Optimal tuning of PID controllers for Type-III control loops

We extend the Symmetrical Optimum criterion to the design of type-Ill closed loop control systems by introducing a robust PID type control law. Type-III control loops have the advantage of tracking fast reference signals, since they exhibit zero steady state position, velocity and acceleration error. Type-III control loops are characterized by the presence of three pure integrators in the open loop transfer function. For deriving the proposed control law, the concept of the Symmetrical Optimum criterion is applied to the closed loop control system. For representing the controlled process, a generalized transfer function process model is employed. The proposed PID control law consists of analytical expressions that involve all modelled plant parameters. Simulation results for benchmark processes are presented confirming the potential of the proposed theory.