Dual-Stage Iterative Learning Control With Markov Parameters Toward Pointwise Convergence Evaluation
Abstract
The study proposes iterative Learning Control (ILC) for single-input, single-output, discrete-time, time-invariant linear systems, where system outputs are expressed by the convolution of Markov parameters and historical input data. In the proposed method, the input signals and system parameters are updated in a pointwise manner after every trial. Then, normalization signals are introduced to ensure the boundedness of the magnitude of both the input signals and the estimated parameters. The main feature of the proposed method is the pointwise evaluation of the convergence rate for the input signals to the desired ones. The theoretical analysis is conducted under the assumption that the sign of the initial first Markov parameter estimate is selected to be the same as that of the true value. It should be noted that the convergence of tracking errors could be achieved even when the estimated parameters do not converge to the true values. The feature contrasts with the existing model-based ILC, where the control performance is significantly dependent on the precision of the estimated parameters. Finally, a numerical example is shown that supports the analysis of the proposed method.