PI Controller Performance Analysis Using Lambert W Function Approach for First Order Systems with Time Delay

Abstract

Time delays are inherent in process industry. The presence of time delays limits and degrades the possible performance of the system and also leads to instability. The states of the delay system not only depend on the present state, they also depend on the previous states. With the help of a suitable controller design, the delay systems can be controlled for getting fruitful results. In all industrial feedback control applications most commonly and practically used controllers are Proportional Integral Derivative (PID) controllers. With proper parameter tuning of the controller, required performance can be achieved from the system. In general, the first order processes with time delay can be easily controlled with PI controllers. By choosing the proper controller gains the effect of time delays can be avoided. In this paper, PI controller design with Lambert W function analysis in smith configuration has been proposed. After the selection of dominant poles, the PI controller gains were chosen accordingly to shift the desired eigen values to required positions using the Lambert W function based analysis. A first order process with time delay has been considered in this paper and the comparative analysis of proposed tuning algorithm with Smith predictor (SP) and Zeigler-Nichols (ZN) methods has been done. By using the time response performance specifications and errors, the performance of different tuning algorithms has been analyzed. From the simulation and different performance indices results, it has been observed that proposed smith configured Lambert W based controller tuning approach gives improved results compared to remaining methods in terms of the measures like overshoot, peak time, settling time, rise time, errors etc.