Design strategy for iterative learning control based on optimal control

This paper deals with the analysis and synthesis of iterative learning control (ILC) systems using a lifted representation of the plant. In this lifted representation the system dynamics are described by a static map whereas the learning dynamics are described by a difference equation. The properties of the lifted system and in particular the role of nonminimum phase zeros and system delays are investigated. Based on the internal model principle a general, integrating update law is suggested. Next, a new multiobjective design method is proposed for the design of the learning gain, based on optimal control theory. The convergence speed is optimized subject to a bound on the closed loop variance due to stochastic initial conditions, process disturbances and measurement noise. An efficient tailor-made solution to the design problem is presented, making optimal use of the specific and nice structure of the lifted system ILC representation. The potential of the design method is demonstrated on a realistic example.