Distributed dissipative model predictive control for process networks with imperfect communication

Results are developed to ensure stability of a dissipative distributed model predictive controller in the case of structured or arbitrary failure of the controller communication network; bounded errors in the communication may similarly be handled. Stability and minimum performance of the process network is ensured by placing a dissipative trajectory constraint on each controller. This allows for the interaction effects between units to be captured in the dissipativity properties of each process, and thus, accounted for by choosing suitable dissipativity constraints for each controller. This approach is enabled by the use of quadratic difference forms as supply rates, which capture detailed dynamic system information. A case study is presented to illustrate the results. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1682–1699, 2014     

从区间模型预测控制到双层结构模型预测控制

模型预测控制算法（MPC）存在设定点控制与区间控制两种策略,区间预测控制较之设定点控制在技术上具有先进性。目前,主流的预测控制软件技术均采用双层结构,即上层稳态优化计算最优设定点,下层动态控制负责动态跟踪最优设定点。从过程稳态的角度出发,分别对区间预测控制和双层结构预测控制进行了机理分析,从定性与定量两个方面比较了这两者的异同点,提出并证明了两者的一致性条件。论述了双层结构预测控制较之单层结构下的区间控制更具先进性。     

A multi-priority hierarchical optimization method for double-layer model predictive control

Considering the demand for the sequential regulation of manipulated variables in actual industrial process control, the conventional solution of double-layer model predictive control faces the problem that the weight coefficients are difficult to tune. This paper proposes an improved hierarchical optimization method for manipulated variables in the steady-state optimization layer of double-layer model predictive control. The proposed method can adjust the manipulated variables sequentially without an accurate weight coefficient to avoid difficulty in tuning the weight coefficients. The relation between the optimal solution and the feasible region of the steady-state optimization layer is analysed to describe the reoptimization of the key manipulated variables. The impact of the economic cost coefficient on the optimal solution with the sensitivity analysis method is studied, and the complexity of using the weight coefficient to solve the priority optimization problem of the manipulated variables is assessed. The steady-state optimization solution procedure is improved based on the theory of the multiobjective complete hierarchical method. The hierarchical and sequential optimization of the manipulated variables results in expanding the space and freedom of the key manipulated variables, increasing efficiency, reducing consumption, and improving economic performance. The improved hierarchical optimization method is direct and simple in achieving optimization sequentially and satisfies the need for adjusting the manipulated variables according to human intentions.     

前馈变量对预测控制可行域的影响分析

实际生产过程中,预测控制因其解耦性能和强鲁棒性得以广泛使用。在预测控制的研究中大都忽略控制过程中的干扰作用。对于控制过程中存在的可测且变化规律已知的干扰作用,干扰对输出的影响具有一定的可预见性,可通过在预测控制器中引入前馈的方法加以利用。前馈变量的引入会对系统的控制效果产生影响,如果不先对其影响进行分析而直接求解优化,最终结果不能反映预测控制的实际效果。本文从可行域的角度出发,通过几何表现形式,直观分析前馈变量的引入造成的可行域变化;进一步使用了凸空间的思想,通过求解可行域的顶点集合来确定可行域的大小,进而得出前馈变量对系统可行域的影响效果,通过仿真验证了本文方法的有效性。     

一类化工过程多变量系统的自适应非线性预测控制

针对化工过程的一类多变量非线性系统,提出了一种自适应非线性预测控制(ANMPC)算法。在采用递归最小二乘法进行预测模型参数在线辨识的基础上,将系统的静态非线性关系用一个反向传播(BP)神经网络稳态模型来表示,通过稳态模型求得的动态增益来进一步校正预测模型的参数。详述了ANMPC控制器设计步骤,通过在一个多变量pH中和过程中的仿真验证了本算法的可行性和有效性。     

Koopman Lyapunov-based model predictive control of nonlinear chemical process systems

In this work, we propose the integration of Koopman operator methodology with Lyapunov-based model predictive control (LMPC) for stabilization of nonlinear systems. The Koopman operator enables global linear representations of nonlinear dynamical systems. The basic idea is to transform the nonlinear dynamics into a higher dimensional space using a set of observable functions whose evolution is governed by the linear but infinite dimensional Koopman operator. In practice, it is numerically approximated and therefore the tightness of these linear representations cannot be guaranteed which may lead to unstable closed-loop designs. To address this issue, we integrate the Koopman linear predictors in an LMPC framework which guarantees controller feasibility and closed-loop stability. Moreover, the proposed design results in a standard convex optimization problem which is computationally attractive compared to a nonconvex problem encountered when the original nonlinear model is used. We illustrate the application of this methodology on a chemical process example.     

