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In practical control systems differences between nominal and real systems arise from internal uncertainties and/or external disturbances. This paper presents a model-based low-order disturbance observer for a sinusoidal disturbance with unknown constant offset. By using the disturbance model of a biased harmonic signal, the proposed method can successfully estimate the biased sinusoidal disturbance with unknown amplitude and phase but known frequency. At the first stage of the observer design, a model-based disturbance observer is designed when all the system states are measurable. Next, a sufficient condition is presented for the proposed observer to estimate the sinusoidal disturbance with a minimal-order additional dynamics using only output measurement. Comparative computer simulations are performed to test the performance of the proposed method. The simulation results show the enhanced performance of the proposed disturbance observer.

Design of a Model-Based Low-Order Disturbance Observer to Estimate a Sinusoidal Disturbance with Unknown Constant Offset