Optimum PIDS controllers, an alternative for unstable delayed systems

PID controllers are broadly used in industrial applications because in many cases it provided satisfactory performances. But if the open loop system is delayed and unstable, the classical PID is not recommended. In order to extend such a practical controller, it is suggested to saturate the integral part of the PID, which becomes a PIDS, so as to improve the closed loop behaviour. This saturation depends on the error signal, which is the input signal of the controller by means of a saturation transfer function. The choice of the latter is given and a criterion is optimized to yield PID and PIDS controller parameters for a wide class of unstable delayed system. A gain of 50% was achieved by the use of PIDS with the criterion described, which proves the interest of such a saturated controller