A hybrid adaptive interval type-2 fuzzy control and descriptor-based observer scheme for liquid sloshing crane systems

This paper investigates the control problem of liquid slosh suppression in overhead crane systems. In industrial applications, the liquid sloshing crane system (LSCS) transfers liquid within a container in a short time with minimal oscillation to ensure process efficiency and safety under model parameter uncertainties and unmeasurable state variables. To address these challenges, an adaptive interval type-2 fuzzy control with descriptor-based observer scheme (AIT2FC-DO) is proposed. The adaptive interval type-2 fuzzy control (AIT2FC) employs a composite sliding surface that couples actuated and unactuated states, combined with a fuzzy approximator to estimate uncertainties based on Interval Type-2 Fuzzy systems using the Nie–Tan type-reduction method to reduce computational complexity, thereby generating the control signal through adaptive update laws, while all state variables required by the AIT2FC are estimated using a descriptor-based observer (DO) constructed from a partially linearized Takagi–Sugeno descriptor model. The stability of the AIT2FC is first established, followed by the convergence of the estimation error of the DO, and finally the stability of the overall AIT2FC-DO system is proven. The ME, RMS, ITAE, and settling time indices are also provided to quantitatively evaluate the controller performance. Compared with input shaping, the proposed closed-loop control scheme demonstrates improved effectiveness and robustness for the LSCS by reducing the liquid elevation during position tracking by approximately 5 mm.