The conventional approach to reducing control signal chattering in sliding mode control is to use the boundary layer design. However, when there is high-level measurement noise, the boundary layer design becomes ineffective in chattering reduction. This paper, therefore, proposes a new design for chattering reduction by low-pass filtering the control signal. The new design is non-trivial since it requires estimation of the sliding variable via a disturbance estimator. The new sliding mode control has the same performance as the boundary layer design in noise-free environments, and outperforms the boundary layer design in noisy environments.

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When there are external disturbances acting on the system, the conventional Luenberger observer design for state estimation usually results in a biased state estimate. This paper presents a robust state and disturbance observer design that gives both accurate state and disturbance estimates in the face of large disturbances. The proposed robust observer is structurally different from the conventional one in the sense that a disturbance estimation term is included in the observer equation. With this disturbance estimation term, the robust observer design problem is skillfully transformed into a disturbance rejection control problem. We then can utilize the standard H ∞ control design tools to optimize the robust observer between the disturbance rejection ability and noise immune ability. An important advantage of the proposed robust observer is that it applies to both minimum-phase systems and non-minimum phase systems.

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