This paper proposes a hybrid data-driven active disturbance rejection sliding mode control (ADRC-SMC) algorithm for tower crane systems. The algorithm combines a second-order continuous-time ADRC with a sliding mode control (SMC) to improve control-loop performance and ensure stability. The ADRC-SMC algorithm uses a metaheuristic slime mould algorithm (SMA) to optimally tune its parameters, reducing heuristic tuning and enabling fair performance comparisons with traditional ADRC. The algorithm is validated experimentally on tower crane laboratory equipment, demonstrating improved performance in position control of the cart, arm, and payload. The ADRC algorithm uses an extended state observer to estimate process outputs and disturbances, while the SMC ensures robustness against parameter variations and disturbances. The hybrid ADRC-SMC algorithm integrates these features, using SMC reaching and existence conditions to guarantee stability. The algorithm's parameters are optimized using SMA, which reduces the need for heuristic tuning and ensures better performance. The design process involves specifying the dynamic regime, tuning the observer and controller parameters, and validating the system through experiments. The experimental results show that the ADRC-SMC algorithm outperforms traditional ADRC in terms of control accuracy and stability. The algorithm is implemented on a tower crane system, with the cart, arm, and payload positions controlled using the ADRC-SMC algorithm. The results demonstrate the effectiveness of the hybrid approach in handling complex, nonlinear systems with unknown dynamics. The paper also discusses future research directions, including the stability analysis of the ADRC-SMC algorithm and the implementation of the control system in discrete time. The study highlights the potential of data-driven control algorithms in improving control performance and stability in complex systems. The results show that the ADRC-SMC algorithm is a promising approach for tower crane systems and other complex, nonlinear applications.This paper proposes a hybrid data-driven active disturbance rejection sliding mode control (ADRC-SMC) algorithm for tower crane systems. The algorithm combines a second-order continuous-time ADRC with a sliding mode control (SMC) to improve control-loop performance and ensure stability. The ADRC-SMC algorithm uses a metaheuristic slime mould algorithm (SMA) to optimally tune its parameters, reducing heuristic tuning and enabling fair performance comparisons with traditional ADRC. The algorithm is validated experimentally on tower crane laboratory equipment, demonstrating improved performance in position control of the cart, arm, and payload. The ADRC algorithm uses an extended state observer to estimate process outputs and disturbances, while the SMC ensures robustness against parameter variations and disturbances. The hybrid ADRC-SMC algorithm integrates these features, using SMC reaching and existence conditions to guarantee stability. The algorithm's parameters are optimized using SMA, which reduces the need for heuristic tuning and ensures better performance. The design process involves specifying the dynamic regime, tuning the observer and controller parameters, and validating the system through experiments. The experimental results show that the ADRC-SMC algorithm outperforms traditional ADRC in terms of control accuracy and stability. The algorithm is implemented on a tower crane system, with the cart, arm, and payload positions controlled using the ADRC-SMC algorithm. The results demonstrate the effectiveness of the hybrid approach in handling complex, nonlinear systems with unknown dynamics. The paper also discusses future research directions, including the stability analysis of the ADRC-SMC algorithm and the implementation of the control system in discrete time. The study highlights the potential of data-driven control algorithms in improving control performance and stability in complex systems. The results show that the ADRC-SMC algorithm is a promising approach for tower crane systems and other complex, nonlinear applications.