In this paper, a frequency-shifting-based (FSB) algebraic approach to the extended state observer (ESO) design is proposed. The proposed algebraic approach provides almost instantaneous convergence toward the exact values of the system states and disturbances. The main benefit of the proposed approach is the elimination of the peaking phenomenon, which is inevitable in the case of the conventional observer design. In comparison with the linear ESO, the proposed algebraic ESO is less sensitive to the choice of the observer bandwidth, and it is more robust to the measurement noise. The simulation and experimental results illustrate the efficiency of the proposed algebraic approach in comparison with the linear ESO.

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