Modified Frequency-Domain-Based Iterative Learning Control for 2-D Discrete Systems

In the existing time-domain based iterative learning control (ILC) results for 2-D discrete systems, iteration-independent boundary states/errors do not have an impact on the complete convergence of P-type and high-order ILC laws. However, it does affect the ILC convergence characteristics in the frequency domain. This paper first investigates the frequency-domain ILC tracking problem for 2-D discrete systems with different boundary states/errors. A modified frequency-domain P-type ILC law is proposed and a frequency-domain based convergence condition can be derived through the rigorous mathematical proof. Extension to iteration-dependent desired trajectory in the frequency domain described by a high-order internal model (HOIM) is discussed and correspondingly, the extended HOIM-based ILC law is designed. Two simulation examples are provided to verify the effectiveness and feasibility of the proposed modified frequency-domain P-type ILC law and extended HOIM-based ILC law. Lastly, some comparison results on a practical dynamical process are presented.