An iterative learning algorithm founded on the normalization principle and inverse triangular dynamic initial error compensation

To address the issues of low convergence accuracy and deteriorated output performance caused by initial state errors in linear time-invariant discrete-time systems, traditional iterative learning control methods typically treat initial errors as passively tolerated conditions. The lack of an active correction mechanism significantly limits the dynamic performance of the system. To overcome this limitation, this paper proposes a proportional-–integral-–derivative–type iterative learning control algorithm based on the normalization principle, incorporating a dynamic compensation term constructed via an inverse tangent function. First, by analyzing the impact mechanism of initial state errors on system output, a gradually decaying dynamic compensation term based on the arctangent function is designed under the normalization principle. This term is integrated into the control gain to enable active learning and smooth correction of initial errors. Second, the convergence condition of the proposed algorithm is derived, and the tuning guidelines for key parameters are provided. Theoretical analysis demonstrates that the system output error converges monotonically in the iteration domain. Finally, numerical simulations verify the effectiveness of the proposed algorithm. The results show that, under identical system conditions, the proposed method reduces the system output error by more than 80% compared to existing typical approaches, significantly improving both convergence speed and steady-state accuracy.