, this dissertation proposes a desired anti-swing trajectory for the trolley, and in the second step, an adaptive control law is designed to make the trolley track the planned trajectory. As shown by Lyapunov Theory, the proposed adaptive controller guarantees asymptotic tracking even in the presence of uncertainties including system parameters and various disturbances. Simulation and experiment results demonstrate that the motion planning based control strategy has a superior performance for the underactuated cranes, and it is especially suitable for long-distance transportation.(5) Emergency braking control for the payload. Emergency braking plays an important role in the safety of overhead crane systems. According to the underactuated nature, this dissertation proposes a switching logic based control strategy. At the first stage, a braking controller is exerted on the trolley to prevent the payload from moving forward as soon as possible. At the second stage, an energy-based damping controller is adopted to stabilize the whole system rapidly. The switching time for the two controllers is selected carefully to ensure that the payload swing will not lead to another collision during the stage of the damping control. Furthermore, a pair of upper bounds are calculated for the braking time and distance of the payload. Both simulation and experiment results are provided to demonstrate the effectiveness of the proposed braking control method.