Active Disturbance Rejection Control Approach for Double Pendulum Cranes with Variable Rope Lengths

Abstract

The overhead crane is a typical underactuated system with complicated dynamics and strong couplings. It is widely employed to transport heavy cargoes in many industrial fields. Due to the complexity of working environments, however, cranes often encounter various unfavorable factors, which may degrade the transportation efficiency. To enhance control performance and anti-disturbance ability, this paper proposes an active disturbance rejection control approach based on differential flatness for double pendulum cranes with variable rope lengths. The proposed approach can position the trolley accurately, regulate rope length, and suppress the swing angles of the payload and the hook simultaneously. During the controller design, flat outputs were constructed based on differential flatness technique to deal with system couplings, and the results prove that double pendulum crane system is differentially flat. After that, model uncertainties and external disturbances were estimated by the designed extended state observer. On this basis, a controller was developed based on the feedback control technique. Finally, a series of simulations were carried out to show that the control scheme is effective and robust.

Efficient Solutions for Nonlinear Diffusion Equations Appeared as Models of Physical Problems

“…for more details see [24,28,29], we also mention here some numerical methods similar to ours, in which mathematical models with physical and engineering applications were processed [30][31][32][33]. Our goal in this paper is to find approximate solutions, via the use of a promising technique called DTM, based on the Taylor series expansion, which generates an analytical solution in the form of a polynomial Symbolic computing is required for the classic high order Taylor series technique.…”