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。     

非线性Hammerstein模型预测控制策略及其在pH中和过程中的应用

所有实际工业过程都包含一定程度的非线性,如pH中和过程由于其本身的强非线性是工业过程控制中具有挑战性的难题,但至今为止仍缺乏有效的非线性控制方法。将基于差分方程模型的模型预测控制策略(model predictive control,MPC)推广到包含一个静态非线性多项式函数和一个线性差分方程动态环节的非线性Hammerstein系统,详细描述了基于静态非线性多项式函数的最优控制作用求解方法,提出了一套新的非线性Hammerstein MPC 控制策略(nonlinear Hammerstein predictive control,NLHPC)。pH中和过程控制仿真和控制实验表明,NLHPC的控制结果好于工业上常用的非线性 PID(nonlinear PID,NL-PID)控制器。     

Economic model predictive control of nonlinear process systems using empirical models

Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained either through application of first principles or through system identification techniques. In industrial practice, it may be difficult in general to obtain an accurate first‐principles model of the process. Motivated by this, in the present work, Lyapunov‐based EMPC (LEMPC) is designed with a linear empirical model that allows for closed‐loop stability guarantees in the context of nonlinear chemical processes. Specifically, when the linear model provides a sufficient degree of accuracy in the region where time varying economically optimal operation is considered, conditions for closed‐loop stability under the LEMPC scheme based on the empirical model are derived. The LEMPC scheme is applied to a chemical process example to demonstrate its closed‐loop stability and performance properties as well as significant computational advantages. © 2014 American Institute of Chemical Engineers AIChE J, 61: 816–830, 2015     

Real‐time economic model predictive control of nonlinear process systems

Closed‐loop stability of nonlinear systems under real‐time Lyapunov‐based economic model predictive control (LEMPC) with potentially unknown and time‐varying computational delay is considered. To address guaranteed closed‐loop stability (in the sense of boundedness of the closed‐loop state in a compact state‐space set), an implementation strategy is proposed which features a triggered evaluation of the LEMPC optimization problem to compute an input trajectory over a finite‐time prediction horizon in advance. At each sampling period, stability conditions must be satisfied for the precomputed LEMPC control action to be applied to the closed‐loop system. If the stability conditions are not satisfied, a backup explicit stabilizing controller is applied over the sampling period. Closed‐loop stability under the real‐time LEMPC strategy is analyzed and specific stability conditions are derived. The real‐time LEMPC scheme is applied to a chemical process network example to demonstrate closed‐loop stability and closed‐loop economic performance improvement over that achieved for operation at the economically optimal steady state. © 2014 American Institute of Chemical Engineers AIChE J, 61: 555–571, 2015     

Sequential and iterative architectures for distributed model predictive control of nonlinear process systems

In this work, we focus on distributed model predictive control of large scale nonlinear process systems in which several distinct sets of manipulated inputs are used to regulate the process. For each set of manipulated inputs, a different model predictive controller is used to compute the control actions, which is able to communicate with the rest of the controllers in making its decisions. Under the assumption that feedback of the state of the process is available to all the distributed controllers at each sampling time and a model of the plant is available, we propose two different distributed model predictive control architectures. In the first architecture, the distributed controllers use a one‐directional communication strategy, are evaluated in sequence and each controller is evaluated only once at each sampling time; in the second architecture, the distributed controllers utilize a bi‐directional communication strategy, are evaluated in parallel and iterate to improve closed‐loop performance. In the design of the distributed model predictive controllers, Lyapunov‐based model predictive control techniques are used. To ensure the stability of the closed‐loop system, each model predictive controller in both architectures incorporates a stability constraint which is based on a suitable Lyapunov‐based controller. We prove that the proposed distributed model predictive control architectures enforce practical stability in the closed‐loop system and optimal performance. The theoretical results are illustrated through a catalytic alkylation of benzene process example. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Selection of control configurations for economic model predictive control systems

