Two Decades of Research on Linear Repetitive Processes Part II: Applications

Repetitive processes make a series of sweeps, or passes, through a set of dynamics defined over the finite pass length. Once a pass is complete the process resets to the starting location ready for the start of the next one. On any pass, the output, or pass profile, generated on the previous one acts as a forcing function on, and therefore contributes to, the dynamics of the new pass profile. These processes are a class of 2D systems where the novel control problem is that the sequence of pass profiles generated can contain oscillations that increase in amplitude from pass-to-pass. These oscillations cannot be removed by standard control action and therefore a 2D systems control theory for them has been under development over the pass two decades. This paper demonstrates that, unlike much of the control theory for other 2D systems, repetitive processes have applications that have led to experimental verification of control laws.