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In real-world applications, industrial cranes commonly suffer from effects caused by the so-called double-pendulum phenomenon in many situations. However, at present, the double-pendulum phenomenon is usually directly roughly neglected when designing control methods. For double-pendulum cranes, most currently available approaches are open loop control; the existing feedback methods are mostly developed based on linearized dynamic models (around the equilibrium point) or designed without adding integral terms in the control laws, which may cause positioning errors in the presence of unmodeled dynamics. To address these problems, this paper proposes a new quasi-proportional integral derivative control method to effectively control underactuated double-pendulum crane systems. Then, we provide rigorous theoretical analysis for the equilibrium point of the closed-loop system based on the original nonlinear dynamic equations. To our knowledge, this paper gives the first plant-parameter-free controller that incorporates both integral action and actuating constraints without any linearizing operations during controller design or closed-loop analysis, which theoretically ensures that the controller can work well in the presence of unmodeled dynamics (e.g., insufficient friction compensation), actuating constraints, and large swing angles (i.e., not satisfying linearization conditions). Finally, hardware experimental results are provided to examine the effectiveness of the suggested control method.
Sun et al. (Fri,) studied this question.