This paper presents the disturbance and uncertainty suppression by using the nonlinear disturbance observer and an extended state observer for a nonlinear active magnetic bearing system. Otherwise, the chattering free is assured by a fuzzy controller, where the fixed sliding mode surface boundary is regulated by fuzzy boundary layer. The stability of the system is guaranteed by Lyapunov condition. First, the nonlinear disturbance observer is presented to estimate the disturbance from outside of the system. Second, the system parameter variations are estimated by an extended state observer with the construction via the estimated disturbance value. Third, the proportional–integral–derivative sliding mode surface has been constructed due to the chattering values that appear from the high-frequency switching control values. Fourth, these chattering values are reduced by using a Mamdani fuzzy logic control. The proposed control methodology was given by the MATLAB simulation. The overshoot value that is equal to zero, narrow settling time, and the average distance tracking error value which is quite small are archived.

The authors acknowledge and thank the Ministry of Science and Technology of the Republic of China for their partial financial support of this study under Contract Number MOST 109-2622-E-992-008 -CC3.

This paper presents a robust control methodology based on a disturbance observer and an optimal states feedback for Takagi–Sugeno fuzzy system. Firstly, the nonlinear systems were solved by applying a sector nonlinearity method to get the inner linear subsystems and outer fuzzy membership functions, which guaranteed the conversion without any loss generality characteristics of the system. Secondly, an exponentially convergent disturbance observer was constructed to the system with an assumption that the system states are temporarily bounded. Thirdly, a states observer was built by poles placement of linear quadratic regulation optimization, which was used to place the system states error poles located on the stable region. Finally, simulation examples were given to figure out that the proposed controller is effective to control the Takagi–Sugeno fuzzy system. The obtained results are disturbance mostly rejected, state estimation errors are quite small, and the output signal precisely tracked input signal.

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The disturbance and uncertainty of the motor drive systems are very complicated terms. There is no exception for the slotless-self bearing motor (SSBM), where the perturbations of the bearing motor are mainly came from the outside as the wind affect, from inside as the thermal changing of the coils, and incorrect modeling of the winding processes. First, to delete these inversed terms, this paper proposes a new super-twisting disturbance observer (STDOB) to obtain the desired goal of the robust control design. The proposed disturbance observer was based on the information of measured and estimated states with the aim of softening the cost of the measurement. Second, to estimate the velocities and accelerations of the movements on x  and y  axes, the stability concept of homogeneous function-based was used to design the fixed-time state observers (FTSOBs) for these axes. The state of the rotational operation on   axis was estimated with a fixed-time state observer. Third, to control the positions and rotational speed, a variable boundary layer thickness (VBLT) fixed-time sliding mode control (FTSMC) was designed to force these positions and speed states converge to the desired goals. Finally, the stability of the proposed control algorithm was theoretically verified by using Lyapunov condition and simulation of MATLAB software. The obtained states were acceptably stable with small overshoots, small settling-times, and stable steadystates.INDEX TERMS Slotless-self bearing motor, super-twisting disturbance observer, variable boundary layer thickness, fixed-time sliding mode control.

This article presents the fast convergent stability of disturbance observer (DO) and sliding mode control (SMC) for a secure communication of fractional-order chaotic-based system. First, the fractional-order is remodeled into a Takagi-Sugeno fuzzy (TSF) system with the aim of softening the calculations of observer and controller design. Second, the master and slave systems (MSSs) were synchronized by the fast convergent stability (FCS) sliding mode control with double phases of the same stability condition. Third, the disturbance observer was newly proposed for estimating the disturbance and uncertainty of the secure communication system (SCS). Fourth, the stability of the proposed method was archived via the Lyapunov condition. The MATLAB simulation with support of FOMCON tool box was used to validate the correction of the proposed control theory. The obtained results such as small tracking errors and small settling-times were used to confirm that the proposed theory is good at rejecting perturbations and used control method is good at synchronizing the chaotic systems.

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