Cross-directional loop-shaping using spatial pole placement

This paper presents a method to design cross-directional (CD) controllers using spatial loop-shaping. The controller is designed to satisfy the performance and robustness conditions at temporal steady state, afterwards the performance and robustness on a grid of temporal and spatial frequencies are investigated. As the CD process is a regulation problem attenuating the spatial disturbances, mainly at low dynamical frequencies, performing control design at steady state is sufficient. This approach simplifies the complicated design problem without any drawbacks. The CD process is modeled by a spatial non-causal transfer function and the closed loop spatial frequency response is shaped using pole placement. In other words, this is shaping the singular values of the MIMO system at steady state and consequently the H_∞ norm. The performance and robustness of the designed controller is compared to the controller obtained by two dimensional loop-shaping.