Repetitive Control for Linear System

Linear time-invariant (LTI) systems are systems that are both linear and time-invariant. A system is considered linear if the output of the system is scaled by the same amount as the input given to the system. Moreover, this system follows the superposition principle, which implies that the sum of all the inputs will be the sum of the outputs of the individual inputs. Time-invariant systems are systems in which the output caused by a particular input does not change with time and only depends on when that input was applied. This class of systems is very important in the control field where many mature tools and methods exist. Before discussing nonlinear systems, the results of LTI systems must be reviewed to allow for the easy introduction of repetitive control (RC, or repetitive controller, which is also designated as RC) for nonlinear systems. On the other hand, any RC methods applicable to nonlinear systems should be first applicable to LTI systems. Therefore, it is necessary to apply these methods to LTI systems first and then move onto nonlinear systems. Moreover, some RC methods for nonlinear systems are an extended form or a combination of the methods in LTI systems. Therefore, it is important and necessary to first be aware of the RC methods for LTI systems. LTI systems often employ two types of models, i.e., transfer function models and state-space models. This chapter aims to answer the following question: How do you design a repetitive controller for LTI systems based on transfer function models and state-space models?