  This paper presents a set of robust PI tuning formulae for a first order plus
dead time process using particle swarm optimization. Also, tuning formulae for
an integrating process with dead time, which is a special case of a first order
plus dead time process, is given. The design problem considers three essential
requirements of control problems, namely load disturbance rejection, setpoint
regulation and robustness of closed-loop system against model uncertainties.
The primary design goal is to optimize load disturbance rejection. Robustness
is guaranteed by requiring that the maximum sensitivity is less than or equal
to a specified value. In the first step, PI controller parameters are
determined such that the IAE criterion to a load disturbance step is minimized
and the robustness constraint on maximum sensitivity is satisfied. Using a
structure with two degrees of freedom which introduces an extra parameter, the
setpoint weight, good setpoint regulation is achieved in the second step. The
main advantage of the proposed method is its simplicity. Once the equivalent
first order plus dead time model is determined, the PI parameters are
explicitly given by a set of tuning formulae. In order to show the performance
and effectiveness of the proposed tuning formulae, they are applied to three
simulation examples.
