ANN model adaptation algorithm based on extended Kalman filter applied to pH control using MPC

Abstract

The performance of model predictive controllers (MPCs) strongly depends on the precision of the prediction model. Nonlinear systems, such as neutralization reactors, provide special challenges to MPC design. Linear prediction models may be inadequate to describe the process at all operating points. One alternative is the use of artificial neural networks (ANNs) as prediction models. ANNs are nonlinear structures that can be trained to reproduce the process behavior. Inside MPC schemes, ANNs can rapidly predict the process response to a control action. The time-consuming step for ANN training is to obtain a representative overall data set from experiments or simulation data from the studied process. In the present work, we propose to obtain this data set from computational simulations using a first principles model. However, mismatches were found between rigorous simulation and actual pH process responses. Those deviations were naturally transferred to the internal neural model, as a consequence, actual control problems were identified. Avoiding high costs of performing actual experimental runs for ANN and MPC design, we used a real-time adaptation algorithm, based on extended Kalman filter (EKF), that acts to correct the ANN prediction while process is running. The adaptive model ANN-based MPC was able to maintain the actual controlled process, in all operating conditions tested. The sum of square error of pH was reduced in 64.3%, compared to the ANN-based MPC without model adaptation. Using a Kalman filter to adapt the internal model has significantly improved the MPC performance, reducing oscillations and maintaining the controlled variable in the setpoint, even in servo regulatory situations of industrial practice. In addition, the proposed scheme has great potential for controlling highly nonlinear processes.