Latent variable iterative learning model predictive control for multivariable control of batch processes

A latent variable iterative learning model predictive control (LV-ILMPC) method is presented for trajectory tracking in batch processes. Different from the iterative learning model predictive control (ILMPC) model built from the original variable space, LV-ILMPC develops a latent variable model based on dynamic partial least squares (DyPLS) to capture the dominant features of each batch. In each latent variable space, we use a state–space model to describe the dynamic characteristics of the internal model, and an LV-ILMPC controller is designed. Each LV-ILMPC controller tracks the set points of the current batch projection in the corresponding latent variable space, and the optimal control law is determined and the persistent process disturbances is rejected along both time and batch horizons. The proposed LV-ILMPC formulation is based on general LV-MPC and incorporates an iterative learning function into LV-MPC. In addition, the real physical input that drives the process can be reconstructed from the latent variable space. Therefore, this algorithm is particularly suitable for multiple-input, multiple-output (MIMO) systems with strong coupling and serious collinearity. Three studies are used to illustrate the effectiveness of the proposed LV-ILMPC .     

State space model predictive fault-tolerant control for batch processes with partial actuator failure

This paper presents a state space model predictive fault-tolerant control scheme for batch processes with unknown disturbances and partial actuator faults. To develop the model predictive fault-tolerant control, the batch process is first treated into a non-minimal representation using state space transformation. The relevant concepts of the corresponding model predictive fault-tolerant control is thus introduced through state space formulation, where improved closed-loop control performance is achieved even with unknown disturbances and actuator faults, because, unlike traditional model predictive fault-tolerant control, the proposed control method can directly regulate the process output/input changes in the design. For performance comparison, a traditional model predictive fault-tolerant control is also designed. Application to injection velocity control shows that the proposed scheme achieve the design objective well with performance improvement.     

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.     

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.     

Multivariate batch to batch optimisation of fermentation processes incorporating validity constraints

This paper presents an innovative optimisation technique, which utilises an adaptive Multiway Partial Least Squares (MPLS) model to track the dynamics of a batch process from one batch to the next. Utilising this model, an optimisation algorithm solves a quadratic cost function that identifies operating conditions for the subsequent batch that should increase yield. Hard constraints are shown to be required when solving the cost function to ensure that batch conditions do not vary too greatly from one batch to the next. Furthermore, validity constraints are imposed to prevent the PLS model from extrapolating significantly when determining new operating conditions. The capabilities of the proposed technique are illustrated through its application to two benchmark fermentation simulations, where its performance is shown to compare favourably with alternative batch-to-batch optimisation techniques.     

Model predictive control: Recent developments and future promise

This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.     

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.     

Iterative learning control-based batch process control technique for integrated control of end product properties and transient profiles of process variables

Importance of batch processes has grown recently with the increasing economic competition that has pushed the manufacturing industries to pursue small quantity production of diverse high value-added products. Accordingly, systems engineering research on advanced control and optimization of batch processes has proliferated. In this paper, we examine the potentials of ‘iterative learning control (ILC)’ as a framework for industrial batch process control and optimization. First, various ILC rules are reviewed to provide a historical perspective. Next it is shown how the concept of ILC can be fused with model predictive control (MPC) to build an integrated end product and transient profile control technique for industrial chemical batch processes. Possible extensions and modifications of the technique are also presented along with some numerical illustrations. Finally, other related techniques are introduced to note the similarities and contemplate the opportunities for synergistic integration with the current ILC framework.     

Control of polystyrene batch reactors using neural network based model predictive control (NNMPC): An experimental investigation

Controlling batch polymerization reactors imposes great operational difficulties due to the complex reaction kinetics, inherent process nonlinearities and the continuous demand for running these reactors at varying operating conditions needed to produce different polymer grades. Model predictive control (MPC) has become the leading technology of advanced nonlinear control adopted for such chemical process industries. The usual practice for operating polymerization reactors is to optimize the reactor temperature profile since the end use properties of the product polymer depend highly on temperature. This is because the end use properties of the product polymer depend highly on temperature. The reactor is then run to track the optimized temperature set-point profile. In this work, a neural network-model predictive control (NN-MPC) algorithm was implemented to control the temperature of a polystyrene (PS) batch reactors and the controller set-point tracking and load rejection performance was investigated. In this approach, a neural network model is trained to predict the future process response over the specified horizon. The predictions are passed to a numerical optimization routine which attempts to minimize a specified cost function to calculate a suitable control signal at each sample instant. The performance results of the NN-MPC were compared with a conventional PID controller. Based on the experimental results, it is concluded that the NN-MPC performance is superior to the conventional PID controller especially during process startup. The NN-MPC resulted in smoother controller moves and less variability.     

