Optimal control of a nonlinear fed-batch fermentation process using model predictive approach

Bioprocesses are involved in producing different pharmaceutical products. Complicated dynamics, nonlinearity and non-stationarity make controlling them a very delicate task. The main control goal is to get a pure product with a high concentration, which commonly is achieved by regulating temperature or pH at certain levels. This paper discusses model predictive control (MPC) based on a detailed unstructured model for penicillin production in a fed-batch fermentor. The novel approach used here is to use the inverse of penicillin concentration as a cost function instead of a common quadratic regulating one in an optimization block. The result of applying the obtained controller has been displayed and compared with the results of an auto-tuned PID controller used in previous works. Moreover, to avoid high computational cost, the nonlinear model is substituted with neuro-fuzzy piecewise linear models obtained from a method called locally linear model tree (LoLiMoT).     

Wiener model based nonlinear predictive control

This paper addresses the problem of discrete-time nonlinear predictive control of W iener systems. Wiener-model-based nonlinear predictive control combines the advantages of linear-model-based predictive control and gain scheduling while retaining a moderate level of computational complexity. A clear relation is shown between an iteration in the optimization of the nonlinear control problem and the control problem of the underlying linear-model-based method. This relation has a simple form of gain scheduling, thus the properties of the nonlinear control system can be analysed from the comprehensible linear control aspect. Several disturbance rejection techniques are proposed and compared. The method was tested on a simulated model of a pH neutralization process. The performance was excellent also in the case of a considerable plant-tomodel mismatch. The method can be applied as a first next step in cases where the performance of linear control is unsatisfactory owing to process nonlinearity.     

一类非线性系统的微分平滑反步自适应输出反馈控制

研究了一类含不确定参数且存在未知扰动的严反馈非线性系统输出反馈控制问题,设计了一种新型的反步递推(Backstepping)自适应控制器.为实现输出反馈,设计过程引入了虚拟的全维状态观测器.由于Backstepping的虚拟控制量与未知参数逼近值及其高阶导数有关,为此通过微分平滑算法对原系统进行相应的动态扩展.在稳定性分析中,利用Lyapunov定理,得到了系统全局一致有界稳定的条件,并求出系统的稳态跟踪误差.最后给出的仿真算例验证了本文方法的有效性和可行性.     

基于小波神经网络的板形板厚系统解耦预测控制

带材轧制是一个复杂的非线性过程, 板形控制和板厚控制又是强耦合、非线性、含时延环节的复杂系统. 提出了一种基于小波神经网络的解耦预测控制方案; 利用小波神经网络来辨识原系统的α阶时延逆系统, 将该逆系统与原系统串联后形成一个伪线性复合系统, 从而把多变量系统控制转化为多个单变量系统的控制实现了系统解耦, 并对解耦后的系统采用闭环预测控制. 仿真表明该控制方法具有结构简单、易于实现, 且有较强的抗扰性和鲁棒性.     

Glucose concentration control of a fed-batch mammalian cell bioprocess using a nonlinear model predictive controller

A non-linear model predictive controller (NMPC) was investigated as a route to delivering improved product quality, batch to batch reproducibility and significant cost reductions by providing a means for better controlling the bioreactor environment in a Chinese hamster ovary (CHO) mammalian cell fed-batch process.A nonlinear fundamental bioprocess model was developed to represent the CHO mammalian cell fed-batch bioprocess under study. This developed nonlinear model aided in the configuration and tuning of a NMPC through off-line simulation. The tuned NMPC was applied to a 15 L pilot-plant bioreactor for glucose concentration fixed set-point control. Traditionally, bioprocesses are characterized by long critical process parameter (CPP) measurement intervals (24 h). However, advances in PAT have helped increase CPP measurement frequency. An in situ Kaiser RXN2 Raman spectroscopy instrument was used to monitor the glucose concentration at 6 min intervals.Glucose concentration control of a bioreactor is not a trivial task due to high process variability, measurement noise and long measurement intervals. Nevertheless, NMPC proved successful in achieving closed loop fixed set-point control in the presence of these common bioprocess operation attributes.     

