Abstract
A novel energy-coupling-based control method for under-actuated double-pendulum overhead cranes with initial control force constraint is proposed in this article. The significant feature of the designed controller is its superior control performance as well as its strong robustness with respect to parameter variations and external disturbances. By incorporating a smooth hyperbolic tangent function into the control law, the proposed controller guarantees soft start of the trolley. Moreover, to improve the transient performance of the crane system, coupling behavior among the trolley movement, the hook swing, and the payload swing is enhanced by introducing a generalized payload horizontal-displacement signal. Lyapunov techniques and LaSalle’s invariance theorem are utilized to prove the stability of the designed closed-loop system. Simulation results demonstrate that the new energy-coupling control method achieves superior control performance and strong robustness over different payload masses, cable lengths, desired positions, and external disturbances with reduced initial control force.
Highlights
Overhead cranes have been widely applied to some industrial fields, such as construction sites, harbors, and factories, for bulky cargoes transportation.[1,2,3] Control problems for overhead crane systems attract much attention due to the under-actuated nature of overhead cranes
The primary goal of horizontal transportation phase is to move the payload from its initial position to its desired position accurately while suppressing and eliminating the payload swing rapidly, so as to put down the payload steadily and vertically in the payload lowering stage
In section ‘‘Dynamic model of a double-pendulum overhead crane system,’’ we present the dynamic model of a double-pendulum overhead crane
Summary
Overhead cranes have been widely applied to some industrial fields, such as construction sites, harbors, and factories, for bulky cargoes transportation.[1,2,3] Control problems for overhead crane systems attract much attention due to the under-actuated nature of overhead cranes. We design a novel energy-couplingbased controller with initial control force constraint by means of analyzing the passivity characteristics of the double-pendulum overhead crane associated with a generalized payload horizontal-displacement signal. = x_T ðFx À FrxÞ = x_ T F which indicates that the double-pendulum overhead crane system with input F(t) and output x_ðtÞ is passive and dissipates.[40] As can be seen from equation (9), there are no terms related to u1 (or u_ 1) and u2 (or u_ 2) in E_ (t) To circumvent this problem and improve the transient control performance, we plan to construct an energy-like storage function Et(t) whose time derivative along the system dynamic model (1) has the following expression. We provide the expressions of the passivity-based controller and the CSMC controller as follows
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