Extended Sliding Mode Observer-Based Output Feedback Control for Motion Tracking of Electro-Hydrostatic Actuators
Abstract
:1. Introduction
- (1)
- For the first time, an ESMO based on a system model was constructed to estimate immeasurable system states, i.e., angular velocity and load pressure, and lumped matched disturbance in the pressure dynamics caused by parameter deviations and modeling errors.
- (2)
- Based on the designed ESMO, a novel output feedback robust control scheme using the backstepping control framework and dynamic surface control technique is synthesized for the motion-tracking problem of the studied EHA.
- (3)
- The stability of the ESMO and the overall closed-loop system is theoretically verified by the Lyapunov theory. Experiments on the real test bench are conducted to illustrate the practicability and advantage of the suggested controller in comparison with some reference methods under various working scenarios.
2. System Modeling and Problem Statement
3. Observer-Based Output Feedback Control Design
3.1. Extended Sliding Mode Observer
3.2. Observer-Based Control Design
3.3. Closed-Loop Stability Analysis
4. Experiment Validation
4.1. Experiment Setup
- (1)
- ESMOBC: The proposed controller, whose control gains are chosen as , , . The time constants of the low-pass filters are and the observer bandwidth is .
- (2)
- PID: Proportional-derivative-integral controller (PID), whose controller gains are ultimately selected as , , and . The larger gains would cause the closed-loop system to be unstable due to measurement noise and unmodeled dynamics.
- (3)
- PIDVFF [6]: Velocity feed-forward-based proportional-derivative-integral controller (PIDVFF), whose PID gains are chosen as the same as the above PID controller, and the velocity feed-forward coefficient is selected as .
- (4)
- STW [41]: Super-twisting-based controller, whose structure is designed as
- (1)
- Maximal tracking error is defined as
- (2)
- Average tracking error is computed as
- (3)
- The standard deviation of the tracking errors is formulated as
4.2. Experiment Results
4.2.1. Slow-Motion Reference Trajectory under Light-Load Condition
4.2.2. Slow-Motion Reference Trajectory under Heavy-Load Condition
4.2.3. Fast-Motion Reference Trajectory under Light-Load Condition
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
BSC | Backstepping Control |
DSC | Dynamic Surface Control |
EHS | Electro-hydraulic System |
EHA | Electro-Hydrostatic Actuator |
PID | Proportional-Integral-Derivative |
PIDVFF | Velocity FeedForward-based PID |
SMC | Sliding Mode Control |
STA | Super-Twisting Algorithm |
DOB | Disturbance Observer |
ESO | Extended State Observer |
SMO | Sliding Mode Observer |
ESMO | Extended Sliding Mode Observer |
UUB | Ultimately Uniformly Bounded |
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Parameter | Notation | Value | SI Unit |
---|---|---|---|
Moment of inertia of the actuator | |||
Hydraulic actuator displacement | |||
Viscous friction coefficient of the actuator | 10 | ||
Coulomb friction coefficient of the actuator | 10 | ||
Total leakage coefficient | |||
Effective bulk modulus of the hydraulic oil | |||
Hydraulic pump displacement | |||
Initial control volume of the forward chamber | |||
Initial control volume of the reverse chamber |
Controller | |||
---|---|---|---|
PID Controller | |||
PIDVFF Controller | |||
STW Controller | |||
ESMOBC Controller |
Controller | |||
---|---|---|---|
PID Controller | |||
PIDVFF Controller | |||
STW Controller | |||
ESMOBC Controller |
Controller | |||
---|---|---|---|
PID Controller | |||
PIDVFF Controller | |||
STW Controller | |||
ESMOBC Controller |
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Nguyen, M.H.; Ahn, K.K. Extended Sliding Mode Observer-Based Output Feedback Control for Motion Tracking of Electro-Hydrostatic Actuators. Mathematics 2023, 11, 4324. https://doi.org/10.3390/math11204324
Nguyen MH, Ahn KK. Extended Sliding Mode Observer-Based Output Feedback Control for Motion Tracking of Electro-Hydrostatic Actuators. Mathematics. 2023; 11(20):4324. https://doi.org/10.3390/math11204324
Chicago/Turabian StyleNguyen, Manh Hung, and Kyoung Kwan Ahn. 2023. "Extended Sliding Mode Observer-Based Output Feedback Control for Motion Tracking of Electro-Hydrostatic Actuators" Mathematics 11, no. 20: 4324. https://doi.org/10.3390/math11204324
APA StyleNguyen, M. H., & Ahn, K. K. (2023). Extended Sliding Mode Observer-Based Output Feedback Control for Motion Tracking of Electro-Hydrostatic Actuators. Mathematics, 11(20), 4324. https://doi.org/10.3390/math11204324