Online set-point optimisation cooperating with predictive control of a yeast fermentation process: A neural network approach

Online set-point optimisation which cooperates with model predictive control (MPC) and its application to a yeast fermentation process are described. A computationally efficient multilayer control system structure with adaptive steady-state target optimisation (ASSTO) and a suboptimal MPC algorithm are presented in which two neural models of the process are used. For set-point optimisation, a steady-state neural model is linearised online and the set-point is calculated from a linear programming problem. For MPC, a dynamic neural model is linearised online and the control policy is calculated from a quadratic programming problem. In consequence of linearisation of neural models, the necessity of online nonlinear optimisation is eliminated. Results obtained in the proposed structure are comparable with those achieved in a computationally demanding structure with nonlinear optimisation used for set-point optimisation and MPC.     

一种无约束多步递归神经网络预测控制器

本文针对具有强非线性、多工作点特性的控制系统, 提出了一种基于递归BP神经网络的多步预测模型; 通过分析预测模型的内在数学关系, 选择了二次型函数作为预测控制器的目标函数, 并给出了目标函数关于控制序列的雅可比矩阵和赫森矩阵的计算方法; 最后使用Newton-Rhapson算法设计出了滚动优化控制策略, 构建了一个非线性多步预测控制器. 仿真结果表明, 文中提出的多步预测控制器具有较好的控制效果.     

基于一种继承模型的多变量非线性预测控制

提出了一种由人工神经网络与线性ＡＲＸ模型相结合的集成模型,给出了其辨识训练方法。以此模型为基础,提出了一种多变量非线性预测控制算法。它利用线性预测控制的成果,得到一解析式的非线性优化控制输入,避免了通常非线性模型（包括普通人工神经网络模型）预测控制所需的在线数值寻优计算,节约了在线计算时间。提高了算法的可靠性和稳定性。进一步给出了在ＣＳＴＲ反应器上的仿真实验结果。     

基于稳态非线性模型和线性ARX模型组合的非线性预测控制

通过点集映射来表示非线性系统的稳态模型,用系统的稳态增益来修正具有外界输入的线性自回归（AutoRegressive with eXternal input, ARX）模型的动态增益,提出了一种基于稳态非线性模型和线性ARX模型组合的非线性预测控制算法．该算法用递归最小二乘法在线辨识系统的动态模型参数,用序列二次规划算法求解目标函数．最后通过对典型化工非线性对象pH中和过程的仿真对本算法进行了验证．结果表明,本算法比广义预测控制算法具有更好的设定值跟踪性能和抗干扰能力．     

Adaptive air-fuel ratio control with MLP network

This paper presents an application of adaptive neural network model-based predictive control (MPC) to the air-fuel ratio of an engine simulation. A multi-layer perceptron (MLP) neural network is trained using two on-line training algorithms: a back propagation algorithm and a recursive least squares (RLS) algorithm. It is used to model parameter uncertainties in the nonlinear dynamics of internal combustion (IC) engines. Based on the adaptive model, an MPC strategy for controlling air-fuel ratio is realized, and its control performance compared with that of a traditional PI controller. A reduced Hessian method, a newly developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up nonlinear optimization in the MPC.     

基于并行支持向量机的多变量非线性模型预测控制

提出一种基于并行支持向量机的多变量系统非线性模型预测控制算法．首先,通过考虑输入、输出间的耦合,建立基于并行支持向量机的多步预测模型;然后,将该模型用于非线性预测控制,提出新的适用于并行预测模型的反馈校正策略,得到最优控制律．连续搅拌槽式反应器（CSTR）的控制仿真结果表明,该算法的性能优于基于并行神经网络的非线性模型预测控制和基于集成模型的非线性模型预测控制．     

基于逆系统的赖氨酸发酵多变量解耦内模控制

针对赖氨酸发酵过程的时变、非线性和高耦合性,提出基于逆系统的赖氨酸发酵多变量解耦内模控制方法。根据动态递归模糊神经网络(DRFNN)的非线性辨识原理离线建立发酵过程的逆模型,将得到的逆模型串联在发酵系统之前,实现了发酵过程输入输出解耦线性化,从而得到伪线性系统;对复合后的伪线性系统采用内模控制。仿真结果表明,该方法能够适应赖氨酸发酵过程模型的不确定性和参数的时变性,具有较强的鲁棒性,且结构简单,易于实现。     

Adaptive neural network model based predictive control for air–fuel ratio of SI engines

The dynamics of air manifold and fuel injection of the spark ignition engines are severely nonlinear. This is reflected in nonlinearities of the model parameters in different regions of the operating space. Control of the engines has been investigated using observer-based methods or sliding-mode methods. In this paper, the model predictive control (MPC) based on a neural network model is attempted for air–fuel ratio, in which the model is adapted on-line to cope with nonlinear dynamics and parameter uncertainties. A radial basis function (RBF) network is employed and the recursive least-squares (RLS) algorithm is used for weight updating. Based on the adaptive model, a MPC strategy for controlling air–fuel ratio is realised to a nonlinear simulation of the engines, and its control performance is compared with that of a conventional PI controller. A reduced Hessian method, a new developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up the nonlinear optimisation in MPC.     

