Nonlinear internal model control strategy for neural network models

A nonlinear internal model control (NIMC) strategy based on neural network models is proposed for SISO processes. The neural network model is identified from input—output data using a three-layer feedforward network trained with a conjugate gradient algorithm. The NIMC controller consists of a model inverse controller and a robustness filter with a single tuning parameter. The proposed strategy includes time delay compensation in the form of a Smith predictor and ensures offset-free performance. Extensions for measured disturbances are also presented. The NIMC approach is currently restricted to processes with stable inverses. Two alternative implementations of the control law are discussed and simulations results for a continuous stirred tank reactor and pH neutralization process are presented. The results for these two highly-nonlinear processes demonstrate the ability of the new strategy to outperform conventional PID control.     

A linear model predictive control algorithm for nonlinear large‐scale distributed parameter systems

This work provides a framework for linear model predictive control (MPC) of nonlinear distributed parameter systems (DPS), allowing the direct utilization of existing large‐scale simulators. The proposed scheme is adaptive and it is based on successive local linearizations of the nonlinear model of the system at hand around the current state and on the use of the resulting local linear models for MPC. At every timestep, not only the future control moves are updated but also the model of the system itself. A model reduction technique is integrated within this methodology to reduce the computational cost of this procedure. It follows the equation‐free approach (see Kevrekidis et al., Commun Math Sci. 2003;1:715–762; Theodoropoulos et al., Proc Natl Acad Sci USA. 2000;97:9840‐9843), according to which the equations of the model (and consequently of the simulator) need not be given explicitly to the controller. The latter forms a “wrapper” around an existing simulator using it in an input/output fashion. This algorithm is designed for dissipative DPS, dissipativity being a prerequisite for model reduction. The equation‐free approach renders the proposed algorithm appropriate for multiscale systems and enables it to handle large‐scale systems. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Economic model predictive control of nonlinear process systems using empirical models

Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained either through application of first principles or through system identification techniques. In industrial practice, it may be difficult in general to obtain an accurate first‐principles model of the process. Motivated by this, in the present work, Lyapunov‐based EMPC (LEMPC) is designed with a linear empirical model that allows for closed‐loop stability guarantees in the context of nonlinear chemical processes. Specifically, when the linear model provides a sufficient degree of accuracy in the region where time varying economically optimal operation is considered, conditions for closed‐loop stability under the LEMPC scheme based on the empirical model are derived. The LEMPC scheme is applied to a chemical process example to demonstrate its closed‐loop stability and performance properties as well as significant computational advantages. © 2014 American Institute of Chemical Engineers AIChE J, 61: 816–830, 2015     

一种基于速率线性化的非线性预测控制算法

提出了一种基于速率线性化方法的非线性预测控制算法。该算法采用速率线性化方法得到与原系统非线性模型相对应的线性变参数模型,这类变参数模型在结构上是线性的,而模型参数将随工作条件的变化而变化,在系统的整个工作区间内都能很好地逼近原非线性模型。在此模型的基础上设计了预测控制器,并利用基于置信域的Levenberg-Marquardt算法在线求得预测控制率。最后对连续搅拌反应釜进行了仿真研究,仿真结果表明了该算法的可行性和有效性。     

Nonlinear dimension reduction based neural modeling for distributed parameter processes

Many chemical processes are nonlinear distributed parameter systems with unknown uncertainties. For this class of infinite-dimensional systems, the low-order model identification from process data is very important in practice. The dimension reduction with a principal component analysis (PCA) is only a linear approximation for nonlinear problem. In this study, a nonlinear dimension reduction based low-order neural model identification approach is proposed for nonlinear distributed parameter processes. First, a nonlinear principal component analysis (NL-PCA) network is designed for the nonlinear dimension reduction, which can transform the high-dimensional spatio-temporal data into a low-dimensional time domain. Then, a neural system can be easily identified to model this low-dimensional temporal data. Finally, the spatio-temporal dynamics can be reproduced using the nonlinear time/space reconstruction. The simulations on a typical nonlinear transport-reaction process show that the proposed approach can achieve a better performance than the linear PCA based modeling approach.     

Sequential and iterative architectures for distributed model predictive control of nonlinear process systems

In this work, we focus on distributed model predictive control of large scale nonlinear process systems in which several distinct sets of manipulated inputs are used to regulate the process. For each set of manipulated inputs, a different model predictive controller is used to compute the control actions, which is able to communicate with the rest of the controllers in making its decisions. Under the assumption that feedback of the state of the process is available to all the distributed controllers at each sampling time and a model of the plant is available, we propose two different distributed model predictive control architectures. In the first architecture, the distributed controllers use a one‐directional communication strategy, are evaluated in sequence and each controller is evaluated only once at each sampling time; in the second architecture, the distributed controllers utilize a bi‐directional communication strategy, are evaluated in parallel and iterate to improve closed‐loop performance. In the design of the distributed model predictive controllers, Lyapunov‐based model predictive control techniques are used. To ensure the stability of the closed‐loop system, each model predictive controller in both architectures incorporates a stability constraint which is based on a suitable Lyapunov‐based controller. We prove that the proposed distributed model predictive control architectures enforce practical stability in the closed‐loop system and optimal performance. The theoretical results are illustrated through a catalytic alkylation of benzene process example. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

