In this article, a sliding mode dual-channel disturbance rejection control based on an extended state observer is proposed for the attitude control of a quadrotor under unknown disturbances. There exist an inner disturbance rejection channel (IDRC) and an outer disturbance rejection channel (ODRC) in this control scheme. In the IDRC, a low-frequency disturbance compensator is proposed to obtain the disturbance compensation value and to compensate the low-frequency component of the lumped disturbance. In the ODRC, a novel sliding mode controller with a variable-gain switching term and a constant-gain switching term is designed, and the switching terms are used to compensate the virtual disturbance estimation error and the high-frequency component of the lumped disturbance. The low-frequency and high-frequency components of the lumped disturbance can be estimated and the influence of the virtual disturbance estimation error is reduced by using the proposed control scheme. The stability of the system is proved by using the Lyapunov theory. Finally, the effectiveness of the proposed scheme is tested by numerical simulations and platform experiments.

In this article, an extended two-state observer (ETSO) is proposed for the permanent magnet synchronous motor (PMSM) with the uncertainties of system parameters and load torque. First, the ETSO is designed to estimate the two extended states, namely control input gain and lumped disturbance. The control input gain includes moment of inertia and stator flux linkage. Then, a speed controller with online adjustment for the control input gain is designed by using the estimates obtained from the ETSO to improve the speed tracking performance of PMSM. The convergence of the ETSO and the speed controller is analyzed by Lyapunov theory. Finally, simulations and experiments are carried out to verify the effectiveness of the proposed control scheme. The results demonstrate that the control input gain and the lumped disturbance are effectively estimated, and the speed tracking performance of the PMSM with the uncertainties of moment of inertia, stator flux linkage, and load torque is significantly improved.

In high-precision servo systems, the vibration and noise generated by the periodic disturbances have a significant impact on the accuracy and smoothness of permanent magnet synchronous motors. The usually high frequency of the periodic disturbances and the presence of unknown disturbances in the control system make the estimation and compensation of the periodic disturbances challenging. For this reason, a multielement disturbance observer (MEDOB) is proposed in this article. The rotor position is averaged into a number of intervals, and the corresponding periodic disturbances for each interval can be estimated independently by the MEDOB. As the number of intervals increases, the estimates will approximate the actual periodic disturbances. Separate estimation of periodic and nonperiodic disturbances is realized with the help of the MEDOB. In addition, a single-loop sliding mode speed controller is designed with the disturbance estimates. Lyapunov theory is used to analyze the convergence of the proposed method. Simulations and experiments are implemented, and the results show that the proposed method is competitive in terms of accuracy, response, and robustness.

To enhance the robustness of two-phase buck converter under load variations and uncertain system parameters, a novel voltage regulation strategy is proposed. The voltage regulation strategy consists of a three-switching surface nonsingular terminal sliding mode controller (TSSNTSMC) to regulate the output voltage and a current controller to equalize the inductor currents. Regarding the TSSNTSMC, the phase plot is divided into four regions by three switching surfaces. Depending on the region in which the sliding variable is located, the TSSNTSMC can directly determine the quantity of high-side switches to be turned on. This approach is beneficial in reducing the internal disturbances. The convergence of the designed controllers is analyzed by the Lyapunov theory. The TSSNTSMC is not affected by the current controller in terms of convergence. Simulation and experimental results show that the proposed strategy provides favorable response and disturbance rejection performance under load variations and uncertain system parameters.

The existing methods of alternating current (ac) copper loss primarily focus on analyzing the influence of either frequency or temperature on loss. The variation of copper loss under the coupled effects of temperature and frequency has not been studied. To address this issue, a unified model of ac copper loss considering temperature and frequency is proposed. The transition phenomenon of ac copper loss is discovered during the derivation process of the unified model. As the temperature increases, the direct current (dc) copper loss rises, while the skin effect is suppressed. The combined influence of these factors leads to a nonlinear transition phenomenon in ac copper loss. Take a single-phase transformer as an example, a 3-D finite-element model (3-D FEM) is established to better simulate the actual winding paths. Subsequently, an experimental platform is constructed, and an experiment is conducted for both square and circular windings. Then, the accuracy of the unified model is validated through 3-D FEM and experimental methods, with an error of less than 10.6%. Meanwhile, the transition phenomenon in ac copper loss is observed during both the finite-element and experimental methods. The unified model provides a novel approach for power evaluation of high-density electromagnetic components. And the transition phenomenon of ac copper loss offers new ideas for selecting optimal operating points.