Active disturbance compensation is crucial for realizing high-precision servo control. However, the suppression of rapidly changing disturbances is still a challenging issue. In this article, observer-based disturbance-rejection control is investigated, and an observer with adaptive switching gain is proposed for improved robustness against changing disturbances. First, a disturbance observer (DOB) is established, based on the tracking differentiator technique. Second, a sliding-mode-assisted observer with an adaptive law is designed to estimate the residual-disturbance estimation error of the DOB. The proposed scheme instantly increases the switching gain when the state deviates from a preset boundary, thus eliminating the tuning time. The switching control action with an immediately large switching gain is robust against suddenly changing disturbances. Moreover, the switching gain then decays to zero, reducing chattering in the steady state. The gain adjustment process is designed to have the same dynamic characteristics as the proposed DOB, which guarantees the convergence of the proposed scheme. This method is not only suitable for linear systems, but also extendable to nonlinear systems. The proposed scheme was evaluated experimentally; the results showed that it improves disturbance rejection and decreases servo error.

Piezo-actuated stages are widely applied in the field of high-precision positioning. However, piezo-actuated stages produce hysteresis between the input voltage and the output displacement that negatively influences the positioning accuracy. In this study, the Bouc-Wen model is established and identified using the bat-inspired optimization algorithm. Subsequently, based on the established hysteresis model, we propose a sliding mode control method with a new reaching law to suppress the hysteresis nonlinearity and achieve high-precision tracking control for the piezo-actuated stages. In additon, the proposed control method contains the perturbation estimation part, which can estimate online the modeling uncertainty and the unknown external disturbances. The stability of the proposed control method is demonstrated through the Lyapunov theory. Finally, to validate the effectiveness of the proposed control method, experiments are conducted on the piezo-actuated stages. Experimental results demonstrate that the proposed control method is superior to the feed-forward control and the conventional sliding mode control method.

This study developed a local fixed-time sliding mode control (FTSMC) method based on a novel adaptive disturbance observer (NADOB) dedicated to motion tracking control for piezo-driven microscanning systems with unmodeled uncertainties and external disturbances. First, the NADOB was developed to precisely approximate and compensate for the lumped disturbance, which includes unmodeled uncertainties and external disturbances. The adaptive law of the NADOB method can estimate the upper-bound information of the lumped disturbance, assuming that it is bounded. Its convergence was strictly proven using the Lyapunov theorem. Subsequently, the local FTSMC method with an improved approach law was developed for the piezo-driven microscanning system to achieve high-precision trajectory tracking control. The stability of the tracking controller was proved using the fixed-time convergence theory. Finally, a series of comparative experiments were conducted on a piezo-driven microscanning experimental setup in the presence of a lumped disturbance, illustrating the robustness of the local FTSMC method with the NADOB. Comparative experimental results revealed that the proposed fixed-time tracking control scheme exhibits stronger robustness and higher tracking accuracy compared with existing sliding mode control methods.

Magnetic shape memory alloys (MSMA), which are a class of innovative functional materials, are used as the actuators to be applied widely in high-precision positioning. However, the hysteresis nonlinearity in the MSMA seriously affects the positioning precision of the MSMA-based actuator. In this paper, to study the hysteresis nonlinearity in the MSMA, the Krasnosel’skii-Pokrovskii (KP) model is employed to describe the hysteresis nonlinearity in the MSMA-based actuator and the density function of the KP model is identified by the Elman neural network. The simulations show that the modeling error rate of the KP model using the Elman neural network is 0.81%, which is reduced by 63.5% compared with that of the KP model based on recursive least-squares method. This result demonstrates that the KP model based on the Elman neural network can accurately describe the hysteresis nonlinearity in the MSMA-based actuator.

This paper first presents a rate-dependent Krasnosel’skii-Pokrovskii (RKP) model to capture the hysteresis of piezo-nanopositioning stages. The dynamic density function of the RKP model is obtained via neural network with frequency behavior input signal. Under the persistently exciting condition, the convergence of the neural network with Krasnosel’skii-Pokrovskii (KP) operators is proved rigorously. In order to address the hysteresis issue, a direct compensation control (DCC) approach with the KP compensation operator is proposed, where its dynamic density function is same as that of the RKP model. Some experiments with different reference signals are conducted to verify the effectiveness of the proposed modeling and DCC method on piezo-nanopositioning stages.