Iterative learning controller synthesis using FIR models for batch processes

Adaptive iterative learning control based on the measured input-output data is proposed to solve the traditional iterative learning control problem in the batch process. It produces a control law with self-tuning capability by combining a batch-to-batch model estimation procedure with the control design technique. To build the unknown batch operation system, the finite impulse response (FIR) model with the lifted system is constructed for easy construction of a recursive least squares algorithm. It can identify the pattern of the current operation batch. The proposed model reference control method is applied to feedback control of the lifted system. It finds an appropriate control input so that the desired performance of the batch output can track the prescribed finite-time trajectory by iterative trials. Furthermore, on-line tracking control is developed to explore the possible adjustments of the future input trajectories within a batch. This can remove the disturbances in the current batch rather than the next batch trial and keep the product specifications consistent at the end of each batch. To validate the theoretical findings of the proposed strategies, two simulation problems are investigated.     

On-line optimal control of a seeded batch cooling crystallizer

In this paper, an on-line optimal control methodology is developed for the optimal quality control of a seeded batch cooling crystallizer process. An extended Kalman filter is successfully implemented to predict seven unmeasured state variables based on three measurements in the batch process. A PI controller is used in a feedback control system to implement the optimal path. It is found that the PI controller can ensure tracking of the optimal path. The simulation results show that on-line optimal control strategy leads to a substantial improvement of the end product quality expressed in terms of the mean size and the width of the distribution. The effects of the plant/model mismatch and disturbances are also tested and discussed.     

Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steadystates. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steady states. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

On-line batch process monitoring using dynamic PCA and dynamic PLS models

Producing value-added products of high-quality is the common objective in industries. This objective is more difficult to achieve in batch processes whose key quality measurements are not available on-line. In order to reduce the variations of the product quality, an on-line batch monitoring scheme is developed based on the multivariate statistical process control. It suggests using the past measured process variables without real-time quality measurement at the end of the batch run. The method, referred to as BDPCA and BDPLS, integrates the time-lagged windows of process dynamic behavior with the principal component analysis and partial least square respectively for on-line batch monitoring. Like traditional MPCA and MPLS approaches, the only information needed to set up the control chart is the historical data collected from the past successful batches. This leads to simple monitoring charts, easy tracking of the progress in each batch run and monitoring the occurrence of the observable upsets. BDPCA and BDPLS models only collect the previous data during the batch run without expensive computations to anticipate the future measurements. Three examples are used to investigate the potential application of the proposed method and make a comparison with some traditional on-line MPCA and MPLS algorithms.     

基于线性时变扰动模型的间歇过程最优迭代学习控制

A batch-to-batch optimal iterative learning control (ILC) strategy for the tracking control of product quality in batch processes is presented. The linear time-varying perturbation (LTVP) model is built for product quality around the nominal trajectories. To address problems of model-plant mismatches, model prediction errors in the previous batch run are added to the model predictions for the current batch run. Then tracking error transition models can be built, and the ILC law with direct error feedback is explicitly obtained. A rigorous theorem is proposed, to prove the convergence of tracking error under ILC. The proposed methodology is illustrated on a typical batch reactor and the results show that the performance of trajectory tracking is gradually improved by the ILC.     

Process control of polymer extrusion. Part II: Feedforward control

A feedforward plus feedback control method (FFC) and an adaptive feedforward plus feedback control method (AFFC) were proposed in this study to control the extrudate thickness of polymer extrusion. They were tested by step changes of screw speed and feedstock, and square wave type of screw speed changes. It is found that these feedforward control methods worked very well for various load disturbances but they required a good process model and accurate on-line measurements of manipulated variables and load variables. The feedback function was necessary to compensate the over- or under-corrections of the feedforward controllers and to handle other disturbances which were not considered in the feedforward model.     

基于MPLS的间歇过程终点质量迭代优化控制

提出了多向偏最小二乘(MPLS)模型和迭代学习控制相结合的方法,实现间歇过程终点时刻产品质量指标的控制.利用间歇过程的重复特性,根据前一批次的终点质量偏差调整下-批次控制变量的轨迹,从而使质量指标逐步接近于理想指标.本文提出的方法可以有效地消除由于模型误差和未知扰动引起的质量偏差.在苯乙烯间歇聚合反应模型上进行了仿真分析,验证了该方法的有效性.     

