Speed Fluctuation Suppression Strategy of Servo System with Flexible Load Based on Pole Assignment Fuzzy Adaptive PID
Abstract
:1. Introduction
2. Modeling of a Servo System with Flexible Load
- The shear deformation and axial deformation are ignored, and only the deformation caused by transverse vibration is considered;
- The transverse deformation is small deformation;
- The beam is much longer than its cross-section size.
3. System Control Policy and Parameter Tuning
3.1. Design of Servo System Controller Considering Speed Loop
3.2. The Same Real-Part Pole Assignment Method Is Used to Set PI Parameters
3.3. Fuzzy Adaptive Control Strategy Combined with Pole Assignment
4. Numerical Simulation Analysis of the System
5. Conclusions
- (1)
- The dynamic modeling of the servo-driven flexible-load system established in this paper takes into account that the flexibility in the load will cause significant fluctuations in the system speed output, which will cause a large deviation in the system angle and displacement output. The unified dynamic model of the system is established.
- (2)
- The proposed fuzzy adaptive tuning PID control strategy combined with pole assignment is based on the traditional PID parameters. Firstly, the same real-part pole assignment method is used to adjust PI parameters, and then the fuzzy adaptive control strategy is applied to adjust the adjusted PID parameters to adjust the input variables of the system in real time. The simulation results show that the control strategy is stable and reliable when used to suppress system vibration.
- (3)
- By comparing the system output angle error and flexible load terminal deformation under three different working conditions, it can be seen that the system angle error and flexible load deformation increase with the increase of flexible load length. The control strategy proposed in this paper can reduce the system output angle error and the deformation of the flexible load by 10% on average. From the angle of error analysis, it is proved that the control strategy proposed in this paper can effectively reduce the speed fluctuation of the servo-driven flexible-load system and improve the working accuracy of the system.
Author Contributions
Funding
Conflicts of Interest
References
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The Characteristic Root | |||
The Values | 1.875 | 4.694 | 7.855 |
ec/e | PB | PM | PS | ZO | NS | NM | NB |
---|---|---|---|---|---|---|---|
PB | NB | NB | NM | NM | NM | ZO | ZO |
PM | PB | ZO | PM | PM | ZO | ZO | NS |
PS | PB | PM | PM | PM | PS | PS | NS |
ZO | NM | NM | NS | ZO | PS | PS | PM |
NS | NS | NS | ZO | PS | PS | PM | PM |
NM | NS | ZO | PS | PS | PM | PB | PB |
NB | ZO | ZO | PS | PM | PM | PB | PB |
ec/e | PB | PM | PS | ZO | NS | NM | NB |
---|---|---|---|---|---|---|---|
PB | PB | PB | PM | PS | PS | ZO | ZO |
PM | PB | PB | PM | PM | PS | ZO | ZO |
PS | PB | PM | PS | PS | ZO | NS | NM |
ZO | PM | PS | NS | PS | PS | ZO | ZO |
NS | PM | PS | PS | ZO | PS | ZO | ZO |
NM | ZO | ZO | NS | NS | NM | NB | NB |
NB | ZO | NS | NS | NM | NM | NB | NB |
ec/e | PB | PM | PS | ZO | NS | NM | NB |
---|---|---|---|---|---|---|---|
PB | PB | PS | PS | PS | PM | PB | PB |
PM | PB | PB | PS | PS | PM | PM | PB |
PS | ZO | ZO | NS | NS | ZO | ZO | ZO |
ZO | ZO | NS | NS | ZO | NS | NS | ZO |
NS | ZO | NS | NS | NS | NM | NM | ZO |
NM | ZO | NS | NS | NM | NB | NS | PS |
NB | PS | NM | NB | NB | NB | NS | PS |
Determinants | Condition 1 | Condition 2 | Condition 3 |
---|---|---|---|
Flexible load length l/m | 0.4 | 0.6 | 0.8 |
Flexural stiffness of a flexible load EI/Nm2 | 400 | 400 | 400 |
Line density of flexible load ρA/kg/m2 | 5 | 3.333 | 2.5 |
Modal coupling coefficient Fai/kg1/2m | 0.455 | 0.6826 | 0.9101 |
Inertia of a flexible load Jl/kgm2 | 0.1067 | 0.24 | 0.427 |
Modal frequencies of flexible loads ωi/rad/s | 196.5294 | 106.9771 | 69.4836 |
Characteristic roots of the mode function β1 | 1.875 | 1.875 | 1.875 |
Moment of inertia of motor Jm/kgm2 | 0.36 | 0.72 | 1.28 |
Torsional stiffness ks/Nm/rad | 405 | 405 | 405 |
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Liu, X.; Wang, Y.; Wang, M. Speed Fluctuation Suppression Strategy of Servo System with Flexible Load Based on Pole Assignment Fuzzy Adaptive PID. Mathematics 2022, 10, 3962. https://doi.org/10.3390/math10213962
Liu X, Wang Y, Wang M. Speed Fluctuation Suppression Strategy of Servo System with Flexible Load Based on Pole Assignment Fuzzy Adaptive PID. Mathematics. 2022; 10(21):3962. https://doi.org/10.3390/math10213962
Chicago/Turabian StyleLiu, Xiangchen, Yihan Wang, and Minghai Wang. 2022. "Speed Fluctuation Suppression Strategy of Servo System with Flexible Load Based on Pole Assignment Fuzzy Adaptive PID" Mathematics 10, no. 21: 3962. https://doi.org/10.3390/math10213962
APA StyleLiu, X., Wang, Y., & Wang, M. (2022). Speed Fluctuation Suppression Strategy of Servo System with Flexible Load Based on Pole Assignment Fuzzy Adaptive PID. Mathematics, 10(21), 3962. https://doi.org/10.3390/math10213962