Constrained latent variable model predictive control for trajectory tracking and economic optimization in batch processes

A constrained latent variable model predictive control (LV-MPC) technique is proposed for trajectory tracking and economic optimization in batch processes. The controller allows the incorporation of constraints on the process variables and is designed on the basis of multi-way principal component analysis (MPCA) of a batch data array rearranged by means of a regularized batch-wise unfolding. The main advantages of LV-MPC over other MPC techniques are: (i) requirements for the dataset are rather modest (only around 10–20 batch runs are necessary), (ii) nonlinear processes can efficiently be handled algebraically through MPCA models, and (iii) the tuning procedure is simple. The LV-MPC for tracking is tested through a benchmark process used in previous LV-MPC formulations. The extension to economic LV-MPC includes an economic cost and it is based on model and trajectory updating from batch to batch to drive the process to the economic optimal region. A data-driven model validity indicator is used to ensure the prediction’s validity while the economic cost drives the process to regions with higher profit. This technique is validated through simulations in a case study.     

Latent variable MPC for trajectory tracking in batch processes

A novel multivariate empirical model predictive control strategy (LV-MPC) for trajectory tracking and disturbance rejection for batch processes is presented. The strategy is based on dynamic principal component analysis (PCA) models of the batch process. The solution to the control problem is computed in the low dimensional latent variable space of the PCA model. The trajectories of all variables over the future horizon are then computed from the latent variable solution of the controller. The excellent control performance and the modest closed-loop data requirements for identification are illustrated for the temperature tracking in simulations of an emulsion polymerization process, an exothermic chemical reaction system and for MIMO temperature and pressure tracking in a nylon polymerization autoclave.     

Model predictive control for batch processes: Ensuring validity of predictions

The intuitive and simple ideas that support model predictive control (MPC) along with its capabilities have been the key to its success both in industry and academia. The contribution this paper makes is to further enhance the capabilities of MPC by easing its application to industrial batch processes. Specifically, this paper addresses the problem of ensuring the validity of predictions when applying MPC to such processes. Validity of predictions can be ensured by constraining the decision space of the MPC problem. The performance of the MPC control strategy relies on the ability of the model to predict the behaviour of the process. Using the model in the region in which it is valid improves the resulting performance. In the proposed approach four validity indicators on predictions are defined: two of them consider all the variables in the model, and the other two consider the degrees of freedom of the controller. The validity indicators are defined from the latent variable model of the process. Further to this, these are incorporated as constraints in the MPC optimization problem to bound the decision space and ensure the proper use of the model. Finally, the MPC cost function is modified to enable fine case-specific tuning if desired. Provided the indicators are quadratic, the controller yields a quadratic constrained quadratic programming problem for which efficient solvers are commercially available. A fed-batch fermentation example shows how MPC ensuring validity of predictions improves performance and eases tuning of the controller. The target in the example provided is end-point control accounting for variations in the initial measurable conditions of the batch.     

Iterative learning model predictive control for multi-phase batch processes

Multi-phase batch process is common in industry, such as injection molding process, fermentation and sequencing batch reactor; however, it is still an open problem to control and analyze this kind of processes. Motivated by injection molding processes, the multi-phase batch process in each cycle is formulated as a switched system with internally forced switching instant. Controlling multi-phase batch processes can be decomposed into two subtasks: detecting the dynamics-switching-time; designing the control law for each phase with considering switching effect. In this paper, it is assumed that the dynamics-switching-time can be obtained in real-time and only the second subtask is studied. To exploit the repetitive nature of batch processes, iterative learning control scheme is used in batch direction. To deal with constraints, updating law is designed by using model predictive control scheme. An online iterative learning model predictive control (ILMPC) law is first proposed with a quadratic programming problem to be solved online. To reduce computation burden, an offline ILMPC is also proposed and compared. Applications on injection molding processes show that the proposed algorithms can control multi-phase batch processes well.     

一种间歇过程的综合预测迭代学习控制方法

为了提高迭代学习控制方法在间歇过程轨迹跟踪问题中的收敛速度,本文将批次间的比例型迭代学习控制与批次内的模型预测控制相结合,提出了一种综合应用方法.首先根据间歇过程的线性模型,预测出比例型迭代学习控制的系统输出,然后在批次内采用模型预测控制,通过极小化一个二次型目标函数来获得控制增量.该方法可使系统输出跟踪期望轨迹的速度比比例型迭代学习控制方法更快些.最后通过仿真实例验证了该方法的有效性.     

注塑机注射速度的模型预测迭代学习控制

针对注射过程具有重复运行和非线性的特性,在对预测控制与迭代学习控制进行综合应用并加以改进的基础上,给出一种模型预测迭代学习复合控制新算法,研究了控制器的设计方案.同时,将迭代学习思想引入到预测步长的在线调整,提出了预测步长的迭代学习方法.仿真结果表明,该方法是有效的,其控制性能优于PID迭代学习控制系统.     

