Study of Variable Gain Iterative Learning Control Based on Correlation Coefficient

Aiming at a class of linear time-invariant systems, this paper proposes a new variable-gain iterative learning control tracking strategy using a PD-type learning law as an example. Different from the previous approach of quantifying the current output error of the system as a correction for the next control input gain, the algorithm proposed in this paper judges the learning effect based on the magnitude of the Pearson’s correlation coefficient between the current output sequence of the system and the desired trajectory sequence, and further quantifies this coefficient as a correction for the next gain of the control input. Based on this, the convergence of the algorithm is proved in detail and the convergence conditions are obtained. Finally, the simulation results show that the variable gain learning algorithm proposed in this paper has good convergence performance, can completely track the desired trajectory of the system, and has a faster convergence speed compared with the conventional fixed gain learning algorithm.