基于支持向量机MPLS的间歇过程故障诊断方法

1 INTRODUCTION In batch or fed-batch processes, raw materials are converted to products within a finite duration. In prac- tical production, the process commonly exhibits large variations from batch to batch due to such influencing factors as the quality fluctuation of raw materials, de- fect of equipments, contaminations, and other unpre- dicted disturbances. These variations may have an adverse effect on the final product quantity and quality. But it is generally difficult to discern th…     

强制循环蒸发器的非线性解耦控制

强制循环蒸发器是一个多输入多输出的且回路间存在着较强耦合的强非线性的复杂化工过程。针对单纯的采用常规控制方法很难满足实际的工业要求的问题,在深入研究上述过程的动态特性的基础上,根据模型的结构特点,采用全局输入输出反馈线性化的方法实现了其解耦控制,并证明了系统的零动态稳定性。通过仿真表明采用全局输入输出反馈线性化解耦方法能够有效地解决系统的强非线性对系统带来的影响,而且还能消除密度回路与液位回路间的耦合作用,该方法对提高产品质量和提高系统的蒸发效率具有重要意义。     

Recursive data-based prediction and control of product quality for a PMMA batch process

In many batch processes, frequent process/feedstock disturbances and unavailability of direct on-line quality measurements make it very difficult to achieve tight control of product quality. Motivated by this, we present a simple data-based method in which measurements of other process variables are related to end product quality using a historical data base. The developed correlation model is used to make on-line predictions of end quality, which can serve as a basis for adjusting the batch condition/time so that desired product quality may be achieved. This strategy is applied to a methyl methacrylate (MMA) polymerization process. Important end quality variables, the weight average molecular weight and the polydispersity, are predicted recursively based on the measurements of reactor cooling rate. Subsequently, a shrinking-horizon model predictive control approach is used to manipulate the reaction temperature. The results in this study show promise for the proposed inferential control method.     

Model predictive control for wastewater treatment process with feedforward compensation

Being an optimizing technology, model predictive control (MPC) can now be found in a wide variety of application fields. The main and most obvious control goal to be achieved in a wastewater treatment plant is to fulfill the effluent quality standards, while minimizing the operational costs. In order to maintain the effluent quality within regulation-specified limits, the MPC strategy has been applied to the Benchmark Simulation Model 1 (BSM1) simulation benchmark of wastewater treatment process. After the discussion of open loop responses of outputs to manipulated inputs and measured influent disturbances, the strategies of feedback by linear dynamic matrix control (DMC), quadratic dynamic matrix control (QDMC) and nonlinear model predictive control (NLMPC), and improvement by feedforward based on influent flow rate or ammonium concentration have been investigated. The simulation results indicate that good performance was achieved under steady influent characteristics, especially concerning the nitrogen-related species. Compared to DMC and QDMC, NLMPC with penalty function brings little improvement. Two measured disturbances have been used for feedforward control, the influent flow rate and ammonium concentration. It is shown that the performance of feedforward with respect to the influent ammonium concentration is much higher than for the feedforward with respect to the influent flow rate. However, this latter is slightly better than the DMC feedback. The best performance is obtained by combining both feedforward controllers with respect to the influent ammonium concentration and flow rate. In all cases, the improvement of performance is correlated with more aeration energy consumption.     

Feedback control design for an anaerobic digestion process

An approach for the design of linear feedback controllers for anaerobic digestion systems is presented. The effluent chemical oxigen demand (COD) concentration and the dilution rate are taken respectively as the regulated and the manipulated variables. The control design is based on simple step‐response models of the process endowed with an input delay to account for dead‐times induced by measurement devices. The resulting feedback controller has a traditional proportional‐integral (PI) control structure, so it can be easily implemented with conventional control technologies. Since the concentration of volatile fatty acids can be easily and quickly measured as compared with COD concentration, it is used as a secondary measurement that is incorporated into the feedback loop scheme to enhance the robustness of the control scheme with respect of influent disturbances. The performance of the proposed control scheme is illustrated via numerical simulations and experimental work. © 2002 Society of Chemical Industry     

Design and Analysis of Integrated Predictive Iterative Learning Control for Batch Process Based on Two-dimensional System Theory

