Beyond the Pi Controllers in First-order Time-delay Systems

In this paper the following three control systems for first-order time-delay plants are studied and compared: the feedback proportional-integral controller (PI), the Smith Predictor (SP) and a proposed variable structure consisting of two blocks. This structure acts as an open-loop proportional controller, after a setpoint change, and as a closed-loop integrating controller, when the error enters in a preset band. A chart, provided with the borderlines of the stability zone and with the curves of two design parameters, is implemented for each controller. The first parameter is the overshoot of the controlled variable, evaluated during a step change of the setpoint and made equal to a preset value. The second parameter, only for the PI and SP controllers, is the integral of the squared error (ISE), which must have the minimum allowable value. The ISE is also assumed as comparison index and the proposed controller appears as the best.