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AFD-based ILC designs in frequency domain for linear discrete-time systems

The existing frequency-domain-based iterative learning control (ILC) methods are highly dependent on the mathematical models of the controlled systems. For linear discrete-time single-input single-output (SISO) systems with unknown mathematical models, this paper tries to present fully data-driven ILC designs in frequency domain. With the help of support vector machine (SVM), the input-output data of the linear discrete-time SISO system at the first repetition is utilised to constitute an adaptive Fourier decomposition (AFD) model. Then, based on the AFD model, a P-type ILC law and an extended D-type ILC law with data-driven determining techniques for learning gains are presented. It is noted that comparing with the conventional D-type ILC law, the newly proposed extended D-type ILC law exhibits superior tracking characteristic due to involving the frequency information during the ILC process. A numerical example is utilised to illustrate the effectiveness of the proposed ILC algorithms with the data-driven determining techniques for learning gains.