An Input Dead Zones Considered Adaptive Fuzzy Control Approach for Double Pendulum Cranes With Variable Rope Lengths

Abstract

As commonly used tools for industrial production, overhead crane systems may suffer from the double pendulum effect in practice when the hook is not negligible or the payload cannot be directly considered a mass point, and most control methods designed for single pendulum overhead cranes are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">no</i> longer suitable. Moreover, the actuators in practice cannot be ideal, and the existence of input dead zones will introduce much challenge during the controller design process. To improve the working efficiency, payload hoisting/lowering movement is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">necessary</i> during the trolley horizontal movement, which implies that the rope length is variable and makes the entire system more <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">complex</i> . To solve these problems, an adaptive fuzzy control law is proposed for the double pendulum crane with variable rope lengths in this article, which can regulate the trolley displacement and rope length to the corresponding desired values within finite time and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneously</i> suppress the hook’s swing and payload’s swing. Specifically, fuzzy logic systems are introduced with carefully designed adaptive laws to compensate for input dead zones for the double pendulum crane. Next, an effective regulation control method is proposed, and the convergence of actuated state variables, i.e., the trolley displacement and the rope length, is analyzed and proven by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rigorous</i> mathematical analysis. Then, the elimination of the hook’s swing and payload’s swing is further proven by using the property of the converging input bounded state. Finally, hardware experiment results demonstrate the performance of the proposed method.