PID synthesis under probabilistic parametric uncertainty

In many system identification methods, process model parameters are considered stochastic variables. Several methods do not only yield expectations of these, but in addition their variance, and sometimes higher moments. This paper proposes a method for robust synthesis of the proportional-integral-derivative (PID) controller, taking parametric process model uncertainty explicitly into account. The proposed method constitutes a stochastic extension to the well-studied minimization of integrated absolute error (IAE) under ℋ
_∞
-constraints on relevant transfer functions. The conventional way to find an approximate solution to the extended problem is through Monte Carlo (MC) methods, resulting in high computational cost. In this work, the problem is instead approximated by a deterministic one, through the unscented transform (UT), and its conjugate extension (CUT). The deterministic approximations can be solved efficiently, as demonstrated through several realistic synthesis examples.