The spatial bandwidth of cross-directional control systems for web processes

A PDE viewpoint on basic properties of coordination algorithms with symmetries

“…phenomena due to very different system response to long-range and short-range effects (see e.g. [3], [24], [14], [8], [21], [16]). …”

“…Analysis (see e.g. "spatial bandwidth" discussion in [14], [8], [1]) and constructive controller design results are proposed thanks to a "spatial frequency shaping" approach (see e.g. [25], [13], [2]), similar to the standard "temporal frequency shaping".…”

Design of Cross-Directional Controllers with Optimal Steady State Performance*

“…One possibility is the singular value decomposition [10,13], in which case Σ is diagnonal (if n > m the upper block of Σ is diagonal, while the lower block is zero).…”

“…Ultra-high frequency modes of Φ are uncontrollable [10,17]. With model mismatch the relative uncertainty is greater at high frequencies, and may result in closed-loop instability [13].…”

“…If sufficient modes are excluded it is possible to design robust controllers that do not violate actuator constraints [20,19,10,13,33]. It has been recommended [19] that r should be chosen to ensure no actuator touches the constraint boundary.…”