Local Linear PID Controllers for Nonlinear Control

Nonlinear PID design is difficult if one approaches the problem from a global design perspective. In this paper, we propose coalescing the adaptive local linear modeling approach with traditional linear PID controller design techniques to arrive at a principled, intuitive, and simple nonlinear PID controller design methodology. The paper, in particular, discusses two local linear modeling approaches, one based on competitive linear models attached to a self-organizing map, and one based on cooperative linear models attached to the modes of a Gaussian mixture model. The system identification and closed-loop tracking performances of the proposed PID controller design methodology is demonstrated to be better than inverse and PID controllers for a global nonlinear system identifier and a global linear model respectively. Index Terms PID controller, local linear model, self-organizing maps, Gaussian mixture.