Feedback stabilization of double pendulum: Application to the crane systems with time-varying rope length

TL;DR

This paper develops a feedback control method for stabilizing a double pendulum crane with variable rope length, improving transportation time and providing a comprehensive nonlinear model without simplifications.

Contribution

It introduces a novel feedback-based control approach for double pendulum cranes with time-varying rope length, including a complete nonlinear model and simulation results.

Findings

Significant reduction in transportation time to the target position.

Effective stabilization of the crane system with variable rope length.

Validation through numerical simulations in MATLAB.

Abstract

In the present paper we focus our attention on the design of the feedback-based feed-forward controller asymptotically stabilizing the double-pendulum-type crane system with the time-varying rope length in the desired end position of payload (the origin of the coordinate system). In principle, we will consider two cases, in the first case, the sway angle of payload is uncontrolled and the second case, when the sway angle of payload is controlled by an external force. Mathematical modelling in the framework of Lagrange formalism and numerical simulation in the Matlab environment indicate the substantial reduction of the transportation time to the desired end position. Another principal novelty of this paper lies in deriving and analysis of a complete mathematical model without approximating the nonlinear terms and without neglecting some structural parameters of systems for the reasons described in the Remark 4.2 and Remark 5.1.