A method for PID controller tuning using nonlinear control techniques

In this work, we propose a two-level, optimization-based method for deriving tuning guidelines for proportional-integral-derivative (PID) controllers that take explicitly into account the presence of nonlinear behavior. The central idea behind the proposed method is the selection of the PID controller tuning parameters so as to best "emulate" the control action and closed-loop response under a given nonlinear controller for a broad set of initial conditions and set-point changes. The first level involves using classical tuning guidelines (typically derived on the basis of linear approximations, running open or closed-loop tests) to obtain reasonable bounds on the tuning parameters in order to satisfy various design criteria such as stability, performance and robustness. These bounds are in turn incorporated as constraints on the optimization problem solved at the higher level to yield tuning parameter values that improve upon the values obtained from the first level to better emulate the closed-loop behavior under the nonlinear controller. The efficacy of the proposed tuning method is demonstrated through application to a nonlinear chemical reactor example.