Adaptive fractional-order fast terminal sliding mode with fault-tolerant control for underactuated mechanical systems: Application to tower cranes

We develop a robust controller for tracking a class of underactuated mechanical systems (UMSs) that considers many inconveniences, such as actuator faults, parametric uncertainties, and disturbances, by combining a fast terminal sliding mode with fractional derivatives and integrals. Despite these disadvantages and the lack of actuators, such a controller has some advantages, such as robustness, quick transient responses, finite-time convergence, and the flexibility of fractionally derivative orders. However, this control version still requires a complete knowledge of faults, parametric variations, and disturbances. Hence, to overcome these limitations, we improve the controller by integrating an adaptation estimator to approximate the necessary knowledge through an equivalently unique component. We apply the proposed controller to a Liebherr-130-HC tower crane, which is a highly underactuated system, to investigate control quality. Simulation and comparison of the results with the other control approaches, such as sliding mode control (SMC), terminal SMC, and parametric estimator-based SMC, are conducted to highlight the advantages of the proposed controller.