Robust model predictive control and fault handling of batch processes

This work considers the control of batch processes subject to input constraints and model uncertainty with the objective of achieving a desired product quality. First, a computationally efficient nonlinear robust Model Predictive Control (MPC) is designed. The robust MPC scheme uses robust reverse‐time reachability regions (RTRRs), which we define as the set of process states that can be driven to a desired neighborhood of the target end‐point subject to input constraints and model uncertainty. A multilevel optimization‐based algorithm to generate robust RTRRs for specified uncertainty bounds is presented. We then consider the problem of uncertain batch processes subject to finite duration faults in the control actuators. Using the robust RTRR‐based MPC as the main tool, a robust safe‐steering framework is developed to address the problem of how to operate the functioning inputs during the fault repair period to ensure that the desired end‐point neighborhood can be reached upon recovery of the full control effort. The applicability of the proposed robust RTRR‐based controller and safe‐steering framework subject to limited availability of measurements and sensor noise are illustrated using a fed‐batch reactor system. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Subspace identification for data‐driven modeling and quality control of batch processes

In this work, we present a novel, data‐driven, quality modeling, and control approach for batch processes. Specifically, we adapt subspace identification methods for use with batch data to identify a state‐space model from available process measurements and input moves. We demonstrate that the resulting linear time‐invariant (LTI), dynamic, state‐space model is able to describe the transient behavior of finite duration batch processes. Next, we relate the terminal quality to the terminal value of the identified states. Finally, we apply the resulting model in a shrinking‐horizon, model predictive control scheme to directly control terminal product quality. The theoretical properties of the proposed approach are studied and compared to state‐of‐the‐art latent variable control approaches. The efficacy of the proposed approach is demonstrated through a simulation study of a batch polymethyl methacrylate polymerization reactor. Results for both disturbance rejection and set‐point changes (i.e., new quality grades) are demonstrated. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1581–1601, 2016     

Robust temperature control for batch chemical reactors

Since batch chemical reactors exhibit an integrating response, temperature control for these systems can be a real problem for conventional PID controllers. Tuning can be extremely difficult due to the reduced stability margins proved for this type of processes. In this work, a simple robust control strategy for temperature regulation in batch and semi-batch chemical reactors is proposed. The feedback controller is composed by an approximate I/O linearizing feedback equipped with a calorimetric balance estimator. Based on standard results from singular perturbations, it is proven that the proposed feedback controller (i) can track a bounded temperature trajectory as close as desired (i.e., practical stability) by adjusting a single estimation parameter, and (ii) after a short transient, the performance of the exact I/O linearizing feedback can be recovered as the calorimetric balance estimation rate is increased.     

间歇过程的批间自优化控制

针对间歇过程的实时优化问题,提出了一种基于最优性条件近似法的批间自优化控制策略。首先获取标称工作点的最优输入轨迹形态,将其参数化为少量决策变量,简化问题复杂度。然后根据参数化后的决策变量得到批间优化的最优性条件,并建立批次终端可测变量和最优性条件之间的回归模型,将其作为被控变量进行批间跟踪控制。对一个间歇反应器进行了仿真研究,结果表明方法能有效实现间歇过程的批间自优化控制。     

基于无约束迭代学习的间歇生产过程优化控制

针对基于迭代学习控制的间歇过程优化控制算法难以进行收敛性分析的难题,本文基于数据驱动的神经模糊模型提出一种新颖的间歇过程无约束迭代学习控制方法,通过调节因子的变化去除了约束条件,使控制轨迹在批次轴上收敛,并创新性地对优化问题的收敛性给出了严格的数学证明。在理论研究的基础上,将本文提出的算法用于间歇连续反应釜的终点质量控制研究,仿真结果验证了本文算法的有效性和实用价值,为间歇过程的优化控制提供了一条新途径。     

A model-based control framework for industrial batch crystallization processes

Dynamic optimization is applied for throughput maximization of a semi-industrial batch crystallization process. The control strategy is based on a non-linear moment model. The dynamic model, consisting of a set of differential and algebraic equations, is optimized using the simultaneous optimization approach in which all the state and input trajectories are parameterized. The resulting problem is subsequently solved by a non-linear programming algorithm.     