Neural network based model predictive control for a steel pickling process

A multi-layer feedforward neural network model based predictive control scheme is developed for a multivariable nonlinear steel pickling process in this paper. In the acid baths three variables under controlled are the hydrochloric acid concentrations. The baths exhibit the normal features of an industrial system such as nonlinear dynamics and multi-effects among variables. In the modeling, multiple input, single-output recurrent neural network subsystem models are developed using input–output data sets obtaining from mathematical model simulation. The Levenberg–Marquardt algorithm is used to train the process models. In the control (MPC) algorithm, the feedforward neural network models are used to predict the state variables over a prediction horizon within the model predictive control algorithm for searching the optimal control actions via sequential quadratic programming. The proposed algorithm is tested for control of a steel pickling process in several cases in simulation such as for set point tracking, disturbance, model mismatch and presence of noise. The results for the neural network model predictive control (NNMPC) overall show better performance in the control of the system over the conventional PI controller in all cases.     

Stability of model predictive control with mixed constraints

We derive stability conditions for model predictive control (MPC) with hard constraints on the inputs and “soft” constraints on the outputs for an infinitely long output horizon. We show that with state feedback, MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback, we show that the results hold if all the eigenvalues are strictly inside the unit circle. The online optimization problem defining MPC can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon     

RBF-ARX model-based MPC strategies with application to a water tank system

A hybrid pseudo-linear RBF-ARX model that combines Gaussian radial basis function (RBF) networks and linear ARX model structure is utilized for representing the dynamic behavior of a class of smooth nonlinear and non-stationary systems. This model is locally linear at each working point and globally nonlinear within whole working range. Based on the structural characteristics of the RBF-ARX model, three receding horizon predictive control (RBF-ARX-MPC) strategies are designed: (1) the RBF-ARX-MPC algorithm based on single-point linearization (MPC-SPL); (2) the RBF-ARX-MPC algorithm based on multi-point linearization (MPC-MPL); and (3) the RBF-ARX-MPC algorithm based on globally nonlinear optimization (MPC-GNO). In the MPC-SPL, the future multi-step-ahead predictive output of the system is obtained based on the local linearization of the RBF-ARX model at only current working-point, while in the MPC-MPL the future long-term output prediction is obtained according to the future local characteristics from previous online optimization results of the RBF-ARX model based MPC. In the MPC-GNO, the globally nonlinear characteristics of the RBF-ARX model are fully used for online getting control variables of the MPC. Real-time control experiments for the three type MPCs are carried out on a water tank system, which are also compared with a classical PID control and a traditional linear ARX model-based MPC. The results verify that the modeling method and the model-based predictive control strategies are realizable and effective for the nonlinear and unstable system. Moreover, it is also shown that the MPC-GNO can obtain better control performance but need more computation time compared to the other MPCs, which makes it possible to be applied into some slowly varying processes.     

Nonlinear system modeling and robust predictive control based on RBF-ARX model

An integrated modeling and robust model predictive control (MPC) approach is proposed for a class of nonlinear systems with unknown steady state. First, the nonlinear system is identified off-line by RBF-ARX model possessing linear ARX model structure and state-dependent Gaussian RBF neural network type coefficients. On the basis of the RBF-ARX model, a combination of a local linearization model and a polytopic uncertain linear parameter-varying (LPV) model are built to approximate the present and the future system's nonlinear behavior, respectively. Subsequently, based on the approximate models, a min–max robust MPC algorithm with input constraint is designed for the output-tracking control of the nonlinear system with unknown steady state. The closed-loop stability of the MPC strategy is guaranteed by the use of parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). Simulation study to a NO_x decomposition process illustrates the effectiveness of the modeling and robust MPC approaches proposed in this paper.     

Closed-loop stable model predictive control of integrating systems with dead time

Model predictive control (MPC) applications in the process industry usually deal with process systems that show time delays (dead times) between the system inputs and outputs. Also, in many industrial applications of MPC, integrating outputs resulting from liquid level control or recycle streams need to be considered as controlled outputs. Conventional MPC packages can be applied to time-delay systems but stability of the closed loop system will depend on the tuning parameters of the controller and cannot be guaranteed even in the nominal case. In this work, a state space model based on the analytical step response model is extended to the case of integrating time systems with time delays. This model is applied to the development of two versions of a nominally stable MPC, which is designed to the practical scenario in which one has targets for some of the inputs and/or outputs that may be unreachable and zone control (or interval tracking) for the remaining outputs. The controller is tested through simulation of a multivariable industrial reactor system.     

