Fractional-Proportional-Type Iterative Learning Control With a Novel Gain Selection Rule

Area of Science:

• Control Engineering
• Automation Systems
• Applied Mathematics

Background:

• Iterative Learning Control (ILC) is crucial for repetitive tasks requiring high precision.
• Fractional-order controllers offer improved performance over integer-order counterparts.
• Existing ILC gain selection methods face limitations in balancing convergence speed and tracking accuracy.

Purpose of the Study:

• To develop a novel gain selection scheme for fractional-proportional-type ILC.
• To enhance convergence rates and tracking precision in ILC systems.
• To analyze the theoretical convergence properties and practical performance of the proposed scheme.

Main Methods:

• A new gain selection strategy for fractional-proportional-type ILC is proposed.
• Convergence analysis of tracking errors to adjustable limit cycles.
• Recursive computation and detailed bound estimation for limit cycles.
• Systematic comparison of various gain selection rules and multistage update schemes.

Main Results:

• Demonstrated convergence of tracking errors to adjustable limit cycles with proven bounds.
• Analysis of both local and global convergence rates for the proposed scheme.
• Two novel multistage update schemes combining different gain selections were developed.
• Proposed schemes show faster convergence than the common proportional-type rule, achieving zero-error tracking.

Conclusions:

• The novel gain selection scheme significantly improves convergence speed and tracking precision in fractional-proportional ILC.
• The multistage update schemes offer a quantitative acceleration of convergence, independent of system matrices.
• Theoretical analysis and experimental validation confirm the effectiveness of the proposed ILC approach.