一类非线性系统的变负荷预测控制

生产过程的变负荷运行使得其非线性动态特性的影响凸显。针对变负荷生产过程中机理模型为常微分方程或半显式Heisenberg微分-代数方程的一类非线性动态系统,采用非线性预测控制算法,构造出稳态优化与动态优化的两层控制结构,并采用联立法进行优化数值求解。最后对化工过程的夹套CSTR进行仿真验证,表明该算法的有效性。     

Differential recurrent neural network based predictive control

In this paper an efficient algorithm to train general differential recurrent neural network (DRNN) is developed. The trained network can be directly used in the nonlinear model predictive control (NMPC) context. The neural network is represented in a general nonlinear state-space form and used to predict the future dynamic behavior of the nonlinear process in real time. In the new training algorithms, the ODEs of the model and the dynamic sensitivity are solved simultaneously using Taylor series expansion and automatic differentiation (AD) techniques. The same approach is also used to solve the online optimization problem in the predictive controller. The efficiency and effectiveness of the DRNN training algorithm and the NMPC approach are demonstrated through a two-CSTR case study. A good model fitting for the nonlinear plant at different sampling rates is obtained using the new method. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. The DRNN based NMPC approach results in good control performance under different operating conditions.     

NONLINEAR MODEL PREDICTIVE CONTROL

Nonlinear Model Predictive Control (NMPC), a strategy for constrained, feedback control of nonlinear processes, has been developed. The algorithm uses a simultaneous solution and optimization approach to determine the open-loop optimal manipulated variable trajectory at each sampling instant. Feedback is incorporated via an estimator, which uses process measurements to infer unmeasured state and disturbance values. These are used by the controller to determine the future optimal control policy. This scheme can be used to control processes described by different kinds of models, such as nonlinear ordinary differential/algebraic equations, partial differential/algebraic equations, integra-differential equations and delay equations. The advantages of the proposed NMPC scheme are demonstrated with the start-up of a non-isothermal, non-adiabatic CSTR with an irreversible, first-order reaction. The set-point corresponds to an open-loop unstable steady state. Comparisons have been made with controllers designed using (1) nonlinear variable transformations, (2) a linear controller tuned using the internal model control approach, and (3) open-loop optimal control. NMPC was able to bring the controlled variable to its set-point quickly and smoothly from a wide variety of initial conditions. Unlike the other controllers, NMPC dealt with constraints in an explicit manner without any degradation in the quality of control. NMPC also demonstrated superior performance in the presence of a moderate amount of error in the model parameters, and the process was brought to its set-point without steady-state offset.     

Model predictive control for the self-optimized operation in wastewater treatment plants: Analysis of dynamic issues

This paper describes a procedure to find the best controlled variables in an economic sense for the activated sludge process in a wastewater treatment plant, despite the large load disturbances. A novel dynamic analysis of the closed loop control of these variables has been performed, considering a nonlinear model predictive controller (NMPC) and a particular distributed NMPC-PI control structure where the PI is devoted