Multi-input square iterative learning control with input rate limits and bounds

Area of Science:

• Control Systems Engineering
• Robotics
• Automation

Background:

• Iterative learning control (ILC) is effective for repetitive tasks.
• Standard ILC algorithms may fail with bounded and time-rate-limited inputs.
• Convergence issues in ILC with input constraints are not fully addressed.

Purpose of the Study:

• To modify the Arimoto et al. ILC algorithm for systems with bounded inputs.
• To establish convergence conditions based on input-error norms.
• To provide a novel proof for monotonic error reduction.

Main Methods:

• Modification of the iterative learning control algorithm.
• Analysis of Jacobian error conditions for input-error norm monotonicity.
• Development of a new convergence proof for the modified controller.

Main Results:

• A modified ILC algorithm is presented for bounded and time-rate-limited inputs.
• Input-error norm monotonicity is identified as crucial for convergence, unlike output-error norms.
• The modified controller ensures monotonically decreasing input error norms over the entire trial duration.

Conclusions:

• The proposed modification ensures convergence for ILC with input constraints.
• The study highlights the significance of input-error dynamics for ILC stability.
• This work offers a robust ILC solution for practical applications with input limitations.