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.

This paper aims to present secure communication based on master and slave Lorenz chaotic systems. To apply a form of the linear synchronization control method, the mathematical models of master and slave systems were reformed into Takagi-Sugeno (T-S) fuzzy systems. First, the Lorenz chaotic system was completely changed to the form of the T-S fuzzy model with two sublinear systems and two boundary fuzzy membership functions. Second, a newly adaptive disturbance observer (ADOB) was proposed with a high convergent speed for the synchronization system, which was based on the basic nonlinear disturbance observer. Third, adaptive sliding-mode control (ASMC) has been constructed to synchronize the master and slave systems of a secure communication system. The stability of the proposed control algorithms was shown by solving the Lyapunov condition with the support of Young's inequality. The synchronization of two nonidentical chaotic Lorenz systems was utilized to encrypt and decrypt the data. Transmitted and decrypted signals are used to show that the proposed algorithms are adequate for the secure communication system. To confirm the originality and power of the proposed algorithms, secure communication between two computers was implemented perfectly through an internet router and electronic circuit communication scenarios.

This article presents a synchronization control method based on poles’ placement, disturbances, and uncertainty estimation (DUE) for a pair of Takagi-Sugeno fuzzy systems. First, a 3-D chaotic system was completely converted into a Takagi-Sugeno (T-S) fuzzy model by applying the nonlinearity sector method, which consists of if-then rules and sub-linear systems. Second, two identical T-S fuzzy systems with different initial conditions were synchronized by applying the linear matrix inequality (LMI) to place the eigenvalues of the state error equations in the stable region. Third, the sum of the time-varying disturbances and uncertainties of two nonidentical T-S fuzzy systems were deleted by a disturbance and uncertainty estimation. The given output signals confirmed that the proposed method is suitable and ideal for synchronizing T-S fuzzy systems. The ideas of control theory were implemented by using two experimental scenarios in MATLAB Simulink for two computers connected via an internet router and an electronics circuit’s communication.

This study provides a new development regarding uncertainty and disturbance estimation (UDE) based on fixed-time sliding mode control (FTSMC) for the secure communication of electronic circuits in a chaos-based system. Takagi-Sugeno (T-S) fuzzy systems were used to remodel chaotic systems with the aim of softening the control design for the synchronization of the chaos-based system. The master and slave systems of the secure communication system were maintained in chaotic formats. The originality of the proposed uncertainty and disturbance estimator is a condition associated with the first derivative of these values being free. The stability of the system was proven by using the Lyapunov condition. The states of master and slave systems were used for encryption and decryption, respectively. Finally, the correction of the proposed control theories was verified by MATLAB simulations, the simulation of the electronic circuits in OrCAD capture software, and experiments involving electronic circuit communication.

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 $\omega -$ 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 steady-states.

This paper proposes a new disturbance observer concept based on the information of the estimated and measured signals for a micro-electro-mechanical system. First, the sliding-mode observer based on the linear matrix inequality was designed to estimate the states of a micro-electro-mechanical system gyroscope. Second, a new disturbance observer was proposed for estimating perturbations of the T-S fuzzy micro-electro-mechanical system gyroscope. Third, the double phase’s fixed-time sliding-mode control was designed to control the positions and velocities of the MEMS system. The proposed disturbance observer input signals were taken into account from the measured and estimated signals. Two cases of high magnitudes and high frequencies disturbances were used to test the power of the proposed disturbance observer. Fourth, the Lyapunov condition was used to verify the corrections of the proposed controller and observer. Finally, the simulation by using MATLAB software was used to show the power of the proposed methods. The achievements of the small reaching-time, small tracking error, and stable steady-states under the vibration form outside of the system.