Resource-efficient ILC for LTI/LTV systems through LQ tracking and stable inversion: Enabling large feedforward tasks on a position-dependent printer

Iterative learning control (ILC) enables high performance for systems that execute repeating tasks. Norm-optimal ILC based on lifted system representations provides an analytic expression for the optimal feedforward signal. However, for large tasks the computational load increases rapidly for increasing task lengths, compared to the low computational load associated with so-called frequency domain ILC designs. The aim of this paper is to solve norm-optimal ILC through a Riccati-based approach for a general performance criterion. The approach leads to exactly the same solution as found through lifted ILC, but at a much smaller computational load (O(N)O(N) vs O(N3)O(N3)) for both linear time-invariant (LTI) and linear time-varying (LTV) systems. Interestingly, the approach involves solving a two-point boundary value problem (TPBVP). This is shown to have close connections to stable inversion techniques, which are central in typical frequency domain ILC designs. The proposed approach is implemented on an industrial flatbed printer with large tasks which cannot be implemented using traditional lifted ILC solutions. The proposed methodologies and results are applicable to both ILC and rational feedforward techniques by applying them to suitable closed-loop or open-loop system representations. In addition, they are applied to a position-dependent system, revealing necessity of addressing position-dependent dynamics and confirming the potential of LTV approaches in this situation.