Factorized f-step radial basis function model for model predictive control

This paper proposes a new factorized f-step radial basis function network (FS-RBF) model for model predictive control (MPC). The strategy is to develop a f-step predictor for nonlinear dynamic systems and implement it with a RBF network. In contrast to the popular NARX-RBF model, the developed FS-RBF model is capable of making a designated sequence of future output prediction without requiring the unknown future process measurements. Furthermore, the developed FS-RBF model is factorized into two parts, with one part including past plant input/output and the other part including the future input/output. When this model is used as the internal model in the MPC, the factorization enables an explicit objective function for the on-line optimization in the MPC. Thus, the computing load in solving the optimization problem is greatly reduced. The developed model is used in MPC and applied to a continuous-stirred tank reactor (CSTR). The simulation results are compared with that of MPCs with other two models. The comparison confirms that the developed model make more accurate prediction so that the MPC performance is better, it also uses much less computing time than the other two models based MPC

Development of Adaptive and Factorized Neural Models for MPC of Industrial Systems

Many industrial processes have non-linear and time-varying dynamics, for which the control and optimization require further investigations. Adaptive modelling techniques using radial basis function (RBF) networks often provide competitive modelling performances but encounter slow recovery speed when processes operating regions are shifted largely. In addition, RBF networks based model predictive control results as a non-linear programming problem, which restricts the application to fast dynamic systems. To these targets, the thesis presents the development of adaptive and factorized RBF network models. Model predictive control (MPC) based on the factorized RBF model is applied to a non-linear proton exchange membrane fuel cell (PEMFC) stack system. The main contents include three parts: RBF model adaptation; model factorization and fast long-range prediction; and MPC for the PEMFC stack system. The adaptive RBF model employs the recursive orthogonal least squares (ROLS) algorithm for both structure and parameter adaptation. In decomposing the regression matrix of the RBF model, the R matrix is obtained. Principles for adding centres and pruning centres are developed based on the manipulation of the R matrix. While the modelling accuracy is remained, the developed structure adaptation algorithm ensures the model size to be kept to the minimum. At the same time, the RBF model parameters are optimized in terms of minimum Frobenius norm of the model prediction error. A simulation example is used to evaluate the developed adaptive RBF model, and the model performance in output prediction is superior over the existing methods. Considering that a model with fast long-range prediction is needed for the MPC of fast dynamic systems, a f-step factorization algorithm is developed for the RBF model. The model structure is re-arranged so that the unknown future process outputs are not required for output prediction. Therefore, the accumulative error caused by recursive calculation in normal neural network model is avoided. Furthermore, as the information for output prediction is explicitly divided into the past information and the future information, the optimization of the control variable in the MPC based on this developed factorized model can be solved much faster than the normal NARX-RBF model. The developed model adaptation algorithm can be applied to this f-step factorized model to achieve fast and adaptive model prediction. Finally, the developed factorized RBF model is applied to the MPC of a PEMFC stack system with a popular industrial benchmark model in Simulink developed at Michigan University. The optimization algorithms for quadratic and non-linear system without and with constraints are presented and discussed for application purpose in the NMPC. Simulation results confirm the effectiveness of the developed model in both smooth tracking performance and less optimization time used. Conclusions and further work are given at the end of the thesis. Major contributions of the research have been outlined and achievements are checked against the objectives assigned. Further work is also suggested to extend the developed work to industrial applications in real-time simulation. This is to further examine the effectiveness of developed models. Extensive investigations are also recommended on the optimization problems to improve the existing algorithms