The present work proposes a new proportional–integral-derivative (PID) controller for time-delayed stable and unstable second-order processes. The performance of PID controller is augmented by associating a second-order filter. The parameters of the controller as well as the filter are derived analytically using polynomial approach. The Lagrange shift approximation of time delay is employed in the process of deriving controller parameters. The tuning parameter is selected based on the value of maximum sensitivity (MS). A set point filter is employed in order to reduce the overshoot in the servo response. The proposed work is verified against recently published works with the help of various benchmarking examples.