In this article, a novel adaptive super-twisting nonlinear Fractional-order PID sliding mode control (ASTNLFOPIDSMC) strategy using extended state observer (ESO) for the speed operation of permanent magnet synchronous motor (PMSM) is proposed. Firstly, this paper proposes a novel nonlinear Fractional-order PID (NLFOPID) sliding surface with nonlinear proportion term, nonlinear integral term and nonlinear differential term. Secondly, the novel NLFOPID switching manifold and an adaptive supertwisting reaching law (ASTRL) are applied to obtain excellent control performance in the sliding mode phase and the reaching phase, respectively. The novel ASTNLFOPIDSMC strategy is constructed by the ASTRL and the NLFOPID sliding surface. Due to the utilization of NLFOPID switching manifold, the characteristics of fast convergence, good robustness and small steady state error can be ensured in the sliding mode phase. Due to the utilization of ASTRL, the chattering phenomenon can be weakened, and the characteristics of high accuracy and strong robustness can be obtained in the reaching phase. Further, an ESO is designed to achieve dynamic feedback compensation for external disturbance. Furthermore, Lyapunov stability theorem and Fractional calculus are used to prove the stability of the system. Finally, comparison results under different controllers demonstrate that the proposed control strategy not only achieves good stability and dynamic properties, but also is robust to external disturbance.

Tower cranes are widely used in various industrial sites and require a high level of antidisturbance performance from the crane controller due to the variability of the application environment. Although sliding-mode control is a typical antidisturbance control method, most sliding-mode controllers suffer from output chattering and do not reflect well under severe external disturbances. To address these issues from a practical application perspective, a finite-time sliding-mode control method using the super-twisting algorithm (STA) is proposed for underactuated tower cranes operating in the presence of external disturbances. The proposed method includes a finite-time chattering-free sliding-mode controller that eases the output torque chattering problem and a finite-time sliding-mode observer based on STA to observe the uncertain disturbances. The observed values are then applied to the controller through feedforward compensation. Experimental results show that the proposed control method effectively weakens output torque chattering, compensates for disturbance quickly, and accurately completes control tasks.

Overhead cranes with double-pendulum effect seem more practical than those with single-pendulum effect. However, in this case, the dynamic performance analysis and the controller design become more difficult. Moreover, achieving both high-precision trajectory tracking and load sway rejection is a more significant issue for crane systems. For these purposes, the nonlinear dynamics of an overhead crane with double-pendulum effect is derived for the controller design. Then, a novel adaptive hierarchical sliding mode controller is presented. Unlike a traditional approach, the proposed one can make fixed sliding mode surface active to search the state trajectories. Such an adaptive design can make the states of the system to enter the desired sliding surface as soon as possible and, at the same time, can also improve the cart tracking precision. The Lyapunov technique and LaSalle's principle are employed to confirm the stability of the whole system. The experimental results validate that the proposed method has superior control performance and robustness with respect to parameter variations.

The dynamic characteristics of 3-D overhead cranes with double-pendulum effect are complex, which makes the controller design particularly challenging. Besides, in actual conditions, external disturbances cause interference to the system, and the model parameters are uncertain, which further increase the difficulty of controller design. In order to improve the control performance, two composite displacement signals are constructed to increase the coupling relationship of state vectors, and then new error signals and a total mechanicallike energy function are derived. Based on the new energy function, an adaptive control method with enhanced swing suppression is derived. Furthermore, considering the costs of sensors, the velocity signals cannot be obtained directly in many cases of practical application. Hence, auxiliary functions are constructed to replace the velocity feedback signals, and then an improved adaptive tracking control strategy is proposed. Theoretical analysis and experimental results prove that the proposed method can fulfill the control task. Its control result is significantly better than that of the comparison methods. Meanwhile, the experimental results in three different scenarios verify the strong robustness of this method.

To speed up the response and reduce the chattering of a sliding mode control system, a novel reaching law with two variable power terms is proposed, which makes the system have a fast approaching rate either far away from or close to the sliding surface. Moreover, an improved global fast terminal sliding surface with the dynamic coefficients is proposed, which can make the system states arrive at the equilibrium point along the sliding surface with a fast convergence rate. Furthermore, a novel global fast terminal sliding mode controller is designed by employing the proposed reaching law and sliding surface, which can quicken the convergence rate of the system states in both the reaching phase and the sliding phase. Theoretical analysis shows that the proposed controller can ensure finite-time convergence. Experiment results are presented to verify the effectiveness and superiority of the proposed global fast terminal sliding mode control scheme.