Design of Iterative Learning Controller based on Frequency Domain Linear Matrix Inequality

This paper presents an iterative learning controller (ILC) design method based on a frequency domain linear matrix inequality (LMI). It modifies the LMI method for lifted system representation. In lifted system representation, the size of matrices grows as the number of samples in the system increase. In the proposed approach, the size of matrices in LMI is independent of the number of samples in the system, avoiding computational problems due to the size of matrices. The order of controllers can be low, even if the order of the system is high, unlike H-infinity method. Compatibility with frequency domain robust theory and easy extension to MIMO system is another advantage. Zero-phase weighting functions are introduced to shape the filters to increase robustness to the disturbance in high frequency range. This paper also examines the monotonic convergence of the output of the feedback controllers after implementing ILC. The performance of the designed ILC is verified by experiments performed on an industrial robot.