双层结构预测控制研究进展

现代工业大系统的优化控制采用递阶结构,其中以预测控制为代表的先进过程控制已经成为重要的一级.目前,主流的工业预测控制技术均采用双层结构,即包含稳态优化层和动态控制层.双层结构预测控制技术可以有效解决复杂工业过程常见的多目标优化、多变量控制的难点问题.本文简要总结了双层结构预测控制的算法,并从控制输入与被控输出稳态关系入手分析了多变量预测控制稳态解的相容性和唯一性,说明了稳态优化的重要性.针对双层结构预测控制与区间预测控制的性能比较、稳态模型的奇异性以及闭环系统动态特性等提出了一些见解,并指出了需要重点研究的主题.     

状态空间模型的双层结构预测控制算法

双层结构预测控制是指先进行设定值优化、再进行设定值跟踪的预测控制.在已有的双层结构动态矩阵控制的基础上,本文给出基于状态空间模型的双层结构预测控制算法.该算法基于干扰模型和新定义的开环预测值,给出了新的开环预测模块.该开环预测模块采用Kalman滤波方法得到操作变量、被控变量的开环动、稳态预测值.基于这些开环预测值,稳态目标计算模块的基本原理同双层结构动态矩阵控制,但是具体细节上遵循状态空间方法.动态控制模块基于稳态目标计算提供的操作变量、被控变量的稳态目标(设定值),采用二次规划算法计算控制作用.仿真算例证实了该算法的有效性.     

人工神经网络在ERP系统中的应用

在传统的ERP的基础上,增加专家系统模块,即基于人工神经网络技术的预测分析模块,提出了ERP和专家系统的集成管理方法,完成复杂的非线性预测,以使ERP系统智能化、自动化水平更高。该模块采用反向传输BP神经网络模型来实现,通过网络的自适应学习和训练,找出输入和输出之间的内在联系,以求解问题。利用该专家系统对汽车制造企业市场销售量进行预测,结果表明：该方法性能、实用性和通用性好。     

Steady-state target optimization designs for integrating real-time optimization and model predictive control

In industrial practice, the optimal steady-state operation of continuous-time processes is typically addressed by a control hierarchy involving various layers. Therein, the real-time optimization (RTO) layer computes the optimal operating point based on a nonlinear steady-state model of the plant. The optimal point is implemented by means of the model predictive control (MPC) layer, which typically uses a linear dynamical model of the plant. The MPC layer usually includes two stages: a steady-state target optimization (SSTO) followed by the MPC dynamic regulator. In this work, we consider the integration of RTO with MPC in the presence of plant-model mismatch and constraints, by focusing on the design of the SSTO problem. Three different quadratic program (QP) designs are considered: (i) the standard design that finds steady-state targets that are as close as possible to the RTO setpoints; (ii) a novel optimizing control design that tracks the active constraints and the optimal inputs for the remaining degrees of freedom; and (iii) an improved QP approximation design were the SSTO problem approximates the RTO problem. The main advantage of the strategies (ii) and (iii) is in the improved optimality of the stationary operating points reached by the SSTO-MPC control system. The performance of the different SSTO designs is illustrated in simulation for several case studies.     

水泥回转窑优化控制系统的研究与开发

本文通过对水泥生产线的运行数据进行采集、分析和筛选,进而建立神经网络模型和动态ARX模型,设计出水泥回转窑系统的滚动变增益的预测控制器,使用序列二次规划算法（SQP）对控制器的操作变量进行实时最优求解,再通过仿真实验对预测控制算法进行了验证。     

基于PSO的预测控制及在聚丙烯中的应用

输入输出受限非线性系统的预测控制问题,可以看作是一个难以直接求解的约束非线性优化问题。针对预测控制在解决此类优化问题时,存在易收敛到局部极小或者非可行解,对初始值敏感等缺点,提出了一种基于微粒群优化方法的非线性预测控制算法。采用微粒群优化算法（PSO）作为模型预测控制的滚动优化方法,在线实时求解最优控制律。将PSO与序贯二次规划（SQP）算法进行对比仿真实验,求解两个标准函数优化问题,结果表明PSO能够快速有效地求得全局最小点,而SQP则很容易陷入局部极小点。将该算法应用于丙烯聚合反应过程的温度控制中,仿真结果显示了该方法的有效性。     

基于T-S 模型的模糊预测控制研究

提出一种基于T—S模型的模糊预测控制策略．利用模糊聚类算法高线辨识T—S模型，采用带遗忘因子的递推最小二乘法进行模型参数的选择性在线学习；对模糊模型在每一采样点进行线性化，将T—S模型表示的非线性系统转化为线性时变状态空间模型，并将约束非线性优化问题转化为线性二次规划问题，解决了非线性预测控制中如何获得非线性模型和非线性优化在线求解的难题．将预测域内的线性模型序列作为预测模型，减小了模型误差，提高了控制性能．pH中和过程的仿真验证了该方法的有效性．