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     

Robust decision making for hybrid process supply chain systems via model predictive control

Model predictive control (MPC) is a promising solution for the effective control of process supply chains. This paper presents an optimization-based decision support tool for supply chain management, by means of a robust MPC strategy. The proposed formulation: (i) captures uncertainty in model parameters and demand by stochastic programming, (ii) accommodates hybrid process systems with decisions governed by logical conditions/rulesets, and (iii) addresses multiple supply chain performance metrics including customer service and economics, within an integrated optimization framework. Two mechanisms for uncertainty propagation are presented – an open-loop approach, and an approximate closed-loop strategy. The performance of the robust MPC framework is analyzed through its application to two process supply chain case studies. The proposed approach is shown to provide a substantial reduction in the occurrence of back orders when compared to a nominal MPC implementation.     

Fault diagnosis and fault tolerant control using reduced order models

In this work, we have developed a reduced order model relevant for fault diagnosis and control. This model is combined with a generalized likelihood ratio (GLR) method and integrated with fault tolerant control schemes developed earlier. Simulation studies of an ideal binary distillation column show that the use of reduced order model improves the diagnostic performance thereby leading to improved fault tolerance. Furthermore, the proposed strategy is also computational more efficient. In inferential control, such as the use of temperature measurements to infer product compositions, the proposed fault tolerant control scheme performs better than the conventional control scheme when various soft faults occur.     

Safe‐steering of batch process systems

This work considers the problem of controlling batch processes to achieve a desired final product quality subject to input constraints and faults in the control actuators. Specifically, faults are considered that cannot be handled via robust control approaches, and preclude the ability to reach the desired end‐point, necessitating fault‐rectification. A safe‐steering framework is developed to address the problem of determining how to utilize the functioning inputs during fault rectification to ensure that after fault‐rectification, the desired product properties can be reached upon batch termination. To this end, first a novel reverse‐time reachability region (we define the reverse time reachability region as the set of states from where the desired end point can be reached by batch termination) based MPC is formulated that reduces online computations, as well as provides a useful tool for handling faults. Next, a safe‐steering framework is developed that utilizes the reverse‐time reachability region based MPC in steering the state trajectory during fault rectification to enable (upon fault recovery) the achieving of the desired end point properties by batch termination. The proposed controller and safe‐steering framework are illustrated using a fed‐batch process example. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

A fault magnitude based strategy for effective fault classification

A common approach in fault diagnosis is monitoring the deviations of measured variables from the values at normal operations to identify the root causes of faults. When the number of conceivable faults is larger than that of predictive variables, conventional approaches can yield ambiguous diagnosis results including multiple fault candidates. To address the issue, this work proposes a fault magnitude based strategy. Signed digraph is first used to identify qualitative relationships between process variables and faults. Empirical models for predicting process variables under assumed faults are then constructed with support vector regression (SVR). Fault magnitude data are projected onto principal components subspace, and the mapping from scores to fault magnitudes is learned via SVR. This model can estimate fault magnitudes and discriminate a true fault among multiple candidates when different fault magnitudes yield distinguishable responses in the monitored variables. The efficacy of the proposed approach is illustrated on an actuator benchmark problem.     

An embedded fault detection, isolation and accommodation system in a model predictive controller for an industrial benchmark process

Fault detection and isolation (FDI) for industrial processes has been actively studied during the last decades. Traditionally, the most widely implemented FDI methods have been based on model-based approaches. In modern process industry, however, there is a demand for data-based methods due to the complexity and limited availability of the mechanistic models. The aim of this paper is to present a data-based, fault tolerant control (FTC) system for a simulated industrial benchmark process, Shell control problem. Data-based FDI systems, employing principal component analysis (PCA), partial least squares (PLS) and subspace model identification (SMI) are presented for achieving fault tolerance in co-operation with controllers. The effectiveness of the methods is tested by introducing faults in simulated process measurements. The process is controlled by using model predictive control (MPC). To compare the effectiveness of the MPC, the FTC system is also tested with a control strategy based on a set of PI controllers.     

