Control of double integrating process with dead time

In many process industries storage tanks are used to restore liquids requiring level control. Liquid height in each tank shows integrating plus dead time (IPDT) behavior. When two such tanks are connected in series gives us a double integrating plus dead time (DIPDT) process. A DIPDT process itself is unstable for step inputs/changes. Hence it is recommended to use a controller for stabilizing the closed loop response of level. An additional block in the feedback loop is added to nullify the instability of DIPDT process. Relay tests are conducted to find ultimate properties of the system for designing the PID controller. In parallel, process parameters are identified and Internal Model Control (IMC)-PID tuning rule using Laurent Series approximation is synthesized for PID controller. Closed-loop performances are calculated and compared. IAE and Sensitivity of the controller are also found.