Composite fast‐slow MPC design for nonlinear singularly perturbed systems

The design of a composite control system for nonlinear singularly perturbed systems using model predictive control (MPC) is described. Specifically, a composite control system comprised of a “fast” MPC acting to regulate the fast dynamics and a “slow” MPC acting to regulate the slow dynamics is designed. The composite MPC system uses multirate sampling of the plant state measurements, i.e., fast sampling of the fast state variables is used in the fast MPC and slow‐sampling of the slow state variables is used in the slow MPC. Using singular perturbation theory, the stability and optimality of the closed‐loop nonlinear singularly perturbed system are analyzed. A chemical process example which exhibits two‐time‐scale behavior is used to demonstrate the structure and implementation of the proposed fast–slow MPC architecture in a practical setting. © 2012 American Institute of Chemical Engineers AIChE J, 58: 1802–1811, 2012     

An integrated framework for scheduling and control using fast model predictive control

Integration of scheduling and control involves extensive information exchange and simultaneous decision making in industrial practice (Engell and Harjunkoski, Comput Chem Eng. 2012;47:121–133; Baldea and Harjunkoski I, Comput Chem Eng. 2014;71:377–390). Modeling the integration of scheduling and dynamic optimization (DO) at control level using mathematical programming results in a Mixed Integer Dynamic Optimization which is computationally expensive (Flores‐Tlacuahuac and Grossmann, Ind Eng Chem Res. 2006;45(20):6698–6712). In this study, we propose a framework for the integration of scheduling and control to reduce the model complexity and computation time. We identify a piece‐wise affine model from the first principle model and integrate it with the scheduling level leading to a new integration. At the control level, we use fast Model Predictive Control (fast MPC) to track a dynamic reference. Fast MPC also overcomes the increasing dimensionality of multiparametric MPC in our previous study (Zhuge and Ierapetritou, AIChE J. 2014;60(9):3169–3183). Results of CSTR case studies prove that the proposed approach reduces the computing time by at least two orders of magnitude compared to the integrated solution using mp‐MPC. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3304–3319, 2015     

Dynamic real‐time optimization with closed‐loop prediction

Process plants are operating in an increasingly global and dynamic environment, motivating the development of dynamic real‐time optimization (DRTO) systems to account for transient behavior in the determination of economically optimal operating policies. This article considers optimization of closed‐loop response dynamics at the DRTO level in a two‐layer architecture, with constrained model predictive control (MPC) applied at the regulatory control level. A simultaneous solution approach is applied to the multilevel DRTO optimization problem, in which the convex MPC optimization subproblems are replaced by their necessary and sufficient Karush–Kuhn–Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints. The performance of the closed‐loop DRTO strategy is compared to that of the open‐loop prediction counterpart through a multi‐part case study that considers linear dynamic systems with different characteristics. The performance of the proposed strategy is further demonstrated through application to a nonlinear polymerization reactor grade transition problem. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3896–3911, 2017     

MODEL PREDICTIVE CONTROL (MPC) AND ITS CURRENT ISSUES IN CHEMICAL ENGINEERING

Model predictive control (MPC) is one of the main process control techniques explored in the recent past; it is the amalgamation of different technologies used to predict future control action and future control trajectories knowing the current input and output variables and the future control signals. It can be said that the MPC scheme is based on the explicit use of a process model and process measurements to generate values for process input as a solution of an on-line (real-time) optimization problem to predict future process behavior. There have been a number of contributions in the field of nonlinear model–based predictive control dealing with issues like stability, efficient computation, optimization, constraints, and others. New developments in nonlinear MPC (NMPC) approaches come from resolving various issues, from faster optimization methods to different process models. This article specifically deals with chemical engineering systems ranging from reactors to distillation columns where MPC plays a role in the enhancement of the systems’ performance.     

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.     

Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time-scale multiplicity

In this work, we propose a subsystem decomposition approach and a distributed estimation scheme for a class of implicit two-time-scale nonlinear systems. Taking the advantage of the time scale separation, these processes are decomposed into fast subsystem and slow subsystem according to the dynamics. In the proposed method, an approach that combines the approximate solutions obtained from both the fast and slow subsystems to form a composite solution of the original system is proposed. Also, based on the fast and slow subsystems, a distributed state estimation scheme is proposed to handle the implicit time-scale multiplicity. In the proposed design, an extended Kalman filter (EKF) is designed for the fast subsystem and a moving horizon estimator (MHE) is designed for the slow subsystem. In the design, the slow subsystem is only required to send information to the fast subsystem one-directionally. The fast subsystem estimator does not send out any information. The estimators use different sampling times, that is, fast sampling of the fast state variables is considered in the fast EKF and slow sampling of the slow state variables is considered in the slow MHE. Extensive simulations based on a chemical process are performed to illustrate the effectiveness and applicability of the proposed subsystem decomposition and composite estimation architecture.     