Based on the two-dimensional (2D) systemtheory, an integrated predictive iterative learning control (2D-IPILC) strategy for batch processes is presented. First, the output response and the error transition model predictions along the batch index can be calculated analytically due to the 2D Roesser model of the batch process. Then, an integrated framework of combining iterative learning control (ILC) andmodel predictive control(MPC) is formed reasonably. The output of feedforward ILC is estimated on the basis of the predefined process 2D model. By minimizing a quadratic objective function, the feedback MPC is introduced to obtain better control performance for tracking problem of batch processes. Simulations on a typical batch reactor demonstrate that the satisfactory tracking performance as well as faster convergence speed can be achieved than traditional proportion type (Ptype) ILC despite the model error and disturbances.     

Cascade closed-loop optimization and control of batch reactors

In this paper, a cascade closed-loop optimization and control strategy for batch reactors is proposed. Based on the reduction of a physical conservation model a cascade system is developed, which can effectively combine optimization and control to achieve good on-line optimization and tracking performance under the common condition where incomplete knowledge of the reaction system exists. A two-tier estimation scheme using a nonlinear observer for heat production rate and reaction rates is also developed. In the reaction rate estimation, calorimetric information is used. The on-line closed-loop optimization strategy uses a descending horizon dynamic optimization algorithm based on nonlinear programming and an additive unknown disturbance for feedback. A simple adaptive nonlinear tracking system is designed based on the generic model control concept. The efficiency of this strategy is demonstrated through simulations on a batch reactor under various operation conditions, such as noisy measurements, varying initial states and model mismatch.     

Optimization of nonlinear process based on sequential extreme learning machine

In this paper, a new approach to the optimal control with constraints is proposed to achieve a desired end product quality for nonlinear processes based on new kernel extreme learning machine (KELM). The contributions of the paper are as follows: (1) In existing ILC algorithm, the model was built only between manipulated input variables U and output variables Y without considering the state variables. However, the states variables X_state are important in the industrial processes, which are usually constrained. In this paper, the variables are divided into state variables X_state, manipulated input variables U and output Y in the process of modeling. Then ΔU can be obtained by batch-to-batch iterative learning control separately. Kernel algorithm is added to ELM. (2) Constraints of state variables X_state and the input variables U are considered in the current version. PSO is used to solve the optimization problem. (3) Kernel trick is introduced to improve accuracy of ELM modeling. New KELM algorithm is proposed in the current version. The input trajectory for the next batch is accommodated by searching for the optimal value through the error feedback at a minimum cost. The particle swarm optimization algorithm is used to search for the optimal value based on the iterative learning control (ILC). The proposed approach has been shown to be effective and feasible by applying bulk polymerization of the styrene batch process and fused magnesium furnace.     

Development of MBPLS based control for serial operation processes

A control scheme based on the multiblock PLS (MBPLS) model for multi-stage processes (or serially connected processes) is developed. MBPLS arranges a large number of variables into meaningful blocks for each stage of the large-scale system. Two control design strategies, course-to-course (CtC) and within-stage (WS) controls, are proposed for the re-optimization design in the whole multistage course. In CtC, MBPLS control and optimization are done by applying feedback from the finished output quality when one course for all stages is done. It utilizes the information from the current course to improve quality of the next one. In WS, the MBPLS-based re-optimization strategy is developed to explore the possible adjustments of the future inputs at the rest of the stages in order to fix up the disturbances just in time and to maintain the product specification when the current course is finished. The proposed technique is successfully applied to two simulated industrial problems, including a photolithography sequences and a reverse osmosis desalination process, and the advantages of the proposed method are demonstrated.     

Nonlinear control of a batch ester-interchange reactor

Nonlinear control algorithms using feedback input-output linearization and sliding mode control are applied to a lab-scale batch ester-interchange reaction system. Batch ester-interchange reaction requires no overshoot of reaction temperature in earlier stage of reaction and tight temperature control throughout the reaction to keep uniform quality of the final product and to prevent variation of the amount of the byproduct such as diethylene glycol at each batch. Through experimentation we find that the nonlinear controller of input-output linearization algorithm shows better control performance both at setpoint tracking and disturbance rejection than the conventional PID controller. Further, sliding mode control algorithm is supplemented and simulated to show that it improves robustness against plant-model mismatch.     

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