NEURAL NETWORK-BASED PREDICTIVE CONTROL FOR MULTIVARIABLE PROCESSES

In this paper, the systematic derivations of setting up a nonlinear model predictive control based on the neural network are presented. This extends our previous work (Chen, 1998) into a multivariable system to explore the characteristics of the design. There are two stages for the development of nonlinear neural network predictive control: a neural network model and a control design. In the neural network model design, a parallel multiple-input, single-output neural network autoregressive with a model of exogenous inputs (NNARX) is proposed for multistep ahead predictions. In control design, the controller with extended control horizon is developed. The Levenberg-Marquardt algorithm is applied to training the NNARX model. Also, the sequential quadratic programming is used to search for the optimal manipulated inputs. The gradient of the objective function and constraints that require computation of Jacobian matrices are completely derived for optimization calculation. To demonstrate the control ability of MIMO cases, the proposed method is applied through two nonlinear simulation problems.     

The design of experiments,training and implementation of nonlinear controllers based on neural networks

In the area of nonlinear predictive control, several control schemes using artificial neural networks have been proposed. In this work, the issues relating to the information contents of the data used to train the neural network components of these nonlinear predictive control schemes are considered. This raises questions about the design of experiments. A class of feedback-feedforward nonlinear controller based on the model predictive structure (also known as Internal Model Control, IMC, structure) is investigated. The implementation and performance of these neural network based controllers, together with comparisons to other nonlinear and linear controllers, are illustrated on two nonlinear continuous-stirred-tank-reactor simulations.     

基于Tent混沌优化的神经网络预测控制

With the unique ergodicity, irregularity, and special ability to avoid being trapped in local optima, chaos optimization has been a novel global optimization technique and has attracted considerable attention for application in various fields, such as nonlinear programming problems. In this article, a novel neural network nonlinear predictive control (NNPC) strategy based on the new Tent-map chaos optimization algorithm (TCOA) is presented. The feedforward neural network is used as the multi-step predictive model. In addition, the TCOA is applied to perform the nonlinear rolling optimization to enhance the convergence and accuracy in the NNPC. Simulation on a laboratory-scale liquid-level system is given to illustrate the effectiveness of the proposed method.     

Neural‐Networks‐Based Feedback Linearization versus Model Predictive Control of Continuous Alcoholic Fermentation Process

In this work advanced nonlinear neural networks based control system design algorithms are adopted to control a mechanistic model for an ethanol fermentation process. The process model equations for such systems are highly nonlinear. A neural network strategy has been implemented in this work for capturing the dynamics of the mechanistic model for the fermentation process. The neural network achieved has been validated against the mechanistic model. Two neural network based nonlinear control strategies have also been adopted using the model identified. The performance of the feedback linearization technique was compared to neural network model predictive control in terms of stability and set point tracking capabilities. Under servo conditions, the feedback linearization algorithm gave comparable tracking and stability. The feedback linearization controller achieved the control target faster than the model predictive one but with vigorous and sudden controller moves.     

Machine-learning-based construction of barrier functions and models for safe model predictive control

In this paper, we propose a control Lyapunov-barrier function-based model predictive control method utilizing a feed-forward neural network specified control barrier function (CBF) and a recurrent neural network (RNN) predictive model to stabilize nonlinear processes with input constraints, and to guarantee that safety requirements are met for all times. The nonlinear system is first modeled using RNN techniques, and a CBF is characterized by constructing a feed-forward neural network (FNN) model with unique structures and properties. The FNN model for the CBF is trained based on data samples collected from safe and unsafe operating regions, and the resulting FNN model is verified to demonstrate that the safety properties of the CBF are satisfied. Given sufficiently small bounded modeling errors for both the FNN and the RNN models, the proposed control system is able to guarantee closed-loop stability while preventing the closed-loop states from entering unsafe regions in state-space under sample-and-hold control action implementation. We provide the theoretical analysis for bounded unsafe sets in state-space, and demonstrate the effectiveness of the proposed control strategy using a nonlinear chemical process example with a bounded unsafe region.     

