The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain multibody systems with the transfer matrix method for multibody systems (MSTMM). However, for linear tree multibody systems, the recursive relations of the Riccati transfer matrices, especially those for elements with multiple input ends, have not been established yet. Thus, an RTMM formulism for general linear tree multibody systems is formulated based on the transformation of transfer equations and geometrical equations of such elements. The steady-state response under harmonic excitation of a linear tree multibody system is taken as an example and obtained by the proposed method. Comparison with the finite-element method (FEM) validates the proposed method and a numerical example demonstrates that the proposed method has a better numerical stability than the normal MSTMM.
In order to achieve a large displacement output from a piezoelectric actuator, we realized the piezoelectric stack actuator (PSA) by mechanically layering/stacking multi-chip piezoelectric wafers in a series and electrically connecting the electrodes in parallel. In this paper, in order to accurately model the hysteresis and the dynamic characteristics of a PSA, the transfer matrix method for multibody systems (MSTMM) was adopted to describe the dynamic characteristics, and the Bouc-Wen hysteresis operator was used to represent the hysteresis. The vibration characteristics of a PSA and a piezo-actuated positioning mechanism (PPM) are derived and analyzed by the MSTMM; then, the dynamic responses of the PSA and the PPM are calculated. The experimental results show that the new method can accurately portray the hysteresis and the dynamic characteristics of a PSA and a PPM. On one hand, if we use this method to model the dynamic response of the PSA and the PPM, the PSA can be considered as a flexible body, as opposed to a mass-spring-damper system, which is in better agreement with the actual condition. On the other hand, the global dynamics equation is not needed for the study of system dynamics, and the dynamics equation has a small-sized matrix and a higher computational speed. Therefore, this method gives a broad range of possibilities for model-based controller design.
The dynamic test precision of the strapdown inertial measurement unit (SIMU) is the basis of estimating accurate motion of various vehicles such as warships, airplanes, spacecrafts, and missiles. So, it is paid great attention in the above fields to increase the dynamic precision of SIMU by decreasing the vibration of the vehicles acting on the SIMU. In this paper, based on the transfer matrix method for multibody system (MSTMM), the multibody system dynamics model of laser gyro strapdown inertial measurement unit (LGSIMU) is developed; the overall transfer equation of the system is deduced automatically. The computational results show that the frequency response function of the LGSIMU got by the proposed method and Newton-Euler method have good agreements. Further, the vibration reduction performance and the attitude error responses under harmonic and random excitations are analyzed. The proposed method provides a powerful technique for studying dynamics of LGSIMU because of using MSTMM and its following features: without the global dynamics equations of the system, high programming, low order of system matrix, and high computational speed.
This paper outlines an optical beam steering system built using a two-axis fast steering mirror (FSM) with piezoelectric stack actuators to maintain precise pointing control. A novel mathematical model of the FSM is put forward by using a transfer matrix method of a multibody system to describe the dynamics characteristics and a hysteresis model to represent the hysteresis. Based on the proposed model, a model-based hybrid control is applied to force the output angle of the FSM to track the laser beam accurately thereafter. The experimental results are in accordance with the theoretical analysis. The results highlight significantly improved accuracy in the beam tracking control of the FSM.
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