PID based nonlinear processes control model uncertainty improvement by using Gaussian process model

• Gaussian process (GP) model based self-tuning PID is proposed.
• Safety-performance trade-off control is achieved by incorporating the variance.
• Selecting complementary data to update the model is heuristic.
• The instantaneous linearization of GP model reduces calculation load.
• The proposed methodology is applied to pH process and fed-batch fermentation.

Proportional-integral-derivative (PID) controller design based on the Gaussian process (GP) model is proposed in this study. The GP model, defined by its mean and covariance function, provides predictive variance in addition to the predicted mean. GP model highlights areas where prediction quality is poor, due to the lack of data, by indicating the higher variance around the predicted mean. The variance information is taken into account in the PID controller design and is used for the selection of data to improve the model at the successive stage. This results in a trade-off between safety and the performance due to the controller avoiding the region with large variance at the cost of not tracking the set point to ensure process safety. The proposed direct method evaluates the PID controller design by the gradient calculation. In order to reduce computation the characteristic of the instantaneous linearized GP model is extracted for a linearized framework of PID controller design. Two case studies on continuous and batch processes were carried out to illustrate the applicability of the proposed method.