基于遗传算法的非线性模型预测控制方法

介绍了非线性模型预调控制算法结构，提出了基于遗传算法的非线性模型预测控制方法，将遗传算法作为优化技术用于受限非线性模型预测控制器的设计。算法采用双模控制策略，将保证预测控制算法稳定性的终点等式约束转化为终点不等式约束，以利于遗传算法的实施。基于不变集理论，给出了非线性模型预测控制算法的稳定性定理。仿真结果表明了所提出控制算法的可行性和有效性。     

基于多模型的非线性系统广义预测控制

对于复杂的离散时间非线性系统，提出一种基于多模型的广义预测控制方法．通过在平衡点附近建立线性模型，并用径向基函数神经网络来补偿匹配误差，形成了非线性系统的多模型表示，然后采用模糊识别方法作为切换法则，并结合广义预测控制构成了多模型广义预测控制器．通过对连续发酵过程的计算机仿真，表明了该方法的有效性．     

Distributed nonlinear model predictive control based on contraction theory

A novel distributed model predictive control algorithm for continuous‐time nonlinear systems is proposed in this paper. Contraction theory is used to estimate the prediction error in the algorithm, leading to new feasibility and stability conditions. Compared to existing analysis based on Lipschitz continuity, the proposed approach gives a distributed model predictive control algorithm under less conservative conditions, allowing stronger couplings between subsystems and a larger sampling interval when the subsystems satisfy the specified contraction conditions. A numerical example is given to illustrate the effectiveness and advantage of the proposed approach.     

基于粒子群优化的非线性系统最小二乘支持向量机预测控制方法

对于非线性系统预测控制问题, 本文提出了一种基于模型学习和粒子群优化(PSO)的单步预测控制算法.该方法使用最小二乘支持向量机(LS-SVM)建立非线性系统模型并预测系统的输出值, 通过输出反馈和偏差校正减少预测误差, 由PSO滚动优化获得非线性系统的控制量. 该方法能在非线性系统数学模型未知的情况下设计出有效的预测控制器. 通过对单变量多变量非线性系统进行仿真, 证明了该预测控制方法是有效的, 且具有良好的自适应能力和鲁棒性.     

基于神经网络的非线性系统预测函数控制

针对离散非线性系统,利用神经网络非线性激励函数的局部线性表示,提出一种可用于非线性过程的神经网络预测函数控制方法并给出了控制律的收敛性分析.该方法将复杂的神经网络非线性预测方程转化成直观而有效的线性形式,同时利用线性预测函数方法求得解析的控制律,避免了复杂的非线性优化求解,仿真结果表明了算法的有效性.     

Explicit output-feedback nonlinear predictive control based on black-box models

Nonlinear model predictive control (NMPC) algorithms are based on various nonlinear models. A number of on-line optimization approaches for output-feedback NMPC based on various black-box models can be found in the literature. However, NMPC involving on-line optimization is computationally very demanding. On the other hand, an explicit solution to the NMPC problem would allow efficient on-line computations as well as verifiability of the implementation. This paper applies an approximate multi-parametric nonlinear programming approach to explicitly solve output-feedback NMPC problems for constrained nonlinear systems described by black-box models. In particular, neural network models are used and the optimal regulation problem is considered. A dual-mode control strategy is employed in order to achieve an offset-free closed-loop response in the presence of bounded disturbances and/or model errors. The approach is applied to design an explicit NMPC for regulation of a pH maintaining system. The verification of the NMPC controller performance is based on simulation experiments.     

Tube‐based robust nonlinear model predictive control

This paper extends tube‐based model predictive control of linear systems to achieve robust control of nonlinear systems subject to additive disturbances. A central or reference trajectory is determined by solving a nominal optimal control problem. The local linear controller, employed in tube‐based robust control of linear systems, is replaced by an ancillary model predictive controller that forces the trajectories of the disturbed system to lie in a tube whose center is the reference trajectory thereby enabling robust control of uncertain nonlinear systems to be achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

基于神经网络的非线性系统多步预测控制

针对离散非线性系统,利用非线性激励函数的局部线性表示,提出一种可用于非线性过程的神经网络多步预测控制方法,并给出了控制律的收敛性分析．该方法将非线性系统处理成简单的线性和非线性两部分,对复杂的非线性多步预测方程给出了直观而有效的线性形式,并用线性预测控制方法求得控制律,避免了复杂的非线性优化求解．仿真结果表明了该算法的有效性．     

Observers in nonlinear model‐based predictive control

A closed‐loop reformulation of the dual‐mode paradigm affords significant advantages in model‐based predictive control of systems subject to uncertainty and/or disturbances and/or nonlinear dynamics. This paper considers earlier results based on ellipsoidal invariant sets and proposes extensions to the output feedback nonlinear case by defining invariant sets both for the system state and the error dynamics of a nonlinear observer. Particular attention is paid to the class of systems with separable nonlinearities but the results carry over to the general case. Copyright © 2000 John Wiley & Sons, Ltd.     

