Research on Three-Closed-Loop ADRC Position Compensation Strategy Based on Winch-Type Heave Compensation System with a Secondary Component
Abstract
:1. Introduction
2. Dynamic Model of Heave Compensation System
2.1. Mathematical Modeling
2.1.1. The Model of the Electro-Hydraulic Servo Valve
2.1.2. Variable Control Oil Cylinder
2.1.3. Secondary Component Displacement
2.1.4. Cable-Winding System
2.2. Simulation Model and Parameter Settings
- The system operated in an ideal constant-temperature and constant-pressure hydraulic environment. The hydraulic components and pipelines were sufficiently rigid, and there was no pressure loss along the pipeline.
- The hydraulic oil was considered to be incompressible, with a constant density and viscosity.
- Friction forces at various locations, such as the cable and valve spool, were assumed to be constant and did not vary with operating conditions and temperature changes.
3. Three-Closed-Loop ADRC Position Control Strategy Design
3.1. ADRC Controller Design and Composition
3.1.1. The Tracking Differentiator (TD)
3.1.2. Extended State Observer (ESO)
3.1.3. Nonlinear States Error Feedback (NLSEF)
3.1.4. Disturbance Estimation Compensation
3.1.5. Stability Analysis
3.2. Controller Design and Parameter Setting
4. Simulation Experiment Research and Analysis
4.1. Step Disturbance Response Analysis
4.2. Sine Disturbance Response Analysis
4.3. A Certain Sea Area in China Ship Heave Motion Disturbance Response Analysis
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Acronyms | Definition |
---|---|
ADRC | Active disturbance rejection control |
PID | Proportional integral derivative |
AMESim | Software name |
A4VSO, A4VSG | Rexroth product model |
HNC | Rexroth controller |
AHC | Active heave compensation system |
SMC | Sliding mode control |
MPC | Model predictive control |
IDA-PBC | Interconnection and damping assignment productivity based control |
ABFTSMC | Adaptive barrier fast terminal sliding mode control |
UAVs | Unmanned aerial vehicles |
FTSMC | Fast terminal sliding mode control |
NMPC | Nonlinear model predictive control |
TD | Tracking differentiator |
ESO | Extended state observer |
NLSEF | Nonlinear states error feedback |
MRU | Motion reference unit |
Symbol | Definition | Symbol | Definition |
---|---|---|---|
Qsf | Output flow | θer | Main shaft rotation angle of the secondary component |
I | Coil input current | Ber | Viscous damping coefficient |
Kv | Flow gain | ML | External load torque |
s | Laplace operator | xl | Displacement of the load |
ωn | Natural frequency | xl0 | Initial position of the load |
ξn | Damping ratio | xh | Displacement due to the heave of the ship |
q | Flow entering the high-pressure chamber | ijt | Reduction ratio of the gearbox |
Ag | Effective piston area inside | R | Radius of the winch drum |
xg | Piston displacement | Δl | Elongation of the cable |
Ct | Total leakage coefficient | Δld | Dynamic elongation of the cable |
p | Pressure difference | Δls | Static elongation of the cable |
Vt | Total volume | meq | Equivalent mass of the load and cable |
βe | Volumetric modulus of oil | kl | Cable’s elastic coefficient |
Ci | Internal leakage coefficient | Cl | Cable’s damping coefficient |
Ce | External leakage coefficient | r | Velocity factor |
mg | Total mass of the moving components | h0 | Filtering factor |
Bg | Viscous damping coefficient | h | Integration step size |
kg | Spring stiffness | fhan | Maximum speed control function |
Ffg | Resistance force acting | β01, β02, β03 | Observer gain parameters |
Der | Secondary component displacement | b0 | Compensation factor |
Dermax | Secondary component maximum displacement | ζ | Heave compensation root-mean-square error compensation rate |
xgmax | Maximum displacement of the piston | Δ | Load position error in heave compensation |
ps | Constant pressure of the oil supply | T | Statistical duration |
Jer | Rotational inertia converted to the output shaft | x | Amplitude of the disturbance |
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Main Components | Sub-Model | Functional Description |
---|---|---|
Motor | PM000 | Standard electric motor |
Pump | PP01 | Constant-pressure variable pump |
Servo valve | SV00 | Three-position four-way directional valve |
Relief valve | RV012 | Safety valve |
Accumulator | HA000 | Diaphragm-type accumulator |
Variable cylinder spring chamber | BAP016 | Variable cylinder reset function chamber |
Variable cylinder piston chamber | BAF01 | Variable cylinder control function chamber |
Mass block | MECMAS21/MAS001 | Variable cylinder mass property simulation |
Hydraulic motor | HYDVPM01 | Bidirectional variable hydraulic motor |
Winch | WINCH01 | Ideal winch |
Cable or wire rope | MECROPE0/REND001 | Rigid rope |
Parameter Name | Value | Unit |
---|---|---|
Hydraulic motor displacement Der | 40 | mL/r |
Maximum motor speed nmdmax | 664 | r/min |
Gearbox reduction ratio ijt | 26.4 | — |
Winch drum radius R | 190 | mm |
System pressure ps | 18 | MPa |
Accumulator volume V | 20 | L |
Parameters | h | rTD | rNLSEF | β01 | β02 | β03 | b0 |
---|---|---|---|---|---|---|---|
Inner loop ADRC | 0.001 | 10000 | |||||
Middle loop ADRC | 0.001 | 900 | 10000 | 780 | |||
Outermost loop ADRC | 0.001 | 900 | 10000 | 7500 |
Parameters | Rise Time (s) | Peak Time (s) | Maximum Overshoot | Settling Time (s) |
---|---|---|---|---|
No-overshoot PID | 1.3445 | 2.3400 | 0 | 1.7077 |
Overshoot PID | 1.3347 | 1.8900 | 1.18% | 1.6563 |
ADRC | 1.0257 | 1.5700 | 0 | 1.3532 |
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Li, S.; Wu, Q.; Liu, Y.; Qiao, L.; Guo, Z.; Yan, F. Research on Three-Closed-Loop ADRC Position Compensation Strategy Based on Winch-Type Heave Compensation System with a Secondary Component. J. Mar. Sci. Eng. 2024, 12, 346. https://doi.org/10.3390/jmse12020346
Li S, Wu Q, Liu Y, Qiao L, Guo Z, Yan F. Research on Three-Closed-Loop ADRC Position Compensation Strategy Based on Winch-Type Heave Compensation System with a Secondary Component. Journal of Marine Science and Engineering. 2024; 12(2):346. https://doi.org/10.3390/jmse12020346
Chicago/Turabian StyleLi, Shizhen, Qinfeng Wu, Yufeng Liu, Longfei Qiao, Zimeng Guo, and Fei Yan. 2024. "Research on Three-Closed-Loop ADRC Position Compensation Strategy Based on Winch-Type Heave Compensation System with a Secondary Component" Journal of Marine Science and Engineering 12, no. 2: 346. https://doi.org/10.3390/jmse12020346