The main objective of this study is to address the challenge of simultaneously ensuring robustness and convergence performance in model-free inversion-based iterative learning control. Initially, this research provides a mathematical analysis of the sources of errors in the iterative process, followed by proposing a design guideline to enhance both convergence speed and the final value error. Based on the design guideline, a gain design method associated with the number of iterations is proposed, resulting in a novel model-free inversion-based iterative learning control algorithm. Subsequently, a robustness analysis of the proposed algorithm is conducted. Finally, a comprehensive simulation and numerical comparison of the proposed algorithm with existing similar algorithms are presented to demonstrate the superior performance of the proposed control algorithm.