Passivity based iterative learning control of differential systems

Repetitive processes complete the same operation defined over a finite interval of time over and over again. Once an execution, termed a pass, is complete the processes resets to the starting location. Once complete, the next pass can begin, either immediately after the end of resetting or after a further period of time. Each pass output is known as the pass profile and on any pass this profile contributes to the dynamics of the next pass profile. This can result in oscillations that increase in amplitude from one pass to the next and so on. These processes are a particular case of 2D systems and the appearance of oscillations in the sequence of pass profiles cannot be prevented by application of standard control action. In this paper new results on control law design for linear dynamics are developed using a passivity based stability theory setting developed for nonlinear dynamics that requires the use of vector Lyapunov functions. As one possible application, the new results are applied, with a supporting example based on model of Quanserr flexible link , to iterative learning control design.