Tuning Proportional−Integral Controllers for Processes with Both Inverse Response and Deadtime

Many tuning methods have been proposed over the last half-century. Most apply to deadtime/lag processes, but several have studied either integrating processes or inverse response processes. Very few have explored processes in which both deadtime and inverse responses occur. This type of response is observed in adiabatic tubular reactors when reactor outlet temperature T out is the controlled variable and reactor inlet temperature T in is the manipulated variable. Typically the control structure uses a cascade arrangement in which the secondary loop uses furnace heat input or heat-exchanger bypassing to control T in. This paper addresses the problem of controlling processes that exhibit both inverse response and deadtime. The Ziegler−Nichols tuning method recommended in the literature is shown to give poor performance at both small and large values of deadtime and positive-zero time constant. A new tuning method is proposed in which the PI tuning constants are presented as functions of the positive zero τz and the deadtime D. Results are given in the form of easy-to-use tuning charts.