Multimodel-based minimum bias control of a benchmark paper machine process

This paper presents a multimodel-based minimum bias (MB), long-range predictive control algorithm that minimizes the bias in the output using a multiobjective optimization method. To enhance the robustness of the control system, the MB control scheme is extended to the multimodel- or multicontroller- based MB control scheme, which establishes several models simultaneously. Models with relatively small prediction errors are selected to form a group of acceptable models. The final control is chosen to be the weighted average of the MB controls. Models with significant or large errors are reinitialized. The proposed MB control scheme is evaluated by application to a paper machine benchmark problem and its performance is compared with that of other controllers.     

Online machine learning modeling and predictive control of nonlinear systems with scheduled mode transitions

This work develops a model predictive control (MPC) scheme using online learning of recurrent neural network (RNN) models for nonlinear systems switched between multiple operating regions following a prescribed switching schedule. Specifically, an RNN model is initially developed offline to model process dynamics using the historical operational data collected in a small region around a certain steady-state. After the system is switched to another operating region under a Lyapunov-based MPC with suitable constraints to ensure satisfaction of the prescribed switching schedule policy, RNN models are updated using real-time process data to improve closed-loop performance. A generalization error bound is derived for the updated RNN models using the notion of regret, and closed-loop stability results are established for the switched nonlinear system under RNN-based MPC. Finally, a chemical process example with the operation schedule that requires switching between two steady-states is used to demonstrate the effectiveness of the proposed RNN-MPC scheme.     

Dynamic simulation and control of a paper machine wet end

A good simulation model for paper machines can be used to identify deficiencies in the design, bottlenecks during operation, and regions of poor control. It also allows users to test their hypotheses and innovations without potentially causing major upsets and reducing throughput. In this work, a dynamic model of the wet end system has been developed using the IDEAS^TM platform, describing the distribution of fines, fillers and fibres throughout the system. The model was then tested at steady state with mill data for the low‐ash and high‐ash production grades, and the results show that over 70% of the predicted values had only 5% deviation. The dynamic simulation was also used to show that the retention aid controller would react in the wrong direction due to changes in the wire pit consistency and the stock ratio would cause major changes in stream compositions and consistencies of the wet end.     

Measurement based modeling and control of bimodal particle size distribution in batch emulsion polymerization

In this article, a novel modeling approach is proposed for bimodal Particle Size Distribution (PSD) control in batch emulsion polymerization. The modeling approach is based on a behavioral model structure that captures the dynamics of PSD. The parameters of the resulting model can be easily identified using a limited number of experiments. The resulting model can then be incorporated in a simple learning scheme to produce a desired bimodal PSD while compensating for model mismatch and/or physical parameters variations using very simple updating rules. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Multiscale modeling and control of Kappa number and porosity in a batch-type pulp digester

This work proposes a multiscale modeling and model-based feedback control framework for the delignification process in a batch-type pulp digester. Specifically, we focus on a hardwood chip in the digester and develop a multiscale model capturing both the evolution of microscopic properties such as the pore size and shape distributions in the solid phase and the dynamic changes in the temperature and component concentrations in the liquor phase. While the macroscopic model adopts the continuum hypothesis based on the Purdue model, a novel microscopic model is developed using a kinetic Monte Carlo algorithm, accounting for the dissolution of lignin, cellulose, and hemicellulose contacting the liquor phase. A reduced-order model was built to design a Luenberger observer for state estimation, which is then used to develop a model-based control system. The simulation results demonstrated that the proposed methodology was able to regulate both the Kappa number and porosity to desired values.     

Some manifold learning considerations toward explicit model predictive control

Model predictive control (MPC) is a de facto standard control algorithm across the process industries. There remain, however, applications where MPC is impractical because an optimization problem is solved at each time step. We present a link between explicit MPC formulations and manifold learning to enable facilitated prediction of the MPC policy. Our method uses a similarity measure informed by control policies and system state variables, to “learn” an intrinsic parametrization of the MPC controller using a diffusion maps algorithm, which will also discover a low-dimensional control law when it exists as a smooth, nonlinear combination of the state variables. We use function approximation algorithms to project points from state space to the intrinsic space, and from the intrinsic space to policy space. The approach is illustrated first by “learning” the intrinsic variables for MPC control of constrained linear systems, and then by designing controllers for an unstable nonlinear reactor.     

