For practical mechanical systems, uncertainties/disturbances, such as unmodeled dynamics and frictions, are nonignorable factors. For existing control methods, these factors are usually neglected or addressed by a robust way. As a consequence, the nominal control performance of these methods is sacrificed. Moreover, there exists the chattering problem for some existing robust methods, such as sliding mode control laws. To deal with these drawbacks, a continuous global sliding mode controller along with a nonlinear disturbance observer is designed for the regulation and disturbance estimation control of the overhead crane system. Specifically, the original crane dynamic model is transformed into a quasi-integrator-chain form through some transformations. Then, a nonlinear disturbance observer is designed and a continuous global sliding mode control method is introduced on the basis of the constructed disturbance observer. The stability and convergence characteristics are proven through rigorous theoretical analysis. Finally, to demonstrate the performance of the designed controller, a series of experimental tests are performed, and a comparison study between the devised method here and an existing method is given.

In this paper, we consider the problem of stabilization of a translational oscillator with a rotational actuator (TORA) system. In practical applications, TORA systems usually suffer from parametric uncertainties. Moreover, existing control methods for TORA systems cannot guarantee the rotational scope of the actuator and often lead to unwanted unwinding behaviour. To handle these issues, we present an adaptive control strategy for TORA systems with uncertain or unknown parameters, which is robust to parameter uncertainties and can guarantee that the rotational actuator rotates in a preset range. Specifically, a Lyapunov function is elegantly constructed on the basis of the nonlinear interaction between the translational oscillator and the eccentric rotational proof mass. Then an adaptive control method, along with an online estimation mechanism, is proposed straightforwardly and the stability of the closed-loop system is proven, invoking Lyapunov techniques and LaSalle’s invariance principle. Simulation results are provided to demonstrate the performance of the presented method.

In this paper, we consider the control issues of the two-dimensional translational oscillator with rotational actuator (2DTORA) system, which has two translational carts and one rotational rotor. An output feedback controller for the 2DTORA system is proposed, which can prevent the unwinding behaviour. In addition, the velocity signal unavailability and actuator saturation are taken into account, simultaneously. In particular, the dynamics of the 2DTORA system are given first. On the basis of the passivity and control objectives of the 2DTORA system, an elaborate Lyapunov function is constructed. Then, based on the introduced Lyapunov function, a novel output feedback control method is proposed straightforwardly for the 2DTORA system. Lyapunov theory and LaSalle’s invariance principle are utilized to analyse the stability of the closed-loop system and the convergence of the states. Finally, simulation results are provided to illustrate the excellent control performance of the proposed controller in comparison with the existing method.