鲁棒模型预测控制系统的评估基准

在控制系统的性能评估中,基准的设计是个重要问题。将基本设计极限理论推广到模型预测控制系统(MPC),建立性能评估基准。直接考虑多输入多输出系统的频域扰动,建立输出反馈鲁棒模型预测控制器。此控制器仅仅依赖于过程参数,也是令闭环系统达到控制性能极限的基准控制器。建立了用于评估的性能指标,提出基于此基准的性能评估程序,用以评价其他模型预测控制系统的性能。数学算例证实了这一评估程序的有效性。     

Lexicographic optimization based MPC: Simulation and experimental study

Multi-variable prioritized control study is carried out using model predictive control (MPC) algorithms. The conventional MPC algorithm implements multi-variable control through one augmented objective function and requires weights adjustment for required performance. In order to implement explicit prioritization in multiple control objectives, we have used lexicographic MPC. To achieve better tracking performance, we have used a new MPC algorithm, by modifying the lexicographic constraint, referred to as MLMPC, where tuning of weights is not required. The effectiveness of MLMPC algorithm is demonstrated on a PMMA reactor for controlling the number average molecular weight and the reactor temperature. We have also verified the benefits of proposed algorithm on an experimental single board heater system (SBHS) for controlling temperature of a thin metal plate. These simulation and experimental studies demonstrate the superiority of the proposed method over conventional MPC and lexicographic MPC. Finally, we have presented generalized mathematical solutions to the optimization problem in MLMPC.     

Control of milk pasteurization process using model predictive approach

A milk pasteurization process, a nonlinear process and multivariable interacting system, is difficult to control by the conventional on–off controllers since the on–off controller can handled the temperature profiles for milk and water oscillating over the plant requirements. The multi-variable control approach with model predictive control (MPC) is proposed in this study. The proposed algorithm was tested for control of a milk pasteurization process in four cases of simulation such as set point tracking, model mismatch, difference control and prediction horizons, and time sample. The results for the proposed algorithm show the well performance in keeping both the milk and water temperatures at the desired set points without any oscillation and overshoot and giving less drastic control action compared to the cascade generic model control (GMC) strategy.     

Multi-block gated recurrent unit network-based fault diagnosis method for multivariate nonlinear process

The increasing complexity of industrial processes brings new challenges to fault diagnosis tasks, and different types of faults have higher and higher requirements on the performance of fault classification models. This paper proposes a novel multivariate nonlinear temporal-related fault diagnosis method based on gated recurrent units (GRUs). First, to improve the performance of the model in local information extraction and global integration, high dimensional variables are divided into multiple sub-blocks according to the structure of chemical process units, and a new block normalization method is proposed to improve the performance of local feature extraction. Second, aiming at the slow drifting faults, the GRU network is adopted inside the sub-block to extract local sparse and nonlinear temporal features. By combining the variance features of variables after block normalization, the performance of the model on multiplicative faults will improve. Finally, aiming at the complex correlation between variables, a new recurrent matrix method is proposed to extract the time transform information inside each variable to improve the comprehensive performance of the model. Through a multi-level feature integration strategy, the model can be trained in parallel to improve the training speed. The proposed method shows good performance in the Tennessee Eastman process, and the extracted multi-class features allow the model to be trained end-to-end and simultaneously diagnose multiple types of faults.     

Model predictive control with learning‐type set‐point: Application to artificial pancreatic β‐cell

A novel combination of model predictive control (MPC) and iterative learning control (ILC), referred to learning‐type MPC (L‐MPC), is proposed for closed‐loop control in an artificial pancreatic β‐cell. The main motivation for L‐MPC is the repetitive nature of glucose‐meal‐insulin dynamics over a 24‐h period. L‐MPC learns from an individual's lifestyle, inducing the control performance to improve from day to day. The proposed method is first tested on the Adult Average subject presented in the UVa/Padova diabetes simulator. After 20 days, the blood glucose concentrations can be kept within 68–145 mg/dl when the meals are repetitive. L‐MPC can produce superior control performance compared with that achieved under MPC. In addition, L‐MPC is robust to random variations in meal sizes within ±75% of the nominal value or meal timings within ±60 min. Furthermore, the robustness of L‐MPC to subject variability is validated on Adults 1–10 in the UVa/Padova simulator. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

An optimal filter based MPC for systems with arbitrary disturbances

In this study, a linear model predictive control (MPC) approach with optimal filters is proposed for handling unmeasured disturbances with arbitrary statistics. Two types of optimal filters are introduced into the framework of MPC to relax the assumption of integrated white noise model in existing approaches. The introduced filters are globally optimal for linear systems with unmeasured disturbances that have unknown statistics. This enables the proposed MPC to better handle disturbances without access to disturbance statistics. As a result, the effort required for disturbance modeling can be alleviated. The proposed MPC can achieve offset-free control in the presence of asymptotically constant unmeasured disturbances. Simulation results demonstrate that the proposed approach can provide an improved disturbance õrejection performance over conventional approaches when applied to the control of systems with unmeasured disturbances that have arbitrary statistics.     

一种对预测控制系统经济性能评估的实用方法及其工业应用

In this article, an approach for economic performance assessment of model predictive control (MPC) system is presented. The method builds on steady-state economic optimization techniques and uses the linear quadratic Gaussian (LQG) benchmark other than conventional minimum variance control (MVC) to estimate the potential of reduction in variance. The LQG control is a more practical performance benchmark compared to MVC for performance assessment since it considers input variance and output variance, and it thus provides a desired basis for determining the theoretical maximum economic benefit potential arising from variability reduction. Combining the LQG benchmark directly with benefit potential of MPC control system, both the economic benefit and the op-timal operation condition can be obtained by solving the economic optimization problem. The proposed algorithm is illustrated by simulated example as well as application to economic performance assessment of an industrial model predictive control system.     

Dantzig–Wolfe decomposition and plant-wide MPC coordination

Due to the enormous success of model predictive control (MPC) in industrial practice, the efforts to extend its application from unit-wide to plant-wide control are becoming more widespread. In general, industrial practice has tended toward a decentralized MPC architecture. Most existing MPC systems work independently of other MPC systems installed within the plant and pursue a unit/local optimal operation. Thus, a margin for plant-wide performance improvement may be available beyond what decentralized MPC can offer. Coordinating decentralized, autonomous MPC has been identified as a practical approach to improving plant-wide performance. In this work, we propose a framework for designing a coordination system for decentralized MPC which requires only minor modification to the current MPC layer. This work studies the feasibility of applying Dantzig–Wolfe decomposition to provide an on-line solution for coordinating decentralized MPC. The proposed coordinated, decentralized MPC system retains the reliability and maintainability of current distributed MPC schemes. An empirical study of the computational complexity is used to illustrate the efficiency of coordination and provide some guidelines for the application of the proposed coordination strategy. Finally, two case studies are performed to show the ease of implementation of the coordinated, decentralized MPC scheme and the resultant improvement in the plant-wide performance of the decentralized control system.     

复杂故障判定的基于结构化残差的多层次分析法

In industrial processes,there exist faults that have complex effect on process variables.Complex and simple faults are defined according to their effect dimensions.The conventional approaches based on structured residuals cannot isolate complex faults.This paper presents a multi-level strategy for complex fault isolation.An extraction procedure is employed to reduce the complex faults to simple ones and assign them to several levels.On each level,faults are isolated by their different responses in the structured residuals.Each residual is obtained insensitive to one fault but more sensitive to others.The faults on different levels are verified to have different residual responses and will not be confused.An entire incidence matrix containing residual response characteristics of all faults is obtained,based on which faults can be isolated.The proposed method is applied in the Tennessee Eastman process example,and the effectiveness and advantage are demonstrated.     

Proactive fault‐tolerant model predictive control

Fault‐tolerant control methods have been extensively researched over the last 10 years in the context of chemical process control applications, and provide a natural framework for integrating process monitoring and control aspects in a way that not only fault detection and isolation but also control system reconfiguration is achieved in the event of a process or actuator fault. But almost all the efforts are focused on the reactive fault‐tolerant control. As another way for fault‐tolerant control, proactive fault‐tolerant control has been a popular topic in the communication systems and aerospace control systems communities for the last 10 years. At this point, no work has been done on proactive fault‐tolerant control within the context of chemical process control. Motivated by this, a proactive fault‐tolerant Lyapunov‐based model predictive controller (LMPC) that can effectively deal with an incipient control actuator fault is proposed. This approach to proactive fault‐tolerant control combines the unique stability and robustness properties of LMPC as well as explicitly accounting for incipient control actuator faults in the formulation of the MPC. Our theoretical results are applied to a chemical process example, and different scenaria were simulated to demonstrate that the proposed proactive fault‐tolerant model predictive control method can achieve practical stability and efficiently deal with a control actuator fault. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2810–2820, 2013     

A MODEL-BASED DIRECT ADAPTIVE PI CONTROLLER FOR NONLINEAR PROCESS CONTROL

This article proposes a model-based direct adaptive proportional-integral (PI) controller for a class of nonlinear processes whose nominal model is input-output linearizable but may not be accurate enough to represent the actual process. The proposed direct adaptive PI controller is composed of two parts: the first is a linearizing feedback control law that is synthesized directly based on the process's nominal model and the second is an adaptive PI controller used to compensate for the model errors. An effective parameter-tuning algorithm is devised such that the proposed direct adaptive PI controller is able to achieve stable and robust control performance under uncertainties. To show the robust stability and performance of the direct adaptive PI control system, a rigorous analysis involving the use of a Lyapunov-based approach is presented. The effectiveness and applicability of the proposed PI control strategy are demonstrated by considering the time-dependent temperature trajectory tracking control of a batch reactor in the presence of plant/model mismatch, unanticipated periodic disturbances, and measurement noises. Furthermore, for use in an environment that lacks full-state measurements, the integration of a sliding observer with the proposed control scheme is suggested and investigated. Extensive simulation results reveal that the proposed model-based direct adaptive PI control strategy enables a highly nonlinear process to achieve robust control performance despite the existence of plant/model mismatch and diversified process uncertainties.     

Model predictive control with non-uniformly spaced optimization horizon for multi-timescale processes

Many chemical processes exhibit disparate timescale dynamics with strong coupling between fast, moderate and slow variables. To effectively handle this issue, a model predictive control (MPC) scheme with a non-uniformly spaced optimization horizon is proposed in this paper. This approach implements the time intervals that are small in the near future but large in the distant future, allowing the fast, moderate and slow dynamics to be included in the optimization whilst reducing the number of decision variables. A sufficient condition for ensuring stability for the proposed MPC is developed. The proposed approach is demonstrated using a case study of an industrial paste thickener control problem. While the performance of the proposed approach remains similar to a conventional MPC, it reduces the computational complexity significantly.     

Soft-constrained model predictive control based on data-driven distributionally robust optimization

This article proposes a novel distributionally robust optimization (DRO)-based soft-constrained model predictive control (MPC) framework to explicitly hedge against unknown external input terms in a linear state-space system. Without a priori knowledge of the exact uncertainty distribution, this framework works with a lifted ambiguity set constructed using machine learning to incorporate the first-order moment information. By adopting a linear performance measure and considering input and state constraints robustly with respect to a lifted support set, the DRO-based MPC is reformulated as a robust optimization problem. The constraints are softened to ensure recursive feasibility. Theoretical results on optimality, feasibility, and stability are further discussed. Performance and computational efficiency of the proposed method are illustrated through motion control and building energy control systems, showing 18.3% less cost and 78.8% less constraint violations, respectively, while requiring one third of the CPU time compared to multi-stage scenario based stochastic MPC.     

A unified framework for detection, isolation and compensation of actuator faults in uncertain particulate processes

This paper presents a methodology for the robust detection, isolation and compensation of control actuator faults in particulate processes described by population balance models with control constraints and time-varying uncertain variables. The main idea is to shape the fault-free closed-loop process response via robust feedback control in a way that enables the derivation of performance-based fault detection and isolation (FDI) rules that are less sensitive to the uncertainty. Initially, an approximate finite-dimensional system that captures the dominant process dynamics is derived and decomposed into interconnected subsystems with each subsystem directly influenced by a single manipulated input. The decomposition is facilitated by the specific structure of the process input operator. A robustly stabilizing bounded feedback controller is then designed for each subsystem to enforce an arbitrary degree of asymptotic attenuation of the effect of the uncertainty in the absence of faults. The synthesis leads to (1) an explicit characterization of the fault-free behavior of each subsystem in terms of a time-varying bound on an appropriate Lyapunov function and (2) an explicit characterization of the robust stability region in terms of the control constraints and the size of the uncertainty. Using the fault-free Lyapunov dissipation bounds as thresholds for FDI in each subsystem, the detection and isolation of faults in a given actuator is accomplished by monitoring the evolution of the system within the stability region and declaring a fault if the threshold is breached. The thresholds are linked to the achievable degree of asymptotic uncertainty attenuation and can therefore be properly tuned by proper tuning of the controllers, thus making the FDI criteria less sensitive to the uncertainty. The robust FDI scheme is integrated with a robust stability-based controller reconfiguration strategy that preserves closed-loop stability following FDI. Finally, the implementation of the fault-tolerant control architecture on the particulate process is discussed and the proposed methodology is applied to the problem of robust fault-tolerant control of a continuous crystallizer with a fines trap.