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Transmission characteristics analysis and disturbance compensation control strategy for two-inertia system with a flexible link

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Abstract

In the process of rotation, a two-inertia system with a flexible link (TISFL) will have the phenomenon of output speed fluctuation under the influence of flexible factors and external disturbances. The output speed fluctuation will excite the vibration of the TISFL and reduce the tracking error of the flexible link. To suppress output speed fluctuation, the proportional-integral control method containing the disturbance observer (DOB) is proposed. First, the mathematical equations of the TISFL are obtained by the flexible beams’ vibration differential equations. Next, the transmission characteristics of the TISFL and the effect of nonlinear terms on modeling accuracy are analyzed according to dynamic equations. Then, the filter parameters in the DOB are determined using the robust stability theorem. The rotation accuracy of the TISFL is improved by compensating for disturbances torque by the DOB. Finally, simulation and control experiments of the TISFL show that the proposed control method can weaken output speed fluctuation.

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Acknowledgements

The authors greatly appreciate the financial support from the Liaoning Province Applied Basic Research Program Project (2023JH2/101300159), the National Natural Science Foundation of China (Grant No. 52275090) and the Natural Science Foundation of Ningxia Province (No.2020AAC03279).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    Dongyang Shang, Xiaopeng Li & Fanjie Li

  2. Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China

    Meng Yin

Authors
  1. Dongyang Shang
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  2. Xiaopeng Li
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  3. Meng Yin
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  4. Fanjie Li
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Correspondence to Dongyang Shang.

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Technical Editor: Adriano Almeida Gonçalves Siqueira.

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Appendix

Appendix

The calculation process of the nominal transfer function and the actual transfer in numerical simulation is shown below.

In Table 2, the flexible link length is set as 0.8 m. This paper assumes that the nominal length of the flexible link is 0.8 m. Under this nominal length, the transfer function obtained according to Eq. (21) is called the nominal transfer function, and its specific value is shown in Eq. (44).

$$G_{{n_{1} }} \left( s \right) = \frac{{{ 0}{\text{.007074}}s^{4} + 5147s^{2} + 6.038 \times {10}^{6} }}{{2.829 \times {10}^{ - 4} {\text{s}}^{5} { + 196}s^{3} + 1.696 \times {10}^{6} s}}$$
(44)

However, due to the measurement error, the actual length of the flexible link is not 0.8 m. This leads to the modeling error between the actual model and the nominal model. In order to illustrate the robustness of this model in the simulation process, this paper assumes that the actual length of the flexible link is 0.85 m. Under the actual length, the transfer function obtained according to Eq. (21) is called the actual transfer function, and its specific expression is shown in Eq. (45).

$$G_{{p_{1} }} \left( s \right) = \frac{{{ 0}{\text{.006266}}s^{4} + 5450s^{2} + 7.242 \times {10}^{6} }}{{2.506 \times {10}^{ - 4} {\text{s}}^{5} { + 207}{\text{.9}}s^{3} + 1.835 \times {10}^{6} s}}$$
(45)

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Shang, D., Li, X., Yin, M. et al. Transmission characteristics analysis and disturbance compensation control strategy for two-inertia system with a flexible link. J Braz. Soc. Mech. Sci. Eng. 45, 270 (2023). https://doi.org/10.1007/s40430-023-04169-y

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