J. Lan, J. Cho, D. Erdogmus, J.C. Principe, M.A. Motter, and J. Xu
PID controller, local linear model, self-organizing maps, Gaussian mixture
Nonlinear PID design is difficult if one approaches the problem from a global design perspective. The authors propose coalescing the adaptive local linear modelling approach with traditional linear PID controller design techniques to arrive at a principled, intuitive, and simple nonlinear PID controller design methodology. The article, in particular, discusses two local linear modelling 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 are demonstrated to be better than inverse and PID controllers for a global nonlinear system identifier and a global linear model, respectively.
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