Robust Backstepping Control with Active Damping Strategy for Separating-Metering Electro-Hydraulic System
Abstract
:Featured Application
Abstract
1. Introduction
2. Problem Statement and Active Damping Strategy Analysis
- The viscous damping coefficient and the leakages of the cylinder are ignored.
- The friction force of piston in the cylinder is negligible.
- The rod is extending.
3. Modeling of SMEHS
3.1. Position Servo System of SMEHS
3.2. Pressure Servo System of SMEHS
4. Controller Design
4.1. Nonlinear Disturbance Observer
4.2. Tracking Differentiator
4.3. Backstepping Controller Design
4.4. Stability Analysis of Nonlinear Disturbance Observer
4.5. Stability Analysis of BSTDNDO
5. Experiment and Discussion
5.1. Experiment Platform
5.2. Displacement Tracking Experiments
5.3. Active Damping Strategy Experiments
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
, | area of piston |
ADRC | active disturbance rejection control |
ADS | active damping strategy |
viscous damping coefficient | |
BSTDNDO | backstepping controller with TD and NDO |
, , , , , , | internal variable |
, , , | internal variable |
disturbance | |
, , , , | tracking error |
viscous damping force | |
load force | |
force exerting on the piston of the cylinder in rod chamber | |
force exerting on the piston of the cylinder in piston chamber | |
internal variable | |
, , , , | gain of controller |
pressure-acceleration coefficient | |
, | flow-pressure coefficient |
, | flow coefficient |
, | servo valve gain |
, | valve coefficient of the orifice |
gain of NDO | |
equivalent mass of piston and attached system | |
NDO | nonlinear disturbance observer |
pressure of piston chamber | |
pressure of rod chamber | |
pressure of oil tank | |
supply pressure | |
PID | proportional–integral–derivative |
flow rate of piston chamber | |
flow rate of rod chamber | |
gain of tracking differentiator | |
Laplace Operator | |
signum function | |
SMC | sliding mode control |
SMEHS | separating-metering electro-hydraulic system |
TD | tracking differentiator |
, , | input signal |
, | volume of hydraulic chamber |
, | initial volume of chamber |
, , , , , | Lyapunov function |
desired displacement of the piston | |
input of tracking differentiator | |
denotes | |
piston displacement | |
, | displacement of spool |
, | state variables |
internal variable | |
denote the estimate value of | |
denote the estimation error of | |
, | pressure drops across the orifice |
, , | uncertain item |
parameter of tracking differentiator | |
, , , | virtual parameters |
, , | disturbance |
, | natural frequency |
, | damping ratio |
bulk modulus | |
internal variable | |
, , | gain of observer |
, , | internal variable |
internal variable |
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Item | Value | Unit |
---|---|---|
Pump displacement (1.1 and 1.2) | 40 | mL/r |
Motor speed | 1500 | rpm |
Servo valve rated flow (3.1) | 63 | L/min |
Servo valve rated flow (3.2) | 38 | L/min |
Piston diameter (5 and 8) | 63 | mm |
Rod diameter (5 and 8) | 36 | mm |
Weight of moving part | 100 | Kg |
Stroke (5 and 8) | 280 | mm |
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Lin, S.; An, G.; Huang, J.; Guo, Y. Robust Backstepping Control with Active Damping Strategy for Separating-Metering Electro-Hydraulic System. Appl. Sci. 2020, 10, 277. https://doi.org/10.3390/app10010277
Lin S, An G, Huang J, Guo Y. Robust Backstepping Control with Active Damping Strategy for Separating-Metering Electro-Hydraulic System. Applied Sciences. 2020; 10(1):277. https://doi.org/10.3390/app10010277
Chicago/Turabian StyleLin, Suhong, Gaocheng An, Jiahai Huang, and Yuhang Guo. 2020. "Robust Backstepping Control with Active Damping Strategy for Separating-Metering Electro-Hydraulic System" Applied Sciences 10, no. 1: 277. https://doi.org/10.3390/app10010277
APA StyleLin, S., An, G., Huang, J., & Guo, Y. (2020). Robust Backstepping Control with Active Damping Strategy for Separating-Metering Electro-Hydraulic System. Applied Sciences, 10(1), 277. https://doi.org/10.3390/app10010277