Finite-time Adaptive Sliding Mode Control of Servo Motors Considering Frictional Nonlinearity and Unknown Loads

ZHANG Tianyu; GUO Qinxia; YANG Tingkai; GUO Xiangji; MING Ming

doi:10.11999/JEIT250521

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ZHANG Tianyu, GUO Qinxia, YANG Tingkai, GUO Xiangji, MING Ming. Finite-time Adaptive Sliding Mode Control of Servo Motors Considering Frictional Nonlinearity and Unknown Loads[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250521

Citation:

ZHANG Tianyu, GUO Qinxia, YANG Tingkai, GUO Xiangji, MING Ming. Finite-time Adaptive Sliding Mode Control of Servo Motors Considering Frictional Nonlinearity and Unknown Loads[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250521

Citation:

ZHANG Tianyu, GUO Qinxia, YANG Tingkai, GUO Xiangji, MING Ming. Finite-time Adaptive Sliding Mode Control of Servo Motors Considering Frictional Nonlinearity and Unknown Loads[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250521

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Finite-time Adaptive Sliding Mode Control of Servo Motors Considering Frictional Nonlinearity and Unknown Loads

doi: 10.11999/JEIT250521 cstr: 32379.14.JEIT250521

1.
Hangzhou Institute for Advanced Study, UCAS School of Physics and Optoelectronic Engineering, ZheJiang HangZhou 310024, China
2.
Chinese Academy of Sciences, Beijing 100049, China

Funds: Innovation Project of HlAS (2023HIAS-V001)

Received Date: 2025-06-09
Accepted Date: 2025-11-03
Rev Recd Date: 2025-10-10

Available Online: 2025-11-08

Abstract

Abstract

Objective Ultra-fast laser processing with an infinite field of view requires servo motor systems with superior tracking accuracy and robustness. However, such systems are highly nonlinear and affected by coupled unknown load disturbances and complex friction, which constrain the performance of conventional controllers. Although Sliding Mode Control (SMC) exhibits inherent robustness, traditional SMC and observer designs cannot achieve accurate finite-time disturbance compensation under strong nonlinearities, thus limiting high-speed and high-precision trajectory tracking. To address this limitation, a novel finite-time adaptive SMC approach is proposed to ensure rapid and precise angular position tracking within a finite time, satisfying the stringent synchronization requirements of advanced laser processing systems. Methods A novel control strategy is developed by integrating an adaptive disturbance observer fused with a Radial Basis Function Neural Network (RBFNN) and finite-time SMC. First, the unknown load disturbance and complex frictional nonlinear dynamics are combined into a unified "lumped disturbance" term, improving model generality and the ability to represent real operating conditions. Second, a finite-time adaptive disturbance observer is constructed to estimate this lumped disturbance. The observer utilizes the universal approximation capability of the RBFNN to learn and approximate the dynamic characteristics of unknown disturbances online. Simultaneously, a finite-time adaptive law based on the error norm is introduced to update the neural network weights in real time, ensuring rapid and accurate finite-time estimation of the lumped disturbance while reducing dependence on precise model parameters. Based on this design, a finite-time SMC is developed. The controller uses the observer’s disturbance estimation as a feedforward compensation term, incorporates a carefully formulated finite-time sliding surface and equivalent control law, and introduces a saturation function to suppress control input chattering. A suitable Lyapunov function is then constructed, and the finite-time stability theory is rigorously applied to prove the practical finite-time convergence of both the adaptive observer and the closed-loop control system, guaranteeing that the system tracking error converges to a bounded neighborhood near the origin within finite time. Results and Discussions To verify the effectiveness and superiority of the proposed control strategy, a typical Permanent Magnet Synchronous Motor (PMSM) servo system model is constructed in the MATLAB environment, and a simulation scenario with desired trajectories of varying frequencies is established. The proposed method is comprehensively compared with the widely used Proportional–Integral (PI) control and the advanced method reported in reference[7]. Simulation results demonstrate the following: 1. Tracking performance: Under various reference trajectories, the proposed controller enables the system to accurately follow the target trajectory with a tracking error substantially smaller than that of the PI controller. Compared with the method in reference[7], it achieves smoother responses and smaller residual errors, effectively eliminating the chattering observed in some operating conditions of the latter. 2 Disturbance rejection and robustness: The adaptive disturbance observer based on the RBFNN rapidly and effectively learns and compensates for the lumped disturbance composed of unknown load variations and frictional nonlinearities. Even in the presence of these disturbances, the proposed controller maintains high-precision trajectory tracking, demonstrating strong disturbance rejection and robustness to system parameter variations. 3. Control input characteristics: Compared with the reference methods, the control signal of the proposed approach quickly stabilizes after the initial transient phase, effectively suppressing chattering caused by high-frequency switching. The amplitude range of the control input remains reasonable, facilitating practical actuator implementation. 4. Comprehensive evaluation: Based on multiple error performance indices, including Integral Squared Error (ISE), Integral Absolute Error (IAE), Time-weighted Integral Absolute Error (ITAE), and Time-weighted Integral Squared Error (ITSE), the proposed controller consistently outperforms both PI control and the method in reference[7]. It demonstrates comprehensive advantages in suppressing transient errors rapidly and reducing overall error accumulation. The method also improves steady-state accuracy and achieves a balanced response speed with effective noise attenuation. 5. Observer performance: The RBFNN weight norm estimation converges rapidly and stabilizes at a low level after initial adaptation, confirming the effectiveness of the proposed adaptive law and the learning efficiency of the observer. Conclusions A finite-time sliding mode control strategy with an adaptive disturbance observer is proposed for servo systems used in ultra-fast laser processing. The method models unknown load disturbances and frictional nonlinearities as a lumped disturbance term. An adaptive observer, integrating an RBF neural network with a finite-time mechanism, accurately estimates this disturbance for real-time compensation. Based on the observer, a finite-time SMC law is formulated, and the practical finite-time stability of the closed-loop system is theoretically proven. Simulations conducted on a permanent magnet synchronous motor platform confirm that the proposed approach achieves superior tracking accuracy, robustness, and control smoothness compared with conventional PI and existing advanced methods. This work offers an effective solution for achieving high-precision control in nonlinear systems subject to strong disturbances.
- Ultra-fast laser infinite field of view processing,
- Servo motor,
- Adaptive disturbance observer,
- Finite-time control,
- Sliding mode control

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References(20)

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