Synthesis of PID controller for unstable and integrating processes

Properly designed controllers provide stable closed-loop response for open-loop unstable processes. Internal model controller equivalent PID tuning rules for low order unstable plus dead time systems are synthesized in this work. The controller is approximated near the vicinity of zero (origin). Controller parameters are derived by equating the closed-loop response to a control-signature (desired closed-loop response) involving a user defined tuning parameter, λ. Simulations are carried out to show the performance of the proposed tuning scheme for both set point and disturbance rejection cases.