Limit Cycles with Imperfect Valves: Implications for Controllability of Processes with Large Gains

There is some disagreement in the literature in regard to whether or not large plant gains are a problem when input-output controllability issues are involved. In this paper, controllability requirements are derived for two types of input errors, namely, restricted (low) input resolution (e.g., caused by a sticky valve) and input disturbances. In both cases, the controllability is limited if the plant gain is large at high frequencies. Limited input resolution causes limit cycle behavior (oscillations) similar to that observed with relay feedback. The magnitude of the output variations is dependent on the plant gain at high frequency but is independent of the controller tuning. Provided frequent input (valve) movements are acceptable, one may reduce the output magnitude by forcing the system to oscillate at a higher frequency, for example by introducing a faster local feedback (e.g., a valve positioner) or by pulse modulating the input signal.