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This paper aims to design a tip state estimation method for a hybrid-structured flexible manipulator (HSFM) with one rotating joint and one telescopic joint in the vertical plane.

The HSFM model is decomposed into a static deflection model and a vibration model. The sliding discrete Fourier transform (SDFT) is used to filter the high frequency noise and obtain main vibration components to represent the vibration model. Then, a novel fuzzy logic adaptive Kalman filter (FLAKF) is designed to estimate the state of a vibrational equilibrium position. The complete tip state of the HSFM is obtained by superimposing the FLAKF filter results with the SDFT vibration analysis results.

Both the simulation results and physical experimental results verify the effectiveness of the proposed tip state estimation method. The vibration analysis based on SDFT is used to represent the vibration model and reduce the computational complexity in the process of solving differential equation. The proposed FLAKF can effectively increase the stability and robustness of the estimator.

In this paper, the tip state estimation problem of the HSFM in vertical plane is first proposed. The effect of gravity on the HSFM is considered by the static deflection model. A precise tip state estimator is designed by a closed loop SDFT and a novel FLAKF, which can provide an accurate feedback for the vibration control controller and make an accurate evaluation of the control effect.