Estimating the Characteristic Curve of a Directional Control Valve in a Combined Multibody and Hydraulic System Using an Augmented Discrete Extended Kalman Filter
Abstract
:1. Introduction
2. Parameter Estimation Methodology
2.1. Multibody Dynamic Formulations
2.1.1. Double-Step Semi-Recursive Formulation
2.1.2. Hydraulic Lumped Fluid Theory
2.1.3. Monolithic Approach: Coupling MBS and Hydraulic Dynamic Systems
2.2. Estimation Algorithm: ADEKF with a Curve-Fitting Method
Covariance Matrices of Process and Measurement Noises
3. Case Example: Hydraulically Actuated System
3.1. Dynamic Model of the System
3.1.1. Real and Estimation Models
3.1.2. Sensor Measurements
3.2. Parameter Estimation Algorithm
4. Results and Discussion
4.1. Estimating the Characteristic Curve of the Valve
4.2. Convergence of the Vector Data Control Points
4.3. Accuracy Requirements of State Estimations
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. The Estimation of the Curve Using Second-Order (Linear) B-Spline Interpolation
Appendix B. Estimation of the Pressure Flow Coefficient and the Flow Gain
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Parameter | Symbol | Value |
---|---|---|
Pump flow rate | 0.001 | |
Tank pressure | 0.1 MPa | |
Volume of the hose p | 3.42 | |
Volume of the hose 1 | 3.42 | |
Volume of the hose 2 | 3.42 | |
Oil density | 869 / | |
Hydraulic parameter | 1600 MPa | |
Hydraulic parameter | 0.5 | |
Area of the piston | 2 | |
Area of the piston-rod | 1.8 | |
Length of the cylinder/piston | l | |
Area of pressure relief valve | 2.24 | |
Area of directional control valve | 1.96 | |
Coulomb friction force | 210 N | |
Static friction force | 830 N | |
Stribeck velocity | 1.25 / | |
Coefficient of viscous friction | 330 / | |
Discharge coefficient | 0.5 | |
Area of throttle | 2.24 |
Errors | Symbol | Real Model | Estimation Model | Simulation Model |
---|---|---|---|---|
State | ||||
State | 7.6 MPa | 5.6 MPa | 5.6 MPa | |
State | 1 MPa | 2 MPa | 2 MPa | |
Parameter | Non-linear | Linear | Linear | |
Parameter | Non-linear | Linear | Linear | |
Parameter | Non-linear | Linear | Linear | |
Parameter | Non-linear | Linear | Linear | |
Parameter | 0.5 | 0.4 | 0.4 | |
Parameter | 1600 MPa | 1500 MPa | 1500 MPa |
Control Points | Control Point Vector | RMSE | RMSE |
---|---|---|---|
Three points | |||
Four points | |||
Five points | |||
Six points |
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Khadim, Q.; Kiani-Oshtorjani, M.; Jaiswal, S.; Matikainen, M.K.; Mikkola, A. Estimating the Characteristic Curve of a Directional Control Valve in a Combined Multibody and Hydraulic System Using an Augmented Discrete Extended Kalman Filter. Sensors 2021, 21, 5029. https://doi.org/10.3390/s21155029
Khadim Q, Kiani-Oshtorjani M, Jaiswal S, Matikainen MK, Mikkola A. Estimating the Characteristic Curve of a Directional Control Valve in a Combined Multibody and Hydraulic System Using an Augmented Discrete Extended Kalman Filter. Sensors. 2021; 21(15):5029. https://doi.org/10.3390/s21155029
Chicago/Turabian StyleKhadim, Qasim, Mehran Kiani-Oshtorjani, Suraj Jaiswal, Marko K. Matikainen, and Aki Mikkola. 2021. "Estimating the Characteristic Curve of a Directional Control Valve in a Combined Multibody and Hydraulic System Using an Augmented Discrete Extended Kalman Filter" Sensors 21, no. 15: 5029. https://doi.org/10.3390/s21155029