Slow stable open-loop poles: to cancel or not to cancel

Abstract

Stable plant poles can either be shifted by feedback, or they can be approximately cancelled by a controller. While it is known that the cancelling design impacts on the transients due to input disturbances, here we show that the alternative, i.e., the shifting design, impacts on closed-loop robustness. In this paper we consider control loops with integral action and show that shifting slow stable real poles, rather than cancelling them, increases the l 1, H ∞, and the point-wise in frequency norms of the complementary sensitivity. Thus, the choice to either cancel or shift any one stable pole emerges as a design issue that requires a deliberate trade-off between input disturbance response versus output disturbance response and robustness.