# Nonlinear Control Based on Affine Neural Networks: Application to a Solar Power Plant

### Authors

Jorge Henriques

Paulo José Carrilho de Sousa Gil

Paulo de Carvalho

Alberto Cardoso

Herminio Duarte-Ramos

António Dourado

Paulo José Carrilho de Sousa Gil

Paulo de Carvalho

Alberto Cardoso

Herminio Duarte-Ramos

António Dourado

### Abstract

One of the main features of solar power plants is that its primary energy source, the solar radiation, cannot be manipulated by the control system. Moreover, since the solar radiation changes substantially due to the daily solar cycle and to atmospheric conditions, significant variations in the dynamics of the plant are observed. Therefore, it is difficult to achieve a satisfactory performance over the whole operating range by employing conventional linear control strategies.The ability of neural networks to learn and generalize based on the input-output behavior of a given process has had a great impact on the development of nonlinear adaptive models. In particular, due to their inherent ability to incorporate time, recurrent neural networks are particularly suited for modeling nonlinear dynamic processes. This work proposes an affine recurrent neural network for modeling the dynamics of a solar power plant. Firstly, the neural network is trained offline, being further improved by means of an online learning strategy using the Lyapunov theory together with nonlinear observation theory. The order of the affine neural network is estimated using a subspace based technique, where the initial estimate is further conditioned taking into account some complexity reduction heuristics.

Based on the affine recurrent neural network a nonlinear control strategy is designed using the output regulation theory which provides a framework for deriving stable closed loop systems and asymptotic convergence of the tracking error to zero. Experimental results collected on a distributed collector field of a solar power plant (Plataforma Solar de Almería, Spain) show the effectiveness of the proposed approach.