Economic model predictive control (EMPC) is a feedback control method that dictates a potentially dynamic (time‐varying) operating policy to optimize the process economics. The objective function used in the EMPC system may be a general nonlinear function that describes the process/system economics. As this function is not derived on the sole basis of classical control considerations (stabilization, tracking, and optimal control action calculation) but rather on the basis of economics, selecting the appropriate control configuration, and quantifying the influence of a given input on an economic cost is an important task for the proper design and computational efficiency of an EMPC scheme. Owing to these considerations, an input selection methodology for EMPC is proposed which utilizes the relative degree and the sensitivity of the economic cost with respect to an input to identify and select stabilizing manipulated inputs with the most dynamic and steady‐state influence on the economic cost function to be assigned to EMPC. Other considerations for input selection for EMPC are also discussed and integrated into a proposed input selection methodology for EMPC. The control configuration selection method for EMPC is demonstrated using a chemical process example. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3230–3242, 2014     

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     

基于多目标分层的预测控制定态优化技术

多目标分层优化要求是从复杂工业过程的现场实际应用背景出发而提出的.详细阐述了复杂工业过程的多目标分层优化要求的含义,在预测控制两级分层结构的基础上提出了基于二次规划的定态优化有效求解方法.通过Shell控制问题等仿真结果,说明所提出的定态优化技术具有良好的控制性能,能够适应生产过程的需要.     

High-order iterative learning model predictive control for batch chemical processes

In order to address two-dimensional (2D) control issue for a class of batch chemical processes, we propose a novel high-order iterative learning model predictive control (HILMPC) method in this paper. A set of local state-space models are first constructed to represent the batch chemical processes by adopting the just-in-time learning (JITL) technique. Meanwhile, a pre-clustered strategy is used to lessen the computational burden of the modelling process and improve the modelling efficiency. Then, a two-stage 2D controller is designed to achieve integrated control by combining high-order iterative learning control (HILC) on the batch domain with model predictive control (MPC) on the time domain. The resulting HILMPC controller can not only guarantee the convergence of the system on the batch domain, but also guarantee the closed-loop stability of the system on the time domain. The convergence of the HILMPC method is ensured by rigorous analysis. Two examples are presented in the end to demonstrate that the developed method provides better control performance than its previous counterpart.     

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.     

Constrained model predictive control in ball mill grinding process

Stable control of grinding process is of great importance for improvements of operation efficiency, the recovery of the valuable minerals, and significant reductions of production costs in concentration plants. Decoupled multi-loop PID controllers are usually carried out to manage to eliminate the effects of interactions among the control loops, but they generally become sluggish due to imperfect process models and a close control of the process is usually impossible in real practice. Based on its inherent decoupling scheme, model predictive control (MPC) is employed to handle such highly interacting system. For high quality requirements, a three-input three-output model of the grinding process is constructed. Constrained dynamic matrix control (DMC) is applied in an iron ore concentration plant, and operation of the process close to their optimum operating conditions is achieved. Some practical problems about the application of MPC in grinding process are presented and discussed in detail.     

Multistage nonlinear model predictive control for pumping treatment in hydraulic fracturing

Hydraulic fracturing has gained increasing attention as it allows the constrained natural gas and crude oil to flow out of low-permeability shale formations and significantly increase production. Perilous operating states of extremely high pressure also raise some safety concerns, requiring us to formulate an appropriate dynamic model, and provide a careful engineering control to ensure safe operating conditions. Moreover, uncertainties due to spatially varying rock properties increase the difficulties in control of the fracturing process. In this work, we formulate a first-principles model by considering the fracture evolution, mass transport of substances in the slurry, changing fluid properties, and the monitored operating pressure on the ground level. Next, we implement nonlinear model predictive control (NMPC) to control the process under a set of final requirements and process constraints. Our results show that the performance of standard NMPC degrades when the rock uncertainty causes the parameter mismatch between the process and the predictive model in the controller. With standard NMPC, designed with a nominal model, the process fails to meet the terminal requirements of fracture geometry, and pressure is violated in one of the parameter mismatch cases. Therefore, we resort to multistage NMPC, which considers uncertainty evolution in a scenario tree with separate control sequences to address constraint violations. We demonstrate that multistage NMPC presents good performance by showing constraint satisfaction whether the uncertain rock parameter realization is time-invariant or time-variant. We also simulate the process with multistage NMPC including different numbers of scenarios and compare their control performance. Our investigation demonstrates that multistage NMPC effectively manages parametric uncertainties attributed to non-homogeneous rock formation, and provides a promising control strategy for the hydraulic fracturing process.