Observer-Based Finite-Time Prescribed Performance Sliding Mode Control of Dual-Motor Joints-Driven Robotic Manipulators with Uncertainties and Disturbances
Abstract
:1. Introduction
- In contrast to existing control strategies [17,18,19,20,23] that overlook transient performance, this paper introduces a non-singular fast terminal sliding mode controller (NFTSMC) for robotic systems that incorporates the prescribed performance principle. An enhanced TSM-type reaching law is proposed to confine the trajectory tracking error within a predefined boundary in a finite-time convergence rate.
- To mitigate the demands on prior knowledge of system uncertainties and disturbances in traditional HSMC controllers, an adaptive sliding mode disturbance observer (ASMDO) is introduced. It is complemented by an adaptive update law designed to estimate the upper bound of the derivative of lumped uncertainties. The ASMDO’s estimation error is proven to achieve practical finite-time stability.
- To the best of our knowledge, this paper presents the preliminary validation of a finite-time PPC sliding-mode controller integrated with a dual-motor anti-backlash strategy on a real serial-type dual-motor joints-driven robotic manipulator. This validation underscores the practical applicability and robustness of the proposed control scheme.
2. System Description and Preliminaries
2.1. Dual-Motor Joints-Driven Robotic Manipulator and Anti-Backlash Strategy
2.2. System Model and Preliminaries
3. Observer-Based Finite-Time Tracking Control for Backlash-Free Robotic Systems
3.1. Design of Adaptive Sliding Mode Observer
3.2. Design of Prescribed Performance Sliding Mode Controller
Algorithm 1 The algorithm of the proposed controller |
1: Initialization: Set dual-motor anti-backlash control parameters , and adaptive sliding mode observer parameters , and prescribed performance function parameters , and sliding mode control parameters ; 2: Run procedure: 2.1: Compute the desired position of auxiliary motor from Equation (8); 2.2: Compute the sliding mode surface from Equation (17); 2.3: Update the adaptive law given in Equation (19); 2.4: Compute the lumped uncertainties via Equation (18); 2.5: Calculate the transformed error from Equation (37); 2.6: Calculate the sliding mode surface via Equation (39); 2.7: Calculate the control law by Equation (42) at , ; 2.8: Continuation: ; 3: End procedure |
4. Simulation and Experimental Results
4.1. Numerical Simulation
- For the sliding mode surface defined by Equation (39), the gain and are selected to facilitate the convergence of the sliding mode. In practical applications, an appropriately chosen can enhance the convergence rate, especially when the sliding mode variable is significantly displaced from the equilibrium point. Subsequently, the designer should primarily focus on adjusting the value of to optimize the system performance.
- Based on the prescribed performance function Equation (36), the initial tracking error condition should be fulfilled by suitable and a.
- The larger gain could improve the convergence rate of ASMDO. However, larger gain will cause large overshoot in the transient stage.
- The parameter play an important roles in convergence time and accuracy for ASMDO.
4.2. Experimental Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Description | Value |
---|---|---|
Length of first link | ||
Length of second link | ||
Mass of first link | ||
Mass of second link | ||
Inertia of first link | ||
Inertia of second link | ||
g | Gravitational constant | |
Coulomb friction coefficient | ||
viscous friction coefficient | ||
Stribeck friction coefficient | ||
Stribeck friction velocity |
Section | Parameters |
---|---|
APDMAB | |
PPF | |
NFTSMC | |
ASMDO |
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Xu, J.; Fang, L.; Wang, H.; Zhao, Q.; Wan, Y.; Gao, Y. Observer-Based Finite-Time Prescribed Performance Sliding Mode Control of Dual-Motor Joints-Driven Robotic Manipulators with Uncertainties and Disturbances. Actuators 2024, 13, 325. https://doi.org/10.3390/act13090325
Xu J, Fang L, Wang H, Zhao Q, Wan Y, Gao Y. Observer-Based Finite-Time Prescribed Performance Sliding Mode Control of Dual-Motor Joints-Driven Robotic Manipulators with Uncertainties and Disturbances. Actuators. 2024; 13(9):325. https://doi.org/10.3390/act13090325
Chicago/Turabian StyleXu, Jiqian, Lijin Fang, Huaizhen Wang, Qiankun Zhao, Yingcai Wan, and Yue Gao. 2024. "Observer-Based Finite-Time Prescribed Performance Sliding Mode Control of Dual-Motor Joints-Driven Robotic Manipulators with Uncertainties and Disturbances" Actuators 13, no. 9: 325. https://doi.org/10.3390/act13090325