时变间歇过程的2D-PID自适应控制方法

针对间歇过程存在的参数时变问题,提出一种基于二维PID(2D-PID)迭代学习框架的自适应控制方法。首先,通过粒子群优化算法快速获取初始的2D-PID控制参数。在批次内,采用自调整神经元PID控制器对其进行在线自适应调节。进一步,考虑批次间的重复特性,通过PID型迭代学习控制,以利用历史批次的信息来修正当前批次的调节变量,最终提高控制性能。通过间歇发酵过程的仿真和比较研究,验证了所提出方法的有效性。     

基于KPLS模型的间歇过程产品质量控制

针对间歇过程所具有的非线性特性,提出了一种基于核偏最小二乘(KPLS)模型的最终产品质量控制策略。利用初始条件、批次展开后的过程数据以及最终产品质量建立了间歇过程的KPLS模型;采用基于主成分分析(PCA)映射的预估方法对未知的过程数据进行补充,实现了最终产品质量的在线预测。为了解决最终产品质量的控制,利用T2统计量确定KPLS模型的适用范围,并作为约束引入产品质量控制问题,提高控制策略的可行性;采用粒子群优化(PSO)算法实现了优化问题的高效求解。仿真结果表明,与基于偏最小二乘(PLS)模型的控制策略相比,所提出的方法具有更高的预测精度,且能有效解决产品质量控制中出现的各种问题。     

Iterative learning model predictive control for constrained multivariable control of batch processes

In this paper, we propose a model predictive control (MPC) technique combined with iterative learning control (ILC), called the iterative learning model predictive control (ILMPC), for constrained multivariable control of batch processes. Although the general ILC makes the outputs converge to reference trajectories under model uncertainty, it uses open-loop control within a batch; thus, it cannot reject real-time disturbances. The MPC algorithm shows identical performance for all batches, and it highly depends on model quality because it does not use previous batch information. We integrate the advantages of the two algorithms. The proposed ILMPC formulation is based on general MPC and incorporates an iterative learning function into MPC. Thus, it is easy to handle various issues for which the general MPC is suitable, such as constraints, time-varying systems, disturbances, and stochastic characteristics. Simulation examples are provided to show the effectiveness of the proposed ILMPC.     

A systematic approach to SMB processes model identification from batch experiments

The optimization, monitoring and control of simulated moving bed (SMB) units require the use of a process model and the estimation of the model parameters. A systematic numerical procedure for determining parameters of SMB models from batch experiments is presented and evaluated. The unknown parameters are estimated by minimizing a cost function measuring the difference between experimental and simulated concentration profiles. In contrast with previous studies, parameter identifiability is studied and errors on the estimated parameters are calculated. A sensitivity analysis is used to design the experiments and to compare the identifiability of different chromatographic models. Then, the influence of local minima is evaluated by applying the numerical procedure on fictitious measurements generated from a model with known parameters.     

Iterative learning reliable control of batch processes with sensor faults

An iterative learning reliable control (ILRC) scheme is developed in this paper for batch processes with unknown disturbances and sensor faults. The batch process is transformed into and treated as a two-dimensional Fornasini-Marchesini (2D-FM) model. Under the proposed control law, the closed-loop system with unknown disturbances and sensor faults not only converges along both the time and the cycle directions, but also satisfies certain H_∞ performance. For performance comparison, a traditional reliable control (TRC) law based on dynamic output feedback is also developed by considering the batch process in each cycle as a continuous process. Conditions for the existence of ILRC scheme are given as biaffine and linear matrix inequalities. Algorithms are given to solve these matrix inequalities and to optimize performance indices. Applications to injection packing pressure control show that the proposed scheme can achieve the design objectives well, with performance improvement along both time and cycle directions, and also has good robustness to uncertain initialization and measurement disturbances.     

A note on the identification and control of batch distillation columns

A method for the identification and control of a batch distillation process is presented in this note. The proposed model consists of a first-order integrating process in composition with a high-frequency gain. The feedback controller is designed in the framework of robust nonlinear control with modeling error compensation techniques for the control of distillate composition via manipulations of the reflux ratio. The proposed identification and control procedures are illustrated via numerical simulations.     

