PI/PID controller design based on direct synthesis and disturbance rejection

A design method for PID controllers based on the direct synthesis approach and specification of the desired closed-loop transfer function for disturbances is proposed. Analytical expressions for PID controllers,are derived for several common types of process models, including first-order and second-order plus time delay models and an integrator plus time delay model. Although the controllers are designed for disturbance rejection, the set-point responses are usually satisfactory and can be tuned independently via a set-point weighting factor. Nine simulation examples demonstrate that the proposed design method results in very good control for a wide variety of processes including those with integrating and/or nonminimum phase characteristics. The simulations show that the proposed design method provides better disturbance rejection than the standard direct synthesis and internal model control methods when the controllers are tuned to have the same degree of robustness.