基于Tent混沌优化的神经网络预测控制

With the unique erggdicity, i rregularity, and.special ability to avoid being trapped in local optima, chaos optimization has been a novel global optimization technique and has attracted considerable attention for application in various fields, such as nonlinear programming problems. In this article, a novel neural network nonlinear predic-tive control （NNPC） strategy baseed on the new Tent-map chaos optimization algorithm （TCOA） is presented. Thefeedforward neural network＇is used as the multi-step predictive model. In addition, the TCOA is applied to perform the nonlinear rolling optimization to enhance the convergence and accuracy in the NNPC. Simulation on a labora-tory-scale liquid-level system is given to illustrate the effectiveness of the proposed method.     

一类化工过程多变量系统的自适应非线性预测控制

针对化工过程的一类多变量非线性系统,提出了一种自适应非线性预测控制(ANMPC)算法。在采用递归最小二乘法进行预测模型参数在线辨识的基础上,将系统的静态非线性关系用一个反向传播(BP)神经网络稳态模型来表示,通过稳态模型求得的动态增益来进一步校正预测模型的参数。详述了ANMPC控制器设计步骤,通过在一个多变量pH中和过程中的仿真验证了本算法的可行性和有效性。     

基于自适应模糊神经网络的非线性系统模型预测控制

针对非线性动态系统的控制问题,提出了一种基于自适应模糊神经网络(adaptive fuzzy neural network, AFNN)的模型预测控制(model predictive control, MPC)方法。首先,在离线建模阶段,AFNN采用规则自分裂技术产生初始模糊规则,采用改进的自适应LM学习算法优化网络参数;然后,在实时控制过程,AFNN根据系统输出和预测输出之间的误差调整网络参数,从而为MPC提供一个精确的预测模型;进一步,AFNN-MPC利用带有自适应学习率的梯度下降寻优算法求解优化问题,在线获取非线性控制量,并将其作用到动态系统实施控制。此外,给出了AFNN-MPC的收敛性和稳定性证明,以保证其在实际工程中的成功应用。最后,利用数值仿真和双CSTR过程进行实验验证。结果表明,AFNN-MPC能够取得优越的控制性能。     

A Comparative Study of Combined Feedforward/Feedback Model Predictive Control for Nonlinear Systems

Model predictive control (MPC) provides a natural framework to realize feedforward and feedback control for nonlinear systems where the effect of disturbances (DVs) cannot be separated from that of manipulated variables (MVs). This study examines the performance of MPC with measured DVs as partial inputs of the model used, which is termed as combined feedforward/feedback MPC (CMPC) in contrast to conventional MPC using a model without input of any measured DV. In the simulation of a pH process, we demonstrate the clear superiority of CMPC over MPC. In the experiment with a bench‐scale ethanol and water distillation column, CMPC and MPC using artificial neural network (ANN) models are applied to the dual temperature control problem. External recurrent neural networks (ERNs) with and without a measured DV (feed rate of the column) as their partial input are built and employed in the experiment, with a result that inclusion of the measured DV in the model makes CMPC perform significantly better than MPC. To strengthen practical experience in applying ANN‐based MPC, a detailed procedure of the experiment is also documented.     

MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

Control of nonisothermal CSTR with time varying parameters via dynamic neural network control (DNNC)

Dynamic neural network control (DNNC) is a model predictive control strategy potentially applicable to nonlinear systems. It uses a neural network to model the process and its mathematical inverse to control the process. The advantages of single hidden layer DNNC are threefold: First, the neural network structure is very simple, having limited nodes in the hidden layer and output layer for the SISO case. Second, DNNC offers potential for better initialization of weights along with fewer weights and bias terms. Third, the controller design and implementation are easier than control strategies such as conventional and hybrid neural networks without loss in performance. The objective of this paper is to present the basic concept of single hidden layer DNNC and illustrate its potential. In addition, this paper provides a detailed case study in which DNNC is applied to the nonisothermal CSTR with time varying parameters including activation energy (i.e., deactivation of catalyst) and heat transfer coefficient (i.e., fouling). DNNC is compared with PID control. Although it is clear that DNNC will perform better than PID, it is useful to compare PID with DNNC to illustrate the extreme range of the nonlinearity of the process. This paper represents a preliminary effort to design a simplified neural network-based control approach for a class of nonlinear processes. Therefore, additional work is required for investigation of the effectiveness of this approach for other chemical processes such as batch reactors. The results show excellent DNNC performance in the region where conventional PID control fails.     