BP神经网络计算乙醇-环己烷-水体系汽-液平衡

基于带动量因子的 BP神经网络 ,以实验测定的乙醇 (1) -环己烷 (2 ) -水 (3)体系在 35℃、5 0℃、6 5℃的汽液平衡数据为训练和预测样本进行了计算 ,选择温度、X1 和 X2 3个参数作为输入 ,Y1 、Y2 和 Y3作为输出 ,隐层单元数为 9,学习速率为 0 .5 ,动量因子为 0 .12 8。对 Y1 ,Y2 ,Y3,神经网络计算的训练平均误差分别为 :0 .0 0 71,0 .0 101,0 .0 0 6 0 ,预测平均误差分别为 :0 .0 0 6 5 ,0 .0 12 4 ,0 .0 0 6 0 ,小于 NRTL 模型计算的相应误差。为相平衡计算提供了新的有效的工具。     

Nonlinear system identification and model reduction using artificial neural networks

We present a technique for nonlinear system identification and model reduction using artificial neural networks (ANNs). The ANN is used to model plant input–output data, with the states of the model being represented by the outputs of an intermediate hidden layer of the ANN. Model reduction is achieved by applying a singular value decomposition (SVD)-based technique to the weight matrices of the ANN. The sequence of state values is used to convert the model to a form that is useful for state and parameter estimation. Examples of chemical systems (batch and continuous reactors and distillation columns) are presented to demonstrate the performance of the ANN-based system identification and model reduction technique.     

转炉炼钢多变量神经网络预报模型

终点钢水温度和碳、硫、磷等成分含量的有效控制是转炉炼钢过程的重要任务。本文基于多变量输入输出的神经网络来建立转炉炼钢的预报模型,首先对采集数据进行预处理,并采用滚动优化方法来提高模型的准确性,仿真与试验对比证实了该方法建立模型的有效性和高命中率。     

Feedback control of hyperbolic distributed parameter systems

Hyperbolic distributed parameter systems (DPS) represent a large number of industrial processes with spatially nonuniform operating variable profiles. Research has been conducted to develop high-performance control strategies for these systems by exploiting their high-fidelity models. In this paper, a feedback control method that yields improved performance is proposed for DPS modelled by first-order hyperbolic partial differential equations (PDEs) using the method of characteristics. Simulation results show that this method can provide effective control for the systems modelled by a scalar PDE as well as a system of PDEs. Further, it can efficiently compensate the effect of model-plant mismatch and effectively reject the disturbances.     

基于全局正交配置的非线性预测控制算法

针对非线性预测控制(NMPC)在线优化计算量大这一关键问题,提出一种基于全局正交配置的非线性预测控制算法。该算法以高阶插值正交多项式为基函数同时配置优化时域内的状态变量和控制变量,将连续动态优化问题转化为非线性规划问题(NLP)求解。全局正交配置可以使用较少的配置点而获得较高的逼近精度,这样即使NMPC使用很长的优化时域,离散化后得到的NLP问题的规模也比较小,能够有效地降低在线优化计算量。最后,以连续聚合反应过程为例验证了算法的有效性。     

Nonlinear model predictive control for dividing wall columns

Dividing wall columns (DWCs) are practical, effective, and promising among distillation process intensification technologies. Nonlinear model predictive control (NMPC) schemes are developed in this study to control the three-product DWCs. As these systems are intensely interactive and highly nonlinear, NMPC may be more suitable than the traditional PI control. The model is established based on Python and Pyomo platforms. As the original mathematical model of the column section is ill-posed, index reduction is used to avoid a high-index differential-algebraic equation (DAE) system. The well-posed index-1 system after index reduction is employed for the steady-state simulation and dynamic control in this study. Case studies with three DWC configurations to separate the mixture of ethanol (A), n-propanol (B), and n-butanol (C) show that the NMPC performs very well with small maximum deviations and short settling times. This demonstrates that the NMPC is a feasible and very effective scheme to control three-product DWCs.     

Differential recurrent neural network based predictive control

In this paper an efficient algorithm to train general differential recurrent neural network (DRNN) is developed. The trained network can be directly used in the nonlinear model predictive control (NMPC) context. The neural network is represented in a general nonlinear state-space form and used to predict the future dynamic behavior of the nonlinear process in real time. In the new training algorithms, the ODEs of the model and the dynamic sensitivity are solved simultaneously using Taylor series expansion and automatic differentiation (AD) techniques. The same approach is also used to solve the online optimization problem in the predictive controller. The efficiency and effectiveness of the DRNN training algorithm and the NMPC approach are demonstrated through a two-CSTR case study. A good model fitting for the nonlinear plant at different sampling rates is obtained using the new method. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. The DRNN based NMPC approach results in good control performance under different operating conditions.     