Multiscale modeling and multiobjective control of wood fiber morphology in batch pulp digester

Even though it is widely known that mechanical properties of papers are dependent upon fiber morphology such as fiber length and cell wall thickness, existing macroscopic models are limited in describing the microscopic traits of pulp. Thus, we proposed a multiscale model by integrating a macroscopic model (i.e., Purdue model) and a microscopic model (i.e., kinetic Monte Carlo algorithm) to capture the dynamic evolution of the fiber morphology as well as conventional pulp quality index such as Kappa number. Then, a reduced-order model is identified to handle the computational requirement of the multiscale model, and implemented to a model-based controller to regulate both the fiber length and the Kappa number which are expressed in the forms of conflicting objective functions. The epsilon-constraint method is employed to find the Pareto optimal sets to provide decision makers with the degree of freedom to choose one according to their preferred end-use paper properties.     

Dynamic modeling and model predictive control of a continuous pulp digester

This work explores the design of a model predictive controller of the continuous pulp digester process consisting of the co-current zone and counter-current zone modeled by a set of nonlinear coupled hyperbolic partial differential equations (PDEs). The distributed parameter system of interest is not spectral, and slow–fast dynamic separation does not hold. To address this challenge, the nonlinear continuous-time model is linearized and discretized in time utilizing the Cayley–Tustin discretization framework, which ensures system theoretic properties and structure preservation without spatial discretization or model reduction. The discrete model is used in the full state model predictive controller design, which is augmented by the Luenberger observer design to achieve the output constrained regulation. Finally, a numerical example is provided to demonstrate the feasibility and applicability of the proposed controller designs.     

Modeling and predictive control of nonlinear processes using transfer learning method

This work develops a transfer learning (TL) framework for modeling and predictive control of nonlinear systems using recurrent neural networks (RNNs) with the knowledge obtained in modeling one process transferred to another. Specifically, transfer learning uses a pretrained model developed based on a source domain as the starting point, and adapts the model to a target process with similar configurations. The generalization error for TL-based RNN (TL-RNN) is first derived to demonstrate the generalization capability on the target process. The theoretical error bound that depends on model capacity and the discrepancy between source and target domains is then utilized to guide the development of pretrained models for improved model transferability. Subsequently, the TL-RNN model is utilized as the prediction model in model predictive controller (MPC) for the target process. Finally, the simulation study of chemical reactors via Aspen Plus Dynamics is used to demonstrate the benefits of transfer learning.     

从区间模型预测控制到双层结构模型预测控制

模型预测控制算法（MPC）存在设定点控制与区间控制两种策略,区间预测控制较之设定点控制在技术上具有先进性。目前,主流的预测控制软件技术均采用双层结构,即上层稳态优化计算最优设定点,下层动态控制负责动态跟踪最优设定点。从过程稳态的角度出发,分别对区间预测控制和双层结构预测控制进行了机理分析,从定性与定量两个方面比较了这两者的异同点,提出并证明了两者的一致性条件。论述了双层结构预测控制较之单层结构下的区间控制更具先进性。     

Nonlinear model predictive control based on support vector machine and genetic algorithm

This paper presents a nonlinear model predictive control (NMPC) approach based on support vector machine (SVM) and genetic algorithm (GA) for multiple-input multiple-output (MIMO) nonlinear systems. Individual SVM is used to approximate each output of the controlled plant. Then the model is used in MPC control scheme to predict the outputs of the controlled plant. The optimal control sequence is calculated using GA with elite preserve strategy. Simulation results of a typical MIMO nonlinear system show that this method has a good ability of set points tracking and disturbance rejection.     

