TUNING PD AND PID CONTROLLERS VIA THE LAMBERT W FUNCTION FOR DOUBLE INTEGRATOR PLUS DEAD TIME PROCESSES

The paper explores the Proportional-derivative controller for a double integrator plus dead time processes, which is a challenging control problem, that is designed based on the existing Proportional-integrative controller for integrator plus dead time processes. The PD controller is extended with an integral action and an ideal PID controller is received. The parameters of both controllers are received by using the pole placement technique, whereby the transcendent characteristics equation of the closed loop system is solved by using the Lambert W function. The paper also examines the influence of the desired poles of the system with a closed feedback as well as the influence of the disturbance and the change of the DIPTD processes parameters onto the received control system performances. The results received by simulation, and the quantitative indicators, show that the proposed control system has better performances in comparison to the control systems obtained by other methods in literature.