A PI controller is to be used in a temperature control system for a bioreactor. For nominal conditions, it has been determined that the closed-loop system is stable when τ1 = 10 min and – 10 < Kc < 0. Would you expect these stability limits to change for any of the following instrumentation changes? Justify your answers using qualitative arguments.
(a) The span on the temperature transmitter is reduced from 40 to 20 °C.
(b) The zero on the temperature transmitter is increased from 10 to 30 °C.
(c) The control valve “trim” is changed from linear to equal percentage.