Moving horizon approach of integrating scheduling and control for sequential batch processes

Online integration of scheduling and control is crucial to cope with process uncertainties. We propose a new online integrated method for sequential batch processes, where the integrated problem is solved to determine controller references rather than process inputs. Under a two‐level feedback loop structure, the integrated problem is solved in a frequency lower than that of the control loops. To achieve the goal of computational efficiency and rescheduling stability, a moving horizon approach is developed. A reduced integrated problem in a resolving horizon is formulated, which can be solved efficiently online. Solving the reduced problem only changes a small part of the initial solution, guaranteeing rescheduling stability. The integrated method is demonstrated in a simulated case study. Under uncertainties of the control system disruption and the processing unit breakdown, the integrated method prevents a large loss in the production profit compared with the simple shifted rescheduling solution. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1654–1671, 2014     

Online identification for batch processes in closed loop incorporating priori controller knowledge

It is of great importance to develop an online modeling method for chemical processes operated in closed loop for better understanding, monitoring the process or other purposes without endangering the system. This paper intends to devise an online system identification method, particularly for the batch process, by fully exploiting its intrinsic repetitiveness. It properly uses the information from the time direction and the batch direction, thus leading to a gradual performance enhancement. In addition, the identification method formulates the priori controller knowledge such as closed-loop stability as optimization constraints to refine the parameter estimates. A trust region method is employed to overcome the significant computation burden of directly handling these constraints such as solving Lyapunov inequalities. An adaptive filter is introduced to further smooth the parameter estimates. Finally, the effectiveness of the approach is verified by three numerical examples including a two-tank system.     

Data‐driven model predictive quality control of batch processes

The problem of driving a batch process to a specified product quality using data‐driven model predictive control (MPC) is described. To address the problem of unavailability of online quality measurements, an inferential quality model, which relates the process conditions over the entire batch duration to the final quality, is required. The accuracy of this type of quality model, however, is sensitive to the prediction of the future batch behavior until batch termination. In this work, we handle this “missing data” problem by integrating a previously developed data‐driven modeling methodology, which combines multiple local linear models with an appropriate weighting function to describe nonlinearities, with the inferential model in a MPC framework. The key feature of this approach is that the causality and nonlinear relationships between the future inputs and outputs are accounted for in predicting the final quality and computing the manipulated input trajectory. The efficacy of the proposed predictive control design is illustrated via closed‐loop simulations of a nylon‐6,6 batch polymerization process with limited measurements. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2852–2861, 2013     

基于MKPLS和SQP方法的间歇过程迭代优化控制

采用多向核偏最小二乘（MKPLS）方法建立间歇过程的模型并进行操作条件的优化。由于存在模型失配和未知扰动，基于MKPLS模型的最优控制轨迹在实际对象上往往难以实现最优的产品质量指标。本文利用间歇过程批次间的重复特性与序贯二次规划（SQP）优化算法中迭代计算的相似特点，提出了一种基于MKPLS模型的批次间优化调整策略，使得经过逐步优化调整得到的控制轨迹作用于实际对象时，可以得到更优的质量指标。该方法的有效性在苯乙烯聚合反应器和乙醇流加发酵过程的仿真对象上得到了验证。     

Integration of scheduling and control for batch processes using multi‐parametric model predictive control

Integration of scheduling and control results in Mixed Integer Nonlinear Programming (MINLP) which is computationally expensive. The online implementation of integrated scheduling and control requires repetitively solving the resulting MINLP at each time interval. (Zhuge and Ierapetritou, Ind Eng Chem Res. 2012;51:8550–8565) To address the online computation burden, we incorporare multi‐parametric Model Predictive Control (mp‐MPC) in the integration of scheduling and control. The proposed methodology involves the development of an integrated model using continuous‐time event‐point formulation for the scheduling level and the derived constraints from explicit MPC for the control level. Results of case studies of batch processes prove that the proposed approach guarantees efficient computation and thus facilitates the online implementation. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3169–3183, 2014     

一类间歇生产过程的迭代学习控制算法及其收敛性分析

针对基于迭代学习控制的间歇过程产品质量优化控制算法难以进行收敛性分析的难题,并且考虑到实际生产中存在外部干扰和不确定因素的影响,本文对间歇过程模型参数动态更新问题进行了分析,建立了间歇生产过程产品质量的神经模糊(NF)预测模型,提出了一种新颖的批次轴参数自适应调节算法。在此基础上,构造了一种基于数据驱动的间歇生产过程产品质量迭代学习控制算法,并对优化问题的收敛性给出了严格的数学证明。最后,将本文提出的算法用于一类典型的间歇过程终点质量控制研究,仿真结果验证了本文算法的有效性和实用价值,为间歇过程的优化控制提供了一条新途径。