Optimized Hierarchical Sliding Mode Control for the Swing-Up and Stabilization of a Rotary Inverted Pendulum
Abstract
:1. Introduction
- Our research introduces a pioneering hierarchical sliding mode controller that streamlines control efforts and outperforms dual-controller methods in both the swing-up and stability control of the rotary inverted pendulum.
- In addition, our paper leverages particle swarm optimization (PSO) to fine-tune the controller’s parameters, resulting in enhanced control performance for the rotary inverted pendulum.
2. HSMC and PSO: Theoretical Foundations and Integration Strategies
2.1. Hierarchical Sliding Mode Control
2.2. Particle Swarm Optimization
3. Application to Rotary Inverted Pendulum
4. Simulations Results
4.1. Parameter-Tuning Process
4.2. Simulation Cases and Evaluations
5. Conclusions and Discussion
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
HSMC | Hierarchical sliding mode control |
RIP | Rotary inverted pendulum |
PSO | Particle swarm optimization |
IAE | Integral absolute error |
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Parameter | Symbol and Value |
---|---|
Mass of pendulum (kg) | |
Mass of arm (kg) | |
Equivalent moment of inertia of pendulum arm and gears () | |
Rotor inertia of DC motor () | |
Pendulum rod’s length to center of mass (m) | |
Length of arm (m) | |
Vicious friction coefficient of motor (Nms/rad) | |
Gravitational acceleration () | |
Motor armature resistance () | |
Gearbox efficiency | |
Gearbox ratio | |
Back EMF constant |
Iteration | k | ||||
---|---|---|---|---|---|
1 | 939.9803 | 57.66961 | 9.858246 | 5.310599 | 0.2627605 |
10 | 598.8002 | 84.27183 | 59.5794 | 3.138694 | 0.4041733 |
15 | 520.8024 | 75.55081 | 59.41921 | 2.426904 | 0.3585694 |
30 | 847.9644 | 65.81239 | 74.8689 | 2.413261 | 0.288982 |
Proposed Controller | SMC | LQR | |
---|---|---|---|
IAE = | 1.976 | 10.840 | 5.739 |
Settling time (s) | 0.216 | 0.750 | 0.719 |
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Pham, D.-B.; Dao, Q.-T.; Nguyen, T.-V.-A. Optimized Hierarchical Sliding Mode Control for the Swing-Up and Stabilization of a Rotary Inverted Pendulum. Automation 2024, 5, 282-296. https://doi.org/10.3390/automation5030017
Pham D-B, Dao Q-T, Nguyen T-V-A. Optimized Hierarchical Sliding Mode Control for the Swing-Up and Stabilization of a Rotary Inverted Pendulum. Automation. 2024; 5(3):282-296. https://doi.org/10.3390/automation5030017
Chicago/Turabian StylePham, Duc-Binh, Quy-Thinh Dao, and Thi-Van-Anh Nguyen. 2024. "Optimized Hierarchical Sliding Mode Control for the Swing-Up and Stabilization of a Rotary Inverted Pendulum" Automation 5, no. 3: 282-296. https://doi.org/10.3390/automation5030017