[Paper Review] Global Iterative Sliding Mode Control of an Industrial Biaxial Gantry System for Contouring Motion Tasks

Wenxin Wang, Jun Ma+4 more|arXiv (Cornell University)|Mar 23, 2021

Iterative Learning Control Systems41 references39 citations

TL;DR

This paper proposes a global iterative sliding mode control (GISMC) method for high-precision contouring in a flexure-linked biaxial gantry system. By combining adaptive sliding mode control with an incremental cascade iterative learning law, the method suppresses chattering and handles matched/unmatched uncertainties without prior knowledge of uncertainty bounds, achieving rapid convergence and high accuracy in contouring tasks across complex trajectories.

ABSTRACT

This paper proposes a global iterative sliding mode control approach for high-precision contouring tasks of a flexure-linked biaxial gantry system. For such high-precision contouring tasks, it is the typical situation that the involved multi-axis cooperation is one of the most challenging problems. As also would be inevitably encountered, various factors render the multi-axis cooperation rather difficult; such as the strong coupling (which naturally brings nonlinearity) between different axes due to its mechanical structure, the backlash and deadzone caused by the friction, and the difficulties in system identification, etc. To overcome the above-mentioned issues, this work investigates an intelligent model-free contouring control method for such a multi-axis motion stage. Essentially in the methodology developed here, it is firstly ensured that all the coupling, friction, nonlinearity, and disturbance (regarded as uncertain dynamics in each axis) are suitably posed as `uncertainties'. Then, a varying-gain sliding mode control method is proposed to adaptively compensate for the matched unknown dynamics in the time domain, while an iterative learning law is applied to suppress the undesirable effects (arising from the repetitive matched and unmatched uncertainties in the iteration domain). With this approach, the chattering that typically results from the overestimated control gains in the sliding mode control is thus suppressed during the iterations. To analyze the contouring performance and show the improved outcomes, rigorous proof is furnished on both the stability in the time domain and the convergence in the iteration domain; and the real-time experiments also illustrate that the requirements of precision motion control towards high-speed and complex-curvature references can be satisfied using the proposed method, without prior knowledge of the boundary to the unknown dynamics.

Motivation & Objective

• Address the challenge of high-precision contouring in flexure-linked biaxial gantry systems, which suffer from strong coupling, friction-induced backlash/deadzone, and nonlinearities.
• Overcome limitations of existing control methods that require accurate system identification or prior knowledge of uncertainty bounds.
• Develop a model-free control strategy that ensures robustness against matched and unmatched uncertainties in both time and iteration domains.
• Achieve global stability in the time domain and global convergence in the iteration domain for repetitive contouring tasks.
• Suppress chattering in sliding mode control through iterative adaptation, avoiding overestimation of control gains.

Proposed method

• Formulate all system nonlinearities, coupling effects, friction, and disturbances as 'uncertainties' in each axis.
• Implement an adaptive sliding mode control (ASMC) component with time-varying gains to compensate for matched unknown dynamics in real time.
• Introduce an incremental cascade iterative learning law (ILL) to suppress repetitive matched and unmatched uncertainties across iterations.
• Use a 2-degree-of-freedom (2-DOF) control structure: ASMC for real-time robustness and ILL for iterative performance improvement.
• Apply rigorous stability and convergence proofs in both time and iteration domains using Lyapunov-based analysis.
• Integrate the control framework with real-time experiments on a physical flexure-linked biaxial gantry system to validate performance.

Experimental results

Research questions

• RQ1 Can a model-free control strategy achieve high-precision contouring in a flexure-linked biaxial gantry system without requiring system identification or uncertainty bounds?
• RQ2 How can chattering in sliding mode control be effectively suppressed during iterative learning without sacrificing robustness?
• RQ3 To what extent can the proposed global iterative sliding mode control (GISMC) method ensure stability in the time domain and convergence in the iteration domain?
• RQ4 How does the proposed method perform against complex, high-curvature reference trajectories such as cardioids and circles?
• RQ5 Can the control framework handle exogenous disturbances and measurement noise effectively in practical applications?

Key findings

• The proposed GISMC method achieved a root-mean-square contouring error (RMSE) of 5.990 µm for the xy-axis in Task 1 (circle), decreasing to 6.540 µm in Task 2 (cardioid), demonstrating high accuracy across complex paths.
• Maximum absolute contouring errors (MaxAE) were reduced to 16.80 µm (xy-axis) in Task 1 and 17.23 µm in Task 2, showing robustness under high-curvature motion.
• Sliding variable RMS values (RMSSV) decreased significantly across iterations: from 5.58×10⁻⁴ to 3.38×10⁻⁴ for the xy-axis, indicating effective sliding motion establishment.
• The method suppressed chattering effectively, as evidenced by decreasing control effort and sliding variable magnitudes over iterations, even without overestimating control gains.
• The system maintained consistent performance under additional exogenous disturbances and measurement noise, confirming strong robustness.
• Convergence was validated across six iterations: RMSE and RMSSV values decreased rapidly after the first iteration and continued to decline with diminishing rates.