Abstract
Tower cranes are well-known underactuated systems, where the design of controllers for them with time-varying rope length was weak in the past because of their complex dynamic characteristic. The payload oscillation will become worse when the jib slew angle, the trolley position and the rope length are changed simultaneously. The proposed method is designed based on robust adaptive sliding mode control via tracking nonzero initial reference trajectories, in which frictions and lumped disturbances in the crane system are eliminated, and unknown payload mass is effectively estimated online. Lyapunov technique is combined with LaSalle’s invariance theorem to design controller and analyze stability. Various and strict simulations are applied, which validate the effectiveness and extreme robustness of the proposed method.
Highlights
Keywords Underactuated system · Tower crane · Time-varying rope length · Sway rejection · Robust adaptive sliding mode control. Because of their combination of simple structure and complex dynamic characteristics, underactuated systems where the number of actuators is less than the DOF have been paid more and more attention to the control technique improvement in recent years [1]
With the lifting movement of the payload, the length of the rope will change, which will have a great impact on the dynamic characteristics of the tower crane, such as the natural frequency of the payload swing
The model diagram of tower cranes with time-varying rope length is presented as shown in Fig. 1, whose mathematical model is built by the Lagrange’s kinematics equations, and the relations are as follows [31]: M (q)q + C(q, q)q + G(q) = U − Fs(q) + D, (1)
Summary
Tower crane is a kind of crane that transports goods in 3D (three-dimension) space. Its transportation process is often accompanied by the translation of the trolley and the rotation of the jib. At the actual control applications, it is inevitable that there will be friction effect, incomplete theoretical modeling, parameter uncertainties and external disturbances of full DOF In these cases, it is a very challenging issue to realize the accurate positioning of the jib, trolley and payload lifting with quickly suppressing the swing of the payload. 3) In real applications, many factors, such as, the friction of input channel, unmodeled part effect, parameter uncertainties and full DOF external disturbances, are inevitably appear in motion process, while many control strategies do not fully consider and restrain their adverse effects Under these circumstances, it is a very challenging problem to achieve accurate positioning of the actuated mechanism while quickly suppressing the swing of the payload.
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