Model predictive functional control for processes with unstable poles

In this paper the coprime‐factorized model predictive functional control for single‐input single‐output processes with an arbitrary number of unstable poles is presented. The predictive functional control algorithm gives a framework for designing the control for a wide range of processes. The main idea in the case of unstable poles is based on the prediction of the process output based on the coprime‐factorized process model. The robust stability of the proposed control algorithm is also discussed, using the small‐gain theorem, which provides a sufficient condition for stability. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Latent variable based model predictive control: Ensuring validity of predictions

This paper presents a methodology to constrain the optimisation problem in LV-MPC so that validity of predictions can be ascertained. LV-MPC is a model-based predictive control methodology implemented in the space of the latent variables and is based on a linear predictor. Provided real processes are non-linear, there is model-process mismatch, and under tight control, the predictor can be used for extrapolation. Extrapolation leads to bad predictions which deteriorates control performance, hence the interest in validity of predictions. In the proposed approach first two validity indicators on predictions are defined. The novelty in the two indicators proposed is they neglect past data, and so validity of predictions is ascertained in terms of future moves which are actually the degrees of freedom in the optimisation. Second, the indicators are introduced in the optimisation as constraints. Provided the indicators are quadratic, recursive optimisation with linearised constraints is implemented. A MIMO example shows how ensuring validity of predictions neglecting past data can improve closed-loop performance, specially under tight control outside the identification region.     

Reinforcement learning for batch process control: Review and perspectives

Batch or semi-batch processing is becoming more prevalent in industrial chemical manufacturing but it has not benefited from advanced control technologies to a same degree as continuous processing. This is due to its several unique aspects which pose challenges to implementing model-based optimal control, such as its highly nonstationary operation and significant run-to-run variabilities. While existing advanced control methods like model predictive control (MPC) have been extended to address some of the challenges, they still suffer from certain limitations which have prevented their widespread industrial adoption. Reinforcement learning (RL) where the agent learns the optimal policy by interacting with the system offers an alternative to the existing model-based methods and has potential for bringing significant improvements to industrial batch process control practice. With such motivation, this paper examines the advantages that RL offers over the traditional model-based optimal control methods and how it can be tailored to better address the characteristics of industrial batch process control problems. After a brief review of the existing batch control methods, the basic concepts and algorithms of RL are introduced and issues for applying them to batch process control problems are discussed. The nascent literature on the use of RL in batch process control is briefly reviewed, both in recipe optimization and tracking control, and our perspectives on future research directions are shared.     

多阶段间歇过程鲁棒模糊预测异步切换控制EI北大核心CSCD

本文针对非线性多阶段间歇过程在切换瞬间存在异步切换的问题,提出了一种鲁棒模糊预测异步切换控制方法.该方法将非线性多阶段间歇过程表示为同步子系统和异步子系统的等效闭环扩展Takagi-Sugeno模糊模型,在此基础上给出了确保每个批次指数稳定和每个阶段渐近稳定的,基于线性矩阵不等式的稳定性条件以及不同情况运行时间的计算方法.根据运行时间采用超前切换思想,避免异步切换情况的出现,保证系统的稳定运行.仿真案例表明所设计的控制器是有效的和可行的.     

Iterative learning control with Smith time delay compensator for batch processes

How to improve the control of batch processes is not an easy task because of modeling errors and time delays. In this work, novel iterative learning control (ILC) strategies, which can fully use previous batch control information and are attached to the existing control systems to improve tracking performance through repetition, are proposed for SISO processes which have uncertainties in modeling and time delays. The dynamics of the process are represented by transfer function plus pure time delay. The stability properties of the proposed strategies for batch processes in the presence of uncertainties in modeling and/or time delays are analyzed in the frequency domain. Sufficient conditions guaranteeing convergence of tracking error are stated and proven. Simulation and experimental examples demonstrating these methods are presented.     

Multiobjective model predictive control

This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.     

Model predictive control suitable for closed-loop re-identification

The main problem of a closed-loop re-identification procedure is that, in general, the dynamic control and identification objectives are conflicting. In fact, to perform a suitable identification, a persistent excitation of the system is needed, while the control objective is to stabilize the system at a given equilibrium point. However, a generalization of the concept of stability, from punctual stability to (invariant) set stability, allows for a flexibility that can be used to avoid the conflict between these objectives. Taking into account that an invariant target set includes not only a stationary component, but also a transient one, the system could be excited without deteriorating the stability of the closed-loop. In this work, a MPC controller is proposed that ensures the stability of invariant sets at the same time that a signal suitable for closed-loop re-identification is generated. Several simulation results show the propose controller formulation properties.     

Distributed model predictive control over network information exchange for large-scale systems

A class of large scale systems, which is naturally divided into many smaller interacting subsystems, are usually controlled by a distributed or decentralized control framework. In this paper, a novel distributed model predictive control (MPC) is proposed for improving the performance of entire system. In which each subsystem is controlled by a local MPC and these controllers exchange a reduced set of information with each other by network. The optimization index of each local MPC considers not only the performance of the corresponding subsystem but also that of its neighbours. The proposed architecture guarantees satisfactory performance under strong interactions among subsystems. A stability analysis is presented for the unconstrained distributed MPC and the provided stability results can be employed for tuning the controller. Experiment of the application to accelerated cooling process in a test rig is provided for validating the efficiency of the proposed method.     

基于模型分解的间歇聚丙烯过程预测控制

针对间歇聚丙烯过程的非线性,间歇性,提出了基于模型分解的非线性前馈一线性反馈相结合的控制方案。在分析过程非线性特性的基础上,采用基于过程模型的前馈抵消反应热对过程的非线性影响。通过引入非线性前馈控制粗调,使反馈控制细调的控制模型得以近似为线性模型,方便地实现了具有优异控制性能的线性预测控制方法,达到了集非线性前馈适应严重非线性过程特性与线性预测控制实现了高精度的控制质量的有机结合。实验结果显示了该方法的有效性。