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

TIANYU Zhang; QINXIA Guo; TINGKAI Yang; XIANGJI Guo; MING Ming

doi:10.11999/JEIT250521

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TIANYU Zhang, QINXIA Guo, TINGKAI Yang, XIANGJI Guo, 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:

TIANYU Zhang, QINXIA Guo, TINGKAI Yang, XIANGJI Guo, 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:

TIANYU Zhang, QINXIA Guo, TINGKAI Yang, XIANGJI Guo, 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

TIANYU Zhang^{1, 2},
QINXIA Guo^{1, 2},
TINGKAI Yang^{1, 2},
XIANGJI Guo^{1, 2},
MING Ming^{1, 2
,
,}

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 (NO.2023HIAS-V001)

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

Available Online: 2025-11-08

Abstract

Abstract

Objective Ultra-fast laser processing with an infinite field of view demands exceptional tracking accuracy and robustness from servo motor systems. However, these systems are highly nonlinear and subject to coupled unknown load disturbances and complex friction, which limit the performance of existing controllers. While sliding mode control is inherently robust, conventional SMC and observers struggle to achieve accurate, finite-time disturbance compensation under such nonlinearities, hindering fast, high-precision trajectory tracking. To overcome this bottleneck, this study proposes a novel finite-time adaptive SMC strategy that ensures rapid and precise angular position tracking within a finite time, meeting the stringent synchronization requirements of advanced laser processing. Methods In this paper, we propose a novel strategy to combine an adaptive disturbance observer fused with RBFNN with finite-time sliding mode control. Firstly, the unknown load disturbance and the complex friction nonlinear dynamics in the system are innovatively integrated into a "lumped disturbance" term, which significantly enhances the universality of the model and the ability to describe the actual complex working conditions. Second, a finite-time adaptive disturbance observer is designed for this lumped disturbance. The core of the observer is to make full use of the universal approximation property of RBF neural network to learn and approximate the dynamic characteristics of unknown disturbances online. At the same time, a finite-time adaptive law based on the form of error norm is introduced to adjust the weights of the neural network in real time, which ensures that the observer can estimate the lumped disturbance quickly and accurately in finite time, and effectively reduces the dependence on accurate model parameters. Based on this, a finite-time sliding mode controller is designed. The controller uses the accurate disturbance estimation of the observer output as the feedforward compensation term, combines a carefully designed finite-time sliding mode surface and an equivalent control law, and introduces a saturation function to effectively suppress the control input chattering. By constructing a suitable Lyapunov function and strictly applying the finite-time stability theory, the practical finite-time convergence of the proposed adaptive observer and the closed-loop control system is rigorously proved, which ensures that the tracking error of the system can converge to a bounded neighborhood near the origin in finite time. Results and Discussions In order to verify the effectiveness and superiority of the proposed control strategy, a typical permanent magnet synchronous motor servo system model is built in Matlab environment, and a simulation scene containing different frequency desired trajectories is set up, which is comprehensively compared with the widely used PI control and the advanced method in reference [7]. Simulation results show that: 1. Tracking performance: Under a variety of reference trajectories , the controller designed in this paper can drive the system to accurately track the target trajectory, and its tracking error is significantly smaller than that of PI control. Compared with the method in reference [7], it also shows better smoothness and smaller residual error, which effectively avoids the obvious chattering phenomenon of the latter in some working conditions. Disturbance rejection and robustness: The designed adaptive disturbance observer based on RBFNN can quickly and effectively learn and compensate the lumped disturbance composed of unknown load variation and friction nonlinearity. In the presence of such disturbances, the proposed controller can still maintain high accuracy tracking performance, which proves its strong disturbance rejection capability and robustness to changes in system parameters. 3. Control input characteristics: Compared with the comparison method, the control signal in this paper can quickly tend to smooth after the initial stage, effectively suppress the chattering problem caused by high-frequency switching, and the amplitude variation range of the control signal is reasonable, which is more conducive to the application of practical actuators. 4. Comprehensive evaluation: Through the comprehensive comparison of multiple error performance indicators such as integral squared Error (ISE), integral Absolute error (IAE), time-weighted integral absolute error (ITAE) and time-weighted integral squared error (ITSE), the proposed controller is comprehensively and significantly better than the PI control and the reference [7] method in all indicators. It shows that the proposed method has comprehensive advantages in rapid suppression of transient error, reduction of overall error accumulation, improvement of long-term steady-state accuracy, and balance of response speed and noise suppression. 5. Observer performance: The RBFNN weight norm estimation can quickly converge and stabilize at a low level after the initial rapid adjustment, which verifies the effectiveness of the adaptation law and the efficiency of observer learning. Conclusions This paper proposes a finite-time sliding mode control strategy with an adaptive disturbance observer for servo systems in ultra-fast laser processing. The approach models unknown load and friction nonlinearities as lumped disturbances. An adaptive observer, combining an RBF neural network with a finite-time mechanism, estimates these disturbances accurately for online compensation. A finite-time SMC law is designed based on the observer, with theoretical proof of the closed-loop system's practical finite-time stability. Simulations on a permanent magnet synchronous motor platform demonstrate superior tracking performance, robustness, and control smoothness over traditional PI and existing advanced methods. This work provides an effective solution for high-precision control of nonlinear systems under 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)

References

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