Distributed model predictive control of switched nonlinear systems with scheduled mode transitions

A method for the design of distributed model predictive control (DMPC) systems for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule is presented. Under appropriate stabilizability assumptions on the existence of a set of feedback controllers that can stabilize the closed‐loop switched, nonlinear system, a cooperative DMPC architecture using Lyapunov‐based model predictive control (MPC) in which the distributed controllers carry out their calculations in parallel and communicate in an iterative fashion to compute their control actions is designed. The proposed DMPC design is applied to a nonlinear chemical process network with scheduled mode transitions and its performance and computational efficiency properties in comparison to a centralized MPC architecture are evaluated through simulations. © 2013 American Institute of Chemical Engineers AIChE J, 59:860‐871, 2013     

Predictive control of particlesize distribution of crystallization process using deep learning based image analysis

The challenges to regulate the particle-size distribution (PSD) stem from on-line measurement of the full distribution and the distributed nature of crystallization process. In this article, a novel nonlinear model predictive control method of PSD for crystallization process is proposed. Radial basis function neural network is adopted to approximate the PSD such that the population balance model with distributed nature can be transformed into the ordinary differential equation (ODE) models. Data driven nonlinear prediction model of the crystallization process is then constructed from the input and output data and further be used in the proposed nonlinear model predictive control algorithm. A deep learning based image analysis technology is developed for online measurement of the PSD. The proposed PSD control method is experimentally implemented on a jacketed batch crystallizer. The results of crystallization experiments demonstrate the effectiveness of the proposed control method.     

SYSTEMATIC DERIVATIONS OF MODEL PREDICTIVE CONTROL BASED ON ARTIFICIAL NEURAL NETWORK

This article presents systematic derivations of setting up a nonlinear model predictive control based on the artifical neural network. Unlike most research in the past, the control law is mathematically developed in detail so that the performance of the ANN-based controller can be improved. In this paper, a three-layer feedforward neural network with hyperbolic tangent functions in the hidden layer and with a linear function in the output layer is used. The two-stage scheme including pseudo Gauss-Newton and least squares is proposed for training ANN. This training method is better than the traditional algorithm in terms of training speed. The Levenberg-Marquardt approximation is also utilized for the minimum of the predictive control criterion. Two typical chemical processes are simulated and the ANN model predictive control applications can reach fairly good results.     

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.     

ROBUST NONLINEAR PREDICTIVE CONTROL USING A DISTURBANCE ESTIMATOR

A robust nonlinear predictive control strategy using a disturbance estimator is presented. The disturbance estimator is comprised of two parts: one is the disturbance model parameter adaptation and the other is future disturbance prediction. A linear discrete model is proposed as a disturbance model which is formulated by using process inputs and available process measurements. The recursive least square (RLS) method with exponential forgetting is used to determine the uncertain disturbance model parameters and for the future disturbance prediction, future disturbances projected by the future process inputs are used. Two illustrative examples: a jacketed CSTR as a SISO system: an adiabatic CSTR as a MIMO system, and experimental results of the distillation column control are presented. The results indicate that a substantial improvement in nonlinear predictive control performance is possible using the disturbance estimator.     

基于神经网络的pH中和过程非线性预测控制

针对pH中和过程这一化工过程系统中的典型非线性对象特点，应用神经网络建模思想和模型预测控制方法，并结合Hammerstein模型特点，研究pH中和过程非线性系统的两种新型模型预测控制手段，分别建立基于神经网络的非线性预测控制系统整体求解策略和基于Hammerstein模型的两步法预测控制策略，并用MATLAB对其进行仿真。控制仿真结果表明，建立的神经网络预测控制策略和非线性Hammerstein模型预测控制均优于传统PID控制方法，具有良好的设定值跟踪效果和抗干扰控制响应，说明这两种控制策略是非线性过程的有效控制方法。     

基于Hammerstein-Wiener模型的连续搅拌反应釜神经网络预测控制

针对化工过程中广泛使用的连续搅拌反应釜(CSTR),提出一种基于神经网络的模型预测控制策略,采用分段最小二乘支持向量机辨识Hammerstein-Wiener模型系数的方法,在此基础上建立线性自回归模式〖DK〗(ARX)结构和高斯径向基神经网络串联的非线性预测控制器。利用BP神经网络训练预测控制输入序列和拟牛顿算法求解非线性预测控制律,从而实现一种基于支持向量机Hammerstein-Wiener辨识模型的非线性神经网络预测控制算法。对CSTR的仿真结果表明,该方法能够更有效地跟踪控制反应物浓度。     

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