Controllability of Processes with Large Gains

There is some disagreement in the literature on whether large plant gains are a problem or not when it comes to input-output controllability. In this paper, the effect of two kinds of input errors is studied and controllability requirements are derived. First, input disturbances are studied. These may pose a problem if the plant gain is large at high frequencies. Second, we study the nonlinear effect of limited input resolution which causes limit cycle behavior similar to that found with relay feedback. The magnitude of these limit cycles depends on the high-frequency process gain, but is independent of the controller tuning. They can be reduced by pulse modulating the input signal, but this may cause excessive input movement. In summary, large gains at frequencies corresponding to the closed-loop bandwidth may cause control problems, but largesteady-state gains are not by themselves a problem.