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An estimation method based on sliding discrete Fourier transform (SDFT) integrated with phase-locked loop is introduced for vibration mode estimation of single-link flexible manipulator (SLFM). Based on Euler-Lagrangian state space model and first vibration mode frequency, SDFT PLL is designed to estimate first vibration mode and harmonics that appear in tip deflection. Instantaneous change in tip deflection due to payload conditions is tracked by adaptive sampling frequency control. State-space model, estimated amplitudes and frequencies of tip deflection including harmonics are validated through experiments. Furthermore, experimental investigation on SLFM demonstrates the effectiveness of online vibration mode estimation method in presence of noise and offset. Index Terms-Phase-locked loop (PLL), single-link flexible manipulator (SLFM), sliding discrete Fourier transform, vibration mode estimation.

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A review of vibration signal estimation techniques employed in ultrasonic vibration measurement systems is presented. The review focuses on the Doppler signal extraction methods including the theory and analysis pertaining to the background of ultrasonic vibration measurement techniques. The phase modulated received signal in the vibration measurement system involves constant phase shift because of ultrasonic path length, phase shift introduced by Doppler effect because of vibrating object and the parametric phase shift caused by interaction of high frequency ultrasonic wave and low pressure developed by vibrating object. Among the three phase shifts, the Doppler phase shift contains the vibrating signal information and the extraction of Doppler signal helps in knowing the velocity of the vibrating object, amplitude and phase of the vibration. Various techniques of Doppler phase shift retrieval are categorised based on the modulation index estimation procedures from the received ultrasonic signal. An analysis is made based on the information retrieval methods for estimation of vibration signal parameters, range of the vibration amplitude, frequency and the preferable carrier frequency for transmission. Further, the analysis also presents various applications in which ultrasonic vibration measurements system are employed successfully.