Reducing prediction uncertainty of weather controlled systems

In closed agricultural systems the weather acts both as a disturbance and as a resource. By using weather forecasts in control strategies the effects of disturbances can be minimized whereas the resources can be utilized. In this situation weather forecast uncertainty and model based control are coupled. In this thesis a model of a storage facility of agricultural produce is used as an example for a weather controlled system.

The first step in reducing prediction uncertainty is taken by reducing the uncertainty in the weather forecast itself. A Kalman filter approach is used for this purpose. Weather forecast uncertainty is significantly reduced up to 10 hours for temperature, up to 32 hours for wind speed and up to 3 hours for global radiation by using this approach.

For a linearized model of the storage facility error propagation rules have been derived. The uncertainty of the output can therefore be analytically calculated. The medium range weather forecast, up to ten days ahead , consists of an ensemble of 50 forecasts. The mean and variance of these forecasts are used for model prediction and model output uncertainty prediction. Furthermore, by using optimal control in conjunction with a cost criterion, the uncertainty of the system state is incorporated into the cost criterion. As a result the control inputs shift towards parts with less uncertainty in the weather forecast. Finally, a numerical risk evaluation showed that if feedback is applied, as in receding horizon optimal control, the cost increase is limited to 5% for a 24 hour feedback interval.

Mathematical models are always an approximation of the real system. Model uncertainties arise in the model structure and/or in unknown parameter values. If measurements from the system are present, the model is fitted to the data by changing parameter values. Generally, parameters that are nonlinear in system model output are estimated by nonlinear least-squares (NLS) optimization algorithms. For systems that rational in their parameters a reparameterization method is proposed such that the new parameters can be estimated with ordinary least squares. As a result a modified predictor appears. In the noise free case this leads to the exact parameter estimates whereas a nonlinear least squares approach might end up in a local minimum. If noise is present, however, the linear estimates might be biased and the modified predictor has only a limited range. Because after linear reparameterization the data structure generally becomes errors-in-variables a bias compensated total least squares approach is used. The predictive performance of the modified predictor in this case largely improves and is regarded as a powerful alternative to the existing least squares methods.