Partial state feedback sliding mode control for double-pendulum overhead cranes with unknown disturbances

Abstract

In this paper, a novel sliding mode controller which requires partial state feedback is proposed for double-pendulum overhead cranes subject to unknown payload parameters and unknown external disturbances. Firstly, it is theoretically proved that the hook and payload tend to their respective equilibrium points concurrently. Secondly, a decoupling transformation is performed on the original nonlinear dynamics of double-pendulum overhead cranes. The novel sliding mode controller that does not require the prior information and motion signals of the payload is designed based on the decoupled nonlinear dynamics. Then, the asymptotic stability of the equilibrium point of double-pendulum overhead cranes is proved by rigorous analysis. Finally, several simulations are conducted to validate the effectiveness and robustness of the proposed controller.

Modeling and control of overhead cranes: A tutorial overview and perspectives

“…SMC is another widely used approach in this topic because of its robustness to matched and unmatched disturbances [90,103,50,263]. It can also handle the elacticity exists in the supporting structure as reported by [61].…”

“…Note that the SMCs in this topic usually need full-state feedback. SMC with a nonlinear sliding surface has also been introduced for the single-pendulum [133] with variable length cable and double-pendulum [181,50,214] systems. The SMC designed for the double pendulum system in [50] does not require the payload feedback, i.e., secondary sway (θ 2 ), length of the second link (l 2 ), and the payload mass (m 2 ).…”

“…SMC with a nonlinear sliding surface has also been introduced for the single-pendulum [133] with variable length cable and double-pendulum [181,50,214] systems. The SMC designed for the double pendulum system in [50] does not require the payload feedback, i.e., secondary sway (θ 2 ), length of the second link (l 2 ), and the payload mass (m 2 ). In addition, SMC has also been designed based on the tangent linearized model of the double-pendulum system integrated with the state observer.…”

Intelligent Positioning System Design for Bridge Crane in Hydropower Plant

“…In the early stage, the focus was mainly on the S-curve velocity trajectory planning [1] and trapezoidal velocity trajectory planning [2], and studied the uniform acceleration and variable acceleration control of the bridge crane respectively. Later, with the deepening of the research, scholars began to focus on applying classical control theory to the anti-swing control of bridge crane, which mainly includes fuzzy PID control [3][4][5][6] and sliding mode control [7,8]. At the same time, many scholars have applied computer vision to the 3D map construction of cranes [9], swing angle measurement [10], and position detection [11,12], etc.…”

Nonlinear Enhanced Coupled Feedback Control for Bridge Crane with Uncertain Disturbances: Theoretical and Experimental Investigations

“…In contrast, closed-loop control has demonstrated superior performance for uncertain parameters and external interference owing to the existence of feedback channels. Based on the linearization of the crane model, a series of linear control methods have been proposed [2,5]. Researchers have also explored adaptive control methods for the bridge crane systems to reduce the sensitivity of the control system to internal parameter perturbations [3,35], Additionally, to minimize the control costs, researchers have applied optimal control methods to crane control systems [18,21] to seek optimal control strategies.…”