When constructing the bridge crane control law, a two-pendulum model with a hook suspension, on which the transported load is suspended, and a load suspension is considered. This model more accurately describes the dynamics of cargo movement, which is especially critical in a number of crane operating modes, including cases when the mass-inertial parameters of the cargo are close to the hook. A mathematical model of the two-pendulum mechanical system of the crane suspension along one axis of its movement is described, taking into account the effect of friction forces when moving the crane trolley and wind disturbance acting on the transported cargo. Also, there is presented linearized model of hook movement with control action in the form of preset speed of crane trolley movement. The latter corresponds to the use of a servo motor or stepper motor to control the trolley. On the basis of the obtained linearized model, an adaptive control law is constructed using a scheme including an algorithm for current parametric identification, an implicit reference model, "simplified" adaptability conditions with direct tracking of hook movement (through it — cargo movement) by the properties of the assigned reference model. This control law allows you to build crane control under the current parametric uncertainty of the properties of the crane, the transported cargo and external disturbances (only approximate information about some parameters is assumed). It is shown that in the case when the natural frequency of the assigned reference model is less than that for the hook suspension, the proposed control law generates asymptotic movement of the hook (load) to the assigned point and damping of angular oscillations of the hook suspension and load suspension. For more efficient damping of angular oscillations in case of large values of load moment of inertia, it is proposed to supplement preset value of hook movement with damping movements based on angular movement of load suspension. Model examples supporting theoretical conclusions are given. It is shown that the proposed solution makes it possible to build a bridge crane control under the action of measurement noise and control signal delays.

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Nowadays, cargo cranes are widely used in various areas of industries. Many of cranes use suspended load fastening, which is associated with load swinging during transportation. Load swinging is most often caused by acceleration or deceleration of the crane trolley, less often it occurs due to external disturbances, such as wind. One of the key directions of the development of this kind of cranes is the development of an automated control system that can dampen pendular oscillations of the load. At present, a considerable number of control systems have been developed, but most of them require preset adjustment of specific parameters of the transported load. The task of this study is to develop and debug a control algorithm using a model of an overhead crane of previously developed adaptive control law that can provide fine positioning and damping of load oscillations under the current parametric uncertainty. The study using the pilot plant will allow us to determine and analyze the features of the implementation of the control law before its application for industrial cranes. An adaptive control law is studied using the model of overhead crane under conditions of a current parametric uncertainty of the load and external disturbances. This control method is based on an adaptive control approach with an identifier and an implicit reference model using “simplified” adaptation conditions. A previously developed adaptive control law for an overhead crane is described. An experimental model of an overhead crane is described. An algorithm for adaptive control of an overhead crane model has been developed. The first experimental studies of the proposed control method have been carried out. They confirm its performance in real conditions. The results of experimental tests have shown the effectiveness of the adaptive control law. The system ensures fine motion of the load in a short period of time, dampens the pendular oscillations of the load during acceleration and deceleration of the trolley, as well as during external disturbances. The adaptive control law allows you to move the load to the designated position and dampen the pendular oscillations with minimal preset adjustment of the control system. Since the identification of parameters occurs at the current time, the changes of the parameters of the load and the length of suspension do not affect the quality of control.

A method is proposed for automatic control of the speed of an overhead-type crane trolley with direct tracking of the horizontal movement of load in conditions of current uncertainty of load parameters and external disturbances. The purpose of the control is to find the precise positioning of the transported cargo with the damping of its pendulum oscillations and the parrying of external disturbances. The dynamics of an overhead crane when moving a trolley along one axis is described. The proposed control method is based on an adaptive control scheme with an identifier and an implicit reference model using «simplified» adaptability conditions. The stability of a closed control system is proved and the conditions for this are determined. For the current identification of load parameters, the recursive least squares method with a forgetting factor is used. This control method was developed specifically for research and debugging on an experimental layout, so all the parameters of the crane and load were approximated to the layout during calculations. The results of computer simulation the proposed control method with different mass-inertial properties of the load, the length of its suspension and perturbations in the Matlab Simulink software environment are presented. The results showed the high efficiency of the proposed adaptive control system. It ensures accurate movement of the load in a short period of time, prevents the load from swinging during acceleration and braking of the cart, and is also able to fend off external disturbances, for example, the impact of wind. The developed approach can be recommended for any crane installations using a suspended load.