Adaptive control Lyapunov function based model predictive control for continuous nonlinear systems

A design of adaptive model predictive control (MPC) based on adaptive control Lyapunov function (aCLF) is proposed in this article for nonlinear continuous systems with part of its dynamics being unknown at the starting time. Specifically, to guarantee the convergence of the closed-loop system with online predictive model updating, a stability constraint is designed. It limits the aCLF of the system under the MPC to be less than that under an online updated auxiliary adaptive control. The auxiliary adaptive control which implements in a sampling-hold fashion can guarantee the convergence of the controlled system. The sufficient conditions that guarantee the states to be steered to a small region near the equilibrium by the proposed MPC are provided. The calculation of the proposed algorithm does not depend on the model mismatch at the starting time. And it does not require the Lyapunov function of the state of the real system always to be reduced at each time. These provide the potential to improve the performance of the closed-loop system. The effectiveness of the proposed method is illustrated through a chemical process example.     

Advanced-multi-step nonlinear model predictive control

Nonlinear model predictive control (NMPC) has gained widespread attention due to its ability to handle variable bounds and deal with multi-input, multi-output systems. However, it is susceptible to computational delay, especially when the solution time of the nonlinear programming (NLP) problem exceeds the sampling time. In this paper we propose a fast NMPC method based on NLP sensitivity, called advanced-multi-step NMPC (amsNMPC). Two variants of this method are developed, the parallel approach and the serial approach. For the amsNMPC method, NLP problems are solved in background multiple sampling times in advance, and manipulated variables are updated on-line when the actual states are available. We present case studies about a continuous stirred tank reactor (CSTR) and a distillation column to show the performance of amsNMPC. Nominal stability properties are also analyzed.     

Globally optimal nonlinear model predictive control based on multi-parametric disaggregation

Nonlinear model predictive control is appropriate for controlling highly nonlinear processes, particularly when operating conditions change frequently. If the problem is nonconvex, the controller must lead the process to a global, rather than a local optimum. This work deals with computation of the control actions which lead to the global optimum via the normalized multi-parametric disaggregation technique. The continuous process model is transformed into a nonlinear programming (NLP) problem via discretization which uses an implicit integration method. The NLP problem is relaxed into a mixed integer linear programming (MILP) model. Iterations between solving MILP (lower bound) and using its solution as a starting point for a local nonlinear optimizer (which computes the upper bound) continue until the gap is closed (an l₁-norm objective function is used). Controller performance is illustrated by several examples. Relative simplicity of the algorithm makes it possible to be implemented by a wide audience.     

Suboptimal nonlinear predictive control based on multivariable neural Hammerstein models

This paper describes a computationally efficient nonlinear Model Predictive Control (MPC) algorithm in which the neural Hammerstein model is used. The Multiple-Input Multiple-Output (MIMO) dynamic model contains a neural steady-state nonlinear part in series with a linear dynamic part. The model is linearized on-line, as a result the MPC algorithm requires solving a quadratic programming problem, the necessity of nonlinear optimization is avoided. A neutralization process is considered to discuss properties of neural Hammerstein models and to show advantages of the described MPC algorithm. In practice, the algorithm gives control performance similar to that obtained in nonlinear MPC, which hinges on non-convex optimization.     

基于Taylor 逼近的非线性系统P ID 型多步预测控制

基于局部递归神经网络对非线性系统进行递归多步向前预测，将系统实际多步向前预测值按泰勒公式在其递归预测值上展开，实现对非线性系统多步预测输出值的二次逼近，减少了预测误差，进而通过对PID型多步预测性能指标函数极小化求取控制量，控制器与广义预测控制器结构相似，其参数通过神经网络在线辨识获得，仿真实验表明了该方法的有效性。