Abstract
Repetitive Control (RC) designed with state feedback that includes past error feedforward and current error feedback schemes for linear time-invariant systems is reintroduced. Periodic disturbances are common within repetitive systems and can be represented with a time-delay model. The proposed design focuses on isolating the disturbance model and finding the overall transfer function around the delay model. The use of the small gain theorem around the delay model assures disturbance accommodation if stability conditions are achieved. This paper reintroduces the designed RC controller within the state feedback in the presence of both past error and current error structures. Robustness conditions are investigated and set to enhance system performance in the presence of modelling mismatch, which represents the novel contribution in this paper. Simulations demonstrate the advantages of the robust conditions obtained while improving system performance for dynamic perturbations.
Highlights
Systems of a repetitive [1] nature are those where the reference trajectory required to follow to a high precision, r (t ), is of a repetitive structure, r (=t ) r (t + T )
The solution considered in [12] [13] uses the internal model principle [10] as well as the small gain theorem to set stability conditions to design the feedback gain and the observer gain using a Linear Quadratic Regulator (LQR) where the periodic disturbances act on the system output. [14] considers a more general case than the work presented in [12] [13] as it incorporates both current error and past error in the designed framework instead of the current error feedback
This paper considers the Repetitive Control (RC) design scheme in the state feedback reported in [14] and the different stability conditions within depending on the error case considered; either current error feedback or past error feed forward
Summary
Systems of a repetitive [1] nature are those where the reference trajectory required to follow to a high precision, r (t ) , is of a repetitive structure, r (=t ) r (t + T ). Repetitive control and iterative learning control (ILC), which is another technique used to accommodate periodic disturbances and to enhance the performance of repetitive systems, are not similar even though they use the same updating technique. The design starts with first defining the periodic signal and setting the required steps to design the RC controller in the lifted model with the presence of the delay model in the feedback loop. As well it presents new robust conditions that set limitations towards the design that are different than those introduced in [15] where the authors discussed the uncertainty condition for the proposed design in the presence of current error feedback alone in the frequency domain.
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