Latent variable model predictive control for trajectory tracking in batch processes: Alternative modeling approaches

Several Latent Variable Model (LVM) structures for modeling the time histories of batch processes are investigated from the view point of their suitability for use in Latent Variable Model Predictive Control (LV-MPC) [1] for trajectory tracking and disturbance rejection in batch processes. The LVMs are based on Principal Component Analysis (PCA). Two previously proposed approaches (Batch-Wise Unfolding (BWU) and Observation-Wise with Time-lag Unfolding (OWTU)) for modeling of batch processes [2] are incorporated in the LV-MPC and the benefits and drawbacks of each are explored. Furthermore, a new modeling approach (Regularized Batch-Wise Unfolding (RBWU)) is proposed to overcome the shortcomings of each of the previous modeling approaches while keeping the major benefits of both. The performances of the three latent variable modeling approaches in the course of LV-MPC for trajectory tracking and disturbance rejection are illustrated using two simulated batch reactor case studies. It is seen that the RBWU approach models the nonlinearity and time-varying properties of the batch almost as accurately as BWU approach, but needs fewer observations (batches) for model identification and results in a smoother PCA model. Recommendations are then given on which modeling approach to use under different scenarios.     

基于变结构径向基函数网络的船舶运动预测PID控制

针对船舶在海上运动的大时滞和动态时变等特点,提出基于一种变结构径向基函数(RBF)神经网络的预测PID控制器.通过建立反映系统动态变化的滑动数据窗口,在线序贯学习窗口内的数据,动态调整隐层节点与隐层至输出层的连接权值,得到结构可自适应变化的RBF网络.将该变结构RBF网络用于预测PID控制器中系统状态的在线多步预测,通过得到的预测模型灵敏度信息在线调整PID控制器参数以控制系统的输出.将该控制器用于船舶航向跟踪控制的仿真实验,结果表明该控制器具有良好的的适应性和鲁棒性.     

基于迭代学习与模型预测控制的交通信号混合控制方法

针对基于迭代学习控制的交通信号控制方法对于路网中存在的非重复性实时干扰不能进行有效处理的问题,本文在基于迭代学习控制的交通信号控制方法基础上,结合模型预测控制滚动优化和实时校正的特点,提出了一种基于迭代学习与模型预测控制的交通信号混合控制方法.该方法在有效利用交通流周期性特征改善路网交通状况的同时,可借助模型预测控制的...     

非线性快速批次过程高效迭代学习预测函数控制EI北大核心CSCD

迭代学习模型预测控制(Iterative learning model predictive control,ILMPC)具备较强的批次学习能力及突出的时域跟踪性能,在批次过程控制中发挥了重要作用.然而对于具有强非线性的快动态批次过程,传统的迭代学习模型预测控制很难实现计算效率与跟踪精度之间的平衡,这给其应用带来了挑战.对此本文提出一种高效迭代学习预测函数控制策略,将原非线性系统沿参考轨迹线性化得到二维跟踪误差预测模型,并在控制器设计中补偿所产生的线性化误差,构造优化目标函数为真实跟踪误差的上界.为加强优化计算效率,在时域上结合预测函数控制以降低待优化变量维数,从而有效降低计算负担.结合终端约束集理论,分析了迭代学习预测函数控制的时域稳定性及迭代收敛性.通过对无人车和典型快速间歇反应器的仿真实验验证所提出算法的有效性.     

A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm

Indirect iterative learning control (ILC) facilitates the application of learning-type control strategies to the repetitive/batch/periodic processes with local feedback control already. Based on the two-dimensional generalized predictive control (2D-GPC) algorithm, a new design method is proposed in this paper for an indirect ILC system which consists of a model predictive control (MPC) in the inner loop and a simple ILC in the outer loop. The major advantage of the proposed design method is realizing an integrated optimization for the parameters of existing feedback controller and design of a simple iterative learning controller, and then ensuring the optimal control performance of the whole system in sense of 2D-GPC. From the analysis of the control law, it is found that the proposed indirect ILC law can be directly obtained from a standard GPC law and the stability and convergence of the closed-loop control system can be analyzed by a simple criterion. It is an applicable and effective solution for the application of ILC scheme to the industry processes, which can be seen clearly from the numerical simulations as well as the comparisons with the other solutions.     

带有迭代学习外环的快速路入口匝道无模型自适应预测控制

针对快速路交通系统复杂时变以及难以建模的特点,首先,本文设计了基于无模型自适应预测控制的快速路入口匝道控制方案.其次,根据快速路交通系统具有重复性特点,本文在无模型自适应预测控制方法的基础上引入开环迭代学习控制,提出一种带有迭代学习前馈外环的无模型自适应入口匝道预测控制方案.相比无模型自适应预测控制方案,该方案可以利用迭代学习前馈控制器补偿系统可重复扰动,实现系统的完全跟踪.值得说明的是,预测控制器和学习控制器可以独立工作也可以联合工作.最后,文章给出了控制方案的收敛性分析,并通过交通流仿真验证了所提控制方案的有效性.     

