Modeling of batch processes using explicitly time-dependent artificial neural networks

Event-Based Switching Iterative Learning Model Predictive Control for Batch Processes With Randomly Varying Trial Lengths

Iterative learning model predictive control (ILMPC) has been recognized as an excellent batch process control strategy for progressively improving tracking performance along trials. However, as a typical learning-based control method, ILMPC generally requires the strict identity of trial lengths to implement 2-D receding horizon optimization. The randomly varying trial lengths extensively existing in practice can result in the insufficiency of learning prior information, and even the suspension of control update. Regarding this issue, this article embeds a novel prediction-based modification mechanism into ILMPC, to adjust the process data of each trial into the same length by compensating the data of absent running periods with the predictive sequences at the end point. Under this modification scheme, it is proved that the convergence of the classical ILMPC is guaranteed by an inequality condition relative with the probability distribution of trial lengths. Considering the practical batch process with complex nonlinearity, a 2-D neural-network predictive model with parameter adaptability along trials is established to generate highly matched compensation data for the prediction-based modification. To best utilize the real process information of multiple past trials while guaranteeing the learning priority of the latest trials, an event-based switching learning structure is proposed in ILMPC to determine different learning orders according to the probability event with respect to the trial length variation direction. The convergence of the nonlinear event-based switching ILMPC system is analyzed theoretically under two situations divided by the switching condition. The simulations on a numerical example and the injection molding process verify the superiority of the proposed control methods.

A two-stage robust iterative learning model predictive control for batch processes

Iterative learning model predictive control (ILMPC) has been considered as potential control strategy for batch processes. ILMPC can converge to the desired reference trajectory with high precision along batches and ensure system stability within batches. However, as a model-based control method, the control performance of the ILMPC algorithm deteriorates when exists model parameter uncertainty. Therefore, guaranteeing system tracking performance in the case of model parameter uncertainty is a challenging task in the framework designing of ILMPC method. To this end, we develop a two-stage robust ILMPC strategy for batch processes, which integrates the robust iterative learning control (ILC) in the domain of batch-axis and robust model predictive control (MPC) in the domain of time-axis into one comprehensive control scheme. The integrated control law of the developed two-stage robust ILMPC algorithm is obtained by solving two convex optimization problems. As a result, the developed control method obtains faster convergence speed and better tracking performance in the case of model parameter uncertainty. Moreover, the convergence analysis of the system is presented. Finally, comparative simulations are provided to verify the superiority of the developed control algorithm.

Iterative Learning Model Predictive Control Based on Iterative Data-Driven Modeling

Iterative learning model predictive control (ILMPC) has been recognized as an effective approach to realize high-precision tracking for batch processes with repetitive nature because of its excellent learning ability and closed-loop stability property. However, as a model-based strategy, ILMPC suffers from the unavailability of accurate first principal model in many complex nonlinear batch systems. On account of the abundant process data, nonlinear dynamics of batch systems can be identified precisely along the trials by neural network (NN), making it enforceable to design a data-driven ILMPC. In this article, by using a control-affine feedforward neural network (CAFNN), the features in the process data of the former batch are extracted to form a nonlinear affine model for the controller design in the current batch. Based on the CAFNN model, the ILMPC is formulated in a tube framework to attenuate the influence of modeling errors and track the reference trajectory with sustained accuracy. Due to the control-affine structure, the gradients of the objective function can be analytically computed offline, so as to improve the online computational efficiency and optimization feasibility of the tube ILMPC. The robust stability and the convergence of the data-driven ILMPC system are analyzed theoretically. The simulation on a typical batch reactor verifies the effectiveness of the proposed control method.

Novel Formulation of Adaptive MPC as EKF Using ANN Model: Multiproduct Semibatch Polymerization Reactor Case Study

In this paper, a novel formulation for nonlinear model predictive control (MPC) has been proposed incorporating the extended Kalman filter (EKF) control concept using a purely data-driven artificial neural network (ANN) model based on measurements for supervisory control. The proposed scheme consists of two modules focusing on online parameter estimation based on past measurements and control estimation over control horizon based on minimizing the deviation of model output predictions from set points along the prediction horizon. An industrial case study for temperature control of a multiproduct semibatch polymerization reactor posed as a challenge problem has been considered as a test bed to apply the proposed ANN-EKFMPC strategy at supervisory level as a cascade control configuration along with proportional integral controller [ANN-EKFMPC with PI (ANN-EKFMPC-PI)]. The proposed approach is formulated incorporating all aspects of MPC including move suppression factor for control effort minimization and constraint-handling capability including terminal constraints. The nominal stability analysis and offset-free tracking capabilities of the proposed controller are proved. Its performance is evaluated by comparison with a standard MPC-based cascade control approach using the same adaptive ANN model. The ANN-EKFMPC-PI control configuration has shown better controller performance in terms of temperature tracking, smoother input profiles, as well as constraint-handling ability compared with the ANN-MPC with PI approach for two products in summer and winter. The proposed scheme is found to be versatile although it is based on a purely data-driven model with online parameter estimation.

Parameterized data-driven fuzzy model based optimal control of a semi-batch reactor

A parameterized data-driven fuzzy (PDDF) model structure is proposed for semi-batch processes, and its application for optimal control is illustrated. The orthonormally parameterized input trajectories, initial states and process parameters are the inputs to the model, which predicts the output trajectories in terms of Fourier coefficients. Fuzzy rules are formulated based on the signs of a linear data-driven model, while the defuzzification step incorporates a linear regression model to shift the domain from input to output domain. The fuzzy model is employed to formulate an optimal control problem for single rate as well as multi-rate systems. Simulation study on a multivariable semi-batch reactor system reveals that the proposed PDDF modeling approach is capable of capturing the nonlinear and time-varying behavior inherent in the semi-batch system fairly accurately, and the results of operating trajectory optimization using the proposed model are found to be comparable to the results obtained using the exact first principles model, and are also found to be comparable to or better than parameterized data-driven artificial neural network model based optimization results.

Nonlinear Model Predictive Control Based on a Self-Organizing Recurrent Neural Network

A nonlinear model predictive control (NMPC) scheme is developed in this paper based on a self-organizing recurrent radial basis function (SR-RBF) neural network, whose structure and parameters are adjusted concurrently in the training process. The proposed SR-RBF neural network is represented in a general nonlinear form for predicting the future dynamic behaviors of nonlinear systems. To improve the modeling accuracy, a spiking-based growing and pruning algorithm and an adaptive learning algorithm are developed to tune the structure and parameters of the SR-RBF neural network, respectively. Meanwhile, for the control problem, an improved gradient method is utilized for the solution of the optimization problem in NMPC. The stability of the resulting control system is proved based on the Lyapunov stability theory. Finally, the proposed SR-RBF neural network-based NMPC (SR-RBF-NMPC) is used to control the dissolved oxygen (DO) concentration in a wastewater treatment process (WWTP). Comparisons with other existing methods demonstrate that the SR-RBF-NMPC can achieve a considerably better model fitting for WWTP and a better control performance for DO concentration.