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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