基于Volterra模型的预测控制及应用

由于工业实践的需要,非线性预测控制近年来受到广泛地关注.Volterra模型是一类特殊的非线性模型,非常适合描述工业过程中的无记忆非线性对象.传统的基于Volterra模型的控制器合成法及迭代计算预测控制器法计算量大,且不便于处理控制约束.非线性模型预测控制求解是典型的非线性规划问题,序列二次规划(sequential quadratic program,SQP)算法是求解非线性规划问题常用方法之一.针对Volterra非线性模型预测控制求解问题,本文将滤子法与一种信赖域SQP算法相结合,提出一种改进SQP算法用于基于非线性Volterra模型的带控制约束的多步预测控制求解,并分析了所提方法的收敛性.工业实例仿真结果证实了所提方法的可行性与有效性.     

Nonlinear fuzzy model predictive iterative learning control for drum-type boiler–turbine system

Advanced control strategy is necessary to ensure high efficiency and high load-following capability in the operation of modern power plant. Model predictive control (MPC) has been widely used for controlling power plant. Nevertheless, MPC needs to further improve its learning ability especially as power plants are nonlinear under load-cycling operation. Iterative learning control (ILC) and MPC are both popular approaches in industrial process control and optimization. The integration of model-based ILC with a real-time feedback MPC constitutes the model predictive iterative learning control (MPILC). Considering power plant, this paper presents a nonlinear model predictive controller based on iterative learning control (NMPILC). The nonlinear power plant dynamic is described by a fuzzy model which contains local liner models. The resulting NMPILC is constituted based on this fuzzy model. Optimal performance is realized within both the time index and the iterative index. Convergence property has been proven under the fuzzy model. Deep analysis and simulations on a drum-type boiler–turbine system show the effectiveness of the fuzzy-model-based NMPILC     

自由漂浮空间机器人轨迹跟踪的模型预测控制

针对传统控制方法难以解决自由漂浮空间机器人(free-floating space robot, FFSR)轨迹跟踪过程中的各类约束的问题,采用模型预测控制对自由漂浮空间机器人的轨迹跟踪问题进行了研究.在自由漂浮空间机器人拉格朗日动力学模型的基础上,建立了系统伪线性化的扩展状态空间模型;在给定系统的性能指标和各类约束的情况下,基于拉盖尔模型设计相应的离散模型预测控制器,并证明控制器的稳定性,控制器中引入任务空间滑模变量实现了对末端期望位置和期望速度的同时跟踪;以平面二杆自由漂浮空间机器人为例,对无约束末端轨迹跟踪和有约束末端轨迹跟踪两种情况进行对比仿真验证.仿真结果表明,该模型预测控制器不仅可以实现对末端期望轨迹的有效跟踪,还能满足各类约束.     

基于2维性能参考模型的2维模型预测迭代学习控制策略

将迭代学习控制(Iterative learning control, ILC)系统看作一类具有2维动态特性的控制系统,根据模型预测控制(Model predictive control, MPC)和性能参考模型控制思想, 提出了一种基于2维性能参考模型的2维模型预测迭代学习控制系统设计方案.在该控制系统设计方案中,可以通过选择适当的2 维性能参考模型来构造2 维动态变化的设定值信号和预测控制信号,从而引导迭代学习控制系统收敛到合理的控制性能,并有效避 免系统性能收敛过程中控制输入可能发生的剧烈波动.通过对控制系统的结构分析可知,所得的迭代学习控制器本质上是由沿时 间指标的参考模型预测控制器和沿周期指标的迭代学习控制器组成,闭环系统的收敛性等价于一个2维滤波系统的稳定性.数值仿 真结果证明了该设计方案的有效性和鲁棒性.     

倒立摆的可变增益迭代学习控制算法

对倒立摆系统的平衡控制问题进行研究。在建立系统数学模型的基础上,提出指数变增益迭代学习控制律,并设计了控制器。通过系统仿真实验,结果表明：与常规迭代学习控制律相比较,本文采用的方法收敛速度大大加快,系统动态性能得到很大改善。     

机械手臂的多模型预测控制

针对机械手臂的非线性特点,提出了基于隶属度函数的多模型预测控制方法。该方法首先根据机械手臂的特点,选择合适的调度变量,将机械手臂的工作空间划分为若干个工作子空间,在每个子空间内的平衡点处对机械手臂进行线性化处理,得到相应的线性子模型,从而得到机械手臂的多模型表示;其次针对每个线性子模型设计局部预测控制器,使其在相应的子空间内达到控制要求;最后选择梯形隶属度函数与局部预测控制器进行加权求和,获得全局多模型预测控制器,以对机械手臂进行控制。仿真结果表明,当机械手臂的工作条件在大范围内变化时,全局多模型预测控制器的控制性能远优于常规PD控制器,达到了预期的控制目的。