An integrated framework for scheduling and control using fast model predictive control

Integration of scheduling and control involves extensive information exchange and simultaneous decision making in industrial practice (Engell and Harjunkoski, Comput Chem Eng. 2012;47:121–133; Baldea and Harjunkoski I, Comput Chem Eng. 2014;71:377–390). Modeling the integration of scheduling and dynamic optimization (DO) at control level using mathematical programming results in a Mixed Integer Dynamic Optimization which is computationally expensive (Flores‐Tlacuahuac and Grossmann, Ind Eng Chem Res. 2006;45(20):6698–6712). In this study, we propose a framework for the integration of scheduling and control to reduce the model complexity and computation time. We identify a piece‐wise affine model from the first principle model and integrate it with the scheduling level leading to a new integration. At the control level, we use fast Model Predictive Control (fast MPC) to track a dynamic reference. Fast MPC also overcomes the increasing dimensionality of multiparametric MPC in our previous study (Zhuge and Ierapetritou, AIChE J. 2014;60(9):3169–3183). Results of CSTR case studies prove that the proposed approach reduces the computing time by at least two orders of magnitude compared to the integrated solution using mp‐MPC. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3304–3319, 2015     

Iterative learning model predictive control for constrained multivariable control of batch processes

In this paper, we propose a model predictive control (MPC) technique combined with iterative learning control (ILC), called the iterative learning model predictive control (ILMPC), for constrained multivariable control of batch processes. Although the general ILC makes the outputs converge to reference trajectories under model uncertainty, it uses open-loop control within a batch; thus, it cannot reject real-time disturbances. The MPC algorithm shows identical performance for all batches, and it highly depends on model quality because it does not use previous batch information. We integrate the advantages of the two algorithms. The proposed ILMPC formulation is based on general MPC and incorporates an iterative learning function into MPC. Thus, it is easy to handle various issues for which the general MPC is suitable, such as constraints, time-varying systems, disturbances, and stochastic characteristics. Simulation examples are provided to show the effectiveness of the proposed ILMPC.     

Machine learning-based model predictive control of hybrid dynamical systems

This article presents a machine learning-based model predictive control (MPC) scheme for stabilization of hybrid dynamical systems, for which the evolution of states exhibits both continuous and discrete dynamics described by differential and difference equations, respectively. We first present the development of two recurrent neural networks (RNNs) for approximating continuous- and discrete-time dynamics of hybrid dynamical systems, respectively, and then construct a unified hybrid RNN by integrating the two RNN models to capture both continuous and discrete dynamics. The hybrid RNN is used as the prediction model in Lyapunov-based MPC (RNN-LMPC), under which closed-loop stability of hybrid dynamical systems is established. Finally, two case studies including a bouncing ball example and a chemical process are utilized to illustrate the open- and closed-loop performance of the proposed RNN-LMPC scheme.     

基于样条插值模型的间歇精馏模拟与预测控制

以Aspen Batch Distillation（ABD）中的间歇精馏仿真系统为过程原型,提出了利用过程的模拟测试数据来建立间歇精馏过程的样条插值简化模型（spline interpolation model, SIM）。结合变回流比下的动态修正函数,构造出了一种简单实用的动态模型。该模型可有效模拟不同组分浓度下回流比发生变化时馏出液浓度和流量的动态变化情况。以该模型作为预测模型,进一步提出了一种变回流比的预测控制（model predictive control, MPC）算法来使馏出液浓度按照期望的设定值变化。控制仿真结果表明该控制方案计算简单,同时具有较好的控制效果。     

Actuator stiction compensation via model predictive control for nonlinear processes

The problem of valve stiction is addressed, which is a nonlinear friction phenomenon that causes poor performance of control loops in the process industries. A model predictive control (MPC) stiction compensation formulation is developed including detailed dynamics for a sticky valve and additional constraints on the input rate of change and actuation magnitude to reduce control loop performance degradation and to prevent the MPC from requesting physically unrealistic control actions due to stiction. Although developed with a focus on stiction, the MPC‐based compensation method presented is general and has potential to compensate for other nonlinear valve dynamics which have some similarities to those caused by stiction. Feasibility and closed‐loop stability of the proposed MPC formulation are proven for a sufficiently small sampling period when Lyapunov‐based constraints are incorporated. Using a chemical process example with an economic model predictive controller (EMPC), the selection of appropriate constraints for the proposed method is demonstrated. The example verified the incorporation of the stiction dynamics and actuation magnitude constraints in the EMPC causes it to select set‐points that the valve output can reach and causes the operating constraints to be met. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2004–2023, 2016