We constitute a control system for overhead crane with simultaneous motion of trolley and payload hoist to destinations and suppression of payload swing. Controller core made by sliding mode control (SMC) assures the robustness. This control structure is inflexible since using fixed gains. For overcoming this weakness, we integrate variable fractional-order derivative into SMC that leads to an adaptive system with adjustable parameters. We use Mittag–Leffler stability, an enhanced version of Lyapunov theory, to analyze the convergence of closed-loop system. Applying the controller to a practical crane shows the efficiency of proposed control approach. The controller works well and keeps the output responses consistent despite the large variation of crane parameters.