Nonlinear predictive control using multi-rate sampling

A nonlinear predictive control (NLPC) strategy based on a nonlinear, lumped parameter model of the process is developed in this paper. A constrained optimization approach is used to estimate unmeasured state variables and load disturbances. Additional model/process mismatch is handled by using an additive output term which is equivalent to the Internal Model Control approach. Similar to linear predictive control methods, an optimal sequence of future control moves is determined in order to minimize an objective function based on a desired output trajectory, subject to manipulated variable constraints (absolute and velocity). Deadtime is explicitly included in the model formulation, giving NLPC the same deadtime compensation feature of linear model-predictive techniques. The multi-rate sampling nature of most chemical processes is also used to improve estimates of process disturbances. Infrequent composition measurements in conjunction with frequent temperature measurements are used to improve the “inferential” control of the composition in a continuous flow stirred tank reactor (CSTR).     

Active design of dynamic GP models for model predictive control using expected improvement

Modelling is a basic and key requirement for model-based controlling, monitoring, or other process strategies. In non-linear model predictive control (NMPC), although data-driven models can be more easily established than first-principle ones, representative data may not be adequately included in advance to train a complete model, which is an attractive research topic. An actively improved Gaussian process (GP) model building strategy is developed, especially for incomplete models based on the idea of Bayesian optimization. The GP model can be used online as the internal model of model predictive control (MPC) directly. The model-building objective is based on the expected improvement strategy, which can exploit information gained from the currently gathered data as well as explore uncharted regions. The proposed method is a real-time design of experiments based on variance information of GP for efficient model building with insufficient initial training data for NMPC. Multi-step ahead prediction model is considered to give full play to predicting features of NPMC. Besides, a novel disturbance rejection strategy is also proposed based on GP outputs. Two simulation results, including comparisons with some traditional algorithms, are presented to demonstrate the effectiveness of the proposed method.     

鲁棒模型预测控制系统的评估基准

在控制系统的性能评估中,基准的设计是个重要问题。将基本设计极限理论推广到模型预测控制系统(MPC),建立性能评估基准。直接考虑多输入多输出系统的频域扰动,建立输出反馈鲁棒模型预测控制器。此控制器仅仅依赖于过程参数,也是令闭环系统达到控制性能极限的基准控制器。建立了用于评估的性能指标,提出基于此基准的性能评估程序,用以评价其他模型预测控制系统的性能。数学算例证实了这一评估程序的有效性。     

Simulation of hydrodesulfurization using artificial neural network

Artificial neural network (ANN) is applied to investigate the hydrodesulfurization (HDS) process with light‐cycle oil as feed and NiMo/Al₂O₃ as catalyst. ANN models frequently work as a “black box” which makes the model invisible to users and always need significant data for training. In this work, a new ANN is proposed. The Langmuir–Hinshelwood kinetic mechanism is incorporated into the model so that the proposed ANN model is forced to follow the given reaction mechanisms. Both advantages of self‐learning ability of ANN and the existing knowledge of HDS were taken into account. Lengthy training process is minimised. Effects of operating temperature, pressure, and LHSV on the sulfur removal rate are studied. The inhibition of nitrogen compounds is also investigated. It is shown that the presence of nitrogen can significantly reduce the conversion rate of sulfur components, in particularly, hard sulfur such as 4,6‐DMDBT.     

Selection of control configurations for economic model predictive control systems

Economic model predictive control (EMPC) is a feedback control method that dictates a potentially dynamic (time‐varying) operating policy to optimize the process economics. The objective function used in the EMPC system may be a general nonlinear function that describes the process/system economics. As this function is not derived on the sole basis of classical control considerations (stabilization, tracking, and optimal control action calculation) but rather on the basis of economics, selecting the appropriate control configuration, and quantifying the influence of a given input on an economic cost is an important task for the proper design and computational efficiency of an EMPC scheme. Owing to these considerations, an input selection methodology for EMPC is proposed which utilizes the relative degree and the sensitivity of the economic cost with respect to an input to identify and select stabilizing manipulated inputs with the most dynamic and steady‐state influence on the economic cost function to be assigned to EMPC. Other considerations for input selection for EMPC are also discussed and integrated into a proposed input selection methodology for EMPC. The control configuration selection method for EMPC is demonstrated using a chemical process example. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3230–3242, 2014     

分布式预测控制全局协调及稳定性分析

实际的化工过程系统维数都较高,对系统进行关联分解并使各子系统进行协调来实现整个大系统全局最优是必要的。对于关联作用存在反馈的化工过程大系统,分散式预测控制算法和基于串联过程推导的邻域优化分布式预测控制算法都不适用,因此在这两个算法的基础上推导出约束条件下基于全局协调的分布式预测控制算法。针对分解后得到的子系统,假设子系统间关联信息的传递存在一个采样时间的滞后,建立每个子系统的预测模型时考虑滞后的关联信息;建立子系统的目标函数时,综合考虑所有关联子系统的输入和输出对本子系统的关联作用;每个子系统滚动优化并行求解各自的最优控制作用。然后,在一定条件下分析了基于全局协调的分布式预测控制算法与集中预测控制算法的一致性,并说明了闭环系统的全局稳定性。最后,通过对Shell公司重油分馏塔和TE过程两个例子进行仿真并与其他算法进行比较,验证了本文提出算法的可行性和有效性。