Frequency Domain Adjoint-Based Iterative Learning Control for MIMO Systems

Abstract The adjoint of the system is a linear operator that can be interpreted as the transposition of the unit pulse response matrix with a Toeplitz structure. In the context of iterative learning control, the system adjoint can be used as the learning filter by performing dedicated experiments on the system, resulting in monotonically convergent algorithms. However, the required number of experiments equals the product of input and output channels, and the convergence speed is limited by the system peak gain. This work aims to reduce the number of dedicated experiments for multivariate systems and improve the convergence speed of the adjoint-based iterative learning control. The proposed algorithm constructs the system adjoint in frequency domain and therefore the required number of experiments equals the number of input channels. Exploiting the independence of frequency response of linear-time-invariant systems, the learning gain can be frequency-dependent, which further accelerates the convergence speed. Algorithm convergence under frequency domain uncertainties are ensured with learning scalar or diagonal gain design. It is shown that for a single-input-single-output system, the proposed approach becomes the inversion-based algorithms. Convergence condition is also developed for multivariable systems through complex analysis. The developed approach is validated through experiments on a multi-axis galvanometer.