基于MLD模型的CSTR建模和控制

A novel control strategy for a continuous stirred tank reactor （CSTR） system, which has the typical characteristic of strongly pronounced nonlinearity, multiple operating points, and a wide operating range, is initiated from the point of hybrid systems. The proposed scheme makes full use of the modeling power of mixed logical dynamical （MLD） systems to describe the highly nonlinear dynamics and multiple operating points in a unified framework as a hybrid system, and takes advantage of the good control quality of model predictive control （MPC） to design a controller. Thus, this approach avoids oscillation during switching between sub-systems, helps to relieve shaking in transition, and augments the stability robustness of the whole system, and finally achieves optimal （i.e. fast and smooth） transition between operating points. The simulation results demonstrate that the presented approach has a satisfactory performance.     

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.     

化工过程预测控制的在线优化实现机制

多层结构的预测控制已逐渐成为工业过程控制领域的主流控制方案。在此控制架构基础上,根据操作工或工艺优化所给定期望值的不同,将稳态优化问题具体化为两种基本情况,并对此提出基于复合目标函数的优化问题,可针对不同过程要求退化为线性、二次或二者兼有的优化问题形式。为保证最优目标的可行性并在一定程度上避免关键变量饱和,对不可行的期望值适当调整。将所得最优目标增量化处理后送入模型预测控制动态控制层,确保了上下层之间变量传递的一致性。包含约束的全混槽反应器系统仿真实例表明,流程的优化实现层可针对不同的过程要求有效给出最优目标以便动态控制,说明了该优化流程的可行性。     

Application of state estimation based NMPC to an unstable nonlinear process

Model predictive control (MPC) has become very popular both in process industry and academia due to its effectiveness in dealing with nonlinear, multivariable and/or hard-constrained plants.Although linear MPC can be applied for controlling nonlinear processes by obtaining a linearized model of the plant, this is only valid in a limited region. Therefore, a substantial improvement can be achieved by using the whole knowledge of the process dynamics, specially in the presence of marked nonlinearities. This effect can be strong if the process to control is open-loop unstable.The purpose of this paper is to introduce a nonlinear model predictive controller (NMPC) based on nonlinear state estimation, in order to exploit the knowledge of the nonlinear dynamics and to avoid modeling simplifications or linearization.A state-space formulation is proposed to achieve the control objective. To update the optimization involved in NMPC strategy, state estimation based on the measured outputs is proposed.As a particular application, we consider an open-loop unstable jacketed exothermic chemical reactor. This CSTR is widely recognized as a difficult problem for the purpose of control. In order to achieve the control goal, a NMPController coupled with a state observer are designed. The observer is also used to estimate some unmeasured disturbances. Finally, computer simulations are developed for showing the performance of both the nonlinear observer and the control strategy.     

Nonlinear model predictive control for distributed parameter systems by time–space-coupled model reduction

Nonlinear high-dimensional distributed parameter systems (DPSs) described by sets of parabolic partial different equations (PDEs) exhibit a dominant, low-dimensional slow behavior that can be captured using model reduction. A time–space-coupled model reduction architecture combining encoder–decoder networks with recurrent neural networks (RNNs) was presented in our previous work, for modeling the spatiotemporal dynamics of DPSs without recourse to the governing equations. In this work, we further understand the stability of the training dynamics of the deep architecture by using the Lyapunov exponents (LEs). Subsequently, we construct nonlinear model predictive control (MPC) formulations for the DPS based on the learned, dimensional-reduced model. We use a path-integral optimal control algorithm for MPC implementation to avoid any analytic derivatives of the dynamics. The effectiveness of integration of a deep neural network-based model with MPC is demonstrated in a tubular reactor with recycle cases. The results of the simulation also show that the LE can serve as a readout of training stability for the learned dynamical model.     

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.     

基于改进DOB的矿物研磨过程最优运行先进反馈控制(英文)

Advanced feedback control for optimal operation of mineral grinding process is usually based on the model predictive control (MPC) dynamic optimization. Since the MPC does not handle disturbances directly by controller design, it cannot achieve satisfactory effects in controlling complex grinding processes in the presence of strong disturbances and large uncertainties. In this paper, an improved disturbance observer (DOB) based MPC advanced feedback control is proposed to control the multivariable grinding operation. The improved DOB is based on the optimal achievable H 2 performance and can deal with disturbance observation for the nonminimum-phase delay systems. In this DOB-MPC advanced feedback control, the higher-level optimizer computes the optimal operation points by maximize the profit function and passes them to the MPC level. The MPC acts as a presetting controller and is employed to generate proper pre-setpoint for the lower-level basic feedback control system. The DOB acts as a compensator and improves the operation performance by dynamically compensating the setpoints for the basic control system according to the observed various disturbances and plant uncertainties. Several simulations are performed to demonstrate the proposed control method for grinding process operation.     

