Adaptive Control of Two-Pendulum Suspension of Overhead Crane

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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