基于高斯模型的聚乙烯过程设计与控制集成优化

聚乙烯反应过程中物流-能流剧烈交叠、反应-传递相互耦合,使得过程具有强非线性以及多重稳态。传统的顺序设计方法不能保证系统有足够的控制自由度,当存在扰动和过程参数不确定性时,仅依靠设计控制器很难提高产品质量。提出一种聚乙烯工艺稳态设计与运行控制的集成优化方案,创造性地引入Kriging高斯模型同时预测模型动态和模型不确定性。另一个重要的贡献是在聚乙烯工艺设计阶段,设计性能指标,定量描述过程稳态设计对闭环动态的影响。所提出的方法已经通过对气相聚乙烯工艺设计和运行控制的集成优化进行了验证,并在参数不确定性和扰动存在情况下仿真证实了集成优化设计方案的高效性。     

一种扰动自适应的鲁棒预测控制算法

针对实际生产中扰动的时变性,提出了一种扰动自适应的鲁棒预测控制（RAMPC）算法以提高扰动抑制性能。采用时间序列（ARMA）模型在线辨识系统的不可测扰动,通过基于多次迭代思想的递推辨识算法（multi-iteration pseudo-linear regression,MIPLR）来保证在线辨识的质量和收敛速度。考虑到数据与辨识模型的不确定性,改用min-max形式描述MPC算法的控制作用优化命题,并将在线辨识过程中的误差数据引入min-max命题,使在线辨识与控制作用鲁棒优化求解紧密结合起来,提高算法鲁棒性。进一步将此min-max问题转换为一个等效的非线性min问题,并采用多步线性化方法实现快速求解,解决了传统min-max方法在线计算负荷高的问题。仿真结果表明了该算法的有效性。     

Capturing dynamics in integrated supply chain management

A major challenge for an enterprise to stay competitive in today’s highly competitive market environment is to be able of capturing and handling the dynamics of its entire supply chain (SC). This work incorporates uncertainty and process dynamics into enterprise wide models which also contemplate cross-functional decisions. The SC integrated solution developed includes a design–planning and a financial formulations. A model predictive control (MPC) methodology is proposed that comprises a stochastic optimization approach. A scenario based multi-stage stochastic mixed integer linear programming (MILP) model is employed to address the problem. The novel control framework introduced constitutes a step-forward in closing the loop for the dynamic supply chain management (SCM) and a supporting platform for the supervisory module handling the incidences that may arise in the SC. The potential of the presented approach is highlighted through a case study, where the results of the deterministic MPC and the joint control framework are compared. It is emphasized the significance of merging uncertainty treatment and control strategies to improve the SC performance.     

A robustly stabilizing fault-tolerant MPC: A performance improvement-based approach

In terms of model predictive control (MPC) performance degradation caused by operational faults, in this article, a robust MPC strategy with active fault tolerance properties is proposed. The proposed strategy incorporates a fault supervision layer into the structure of conventional cost-contracting formulation-based robust MPC for the online update of the nominal controller model in the event of faults. The robust MPC is based on multiplant uncertainty, while the supervisory layer consists of a bank of unknown input observers and a decision-making algorithm. Simulation results in a nonlinear polymerization reactor subject to process faults demonstrate that the proposed approach offers superior performance compared to the conventional strategy.     

Actuator stiction compensation via model predictive control for nonlinear processes

The problem of valve stiction is addressed, which is a nonlinear friction phenomenon that causes poor performance of control loops in the process industries. A model predictive control (MPC) stiction compensation formulation is developed including detailed dynamics for a sticky valve and additional constraints on the input rate of change and actuation magnitude to reduce control loop performance degradation and to prevent the MPC from requesting physically unrealistic control actions due to stiction. Although developed with a focus on stiction, the MPC‐based compensation method presented is general and has potential to compensate for other nonlinear valve dynamics which have some similarities to those caused by stiction. Feasibility and closed‐loop stability of the proposed MPC formulation are proven for a sufficiently small sampling period when Lyapunov‐based constraints are incorporated. Using a chemical process example with an economic model predictive controller (EMPC), the selection of appropriate constraints for the proposed method is demonstrated. The example verified the incorporation of the stiction dynamics and actuation magnitude constraints in the EMPC causes it to select set‐points that the valve output can reach and causes the operating constraints to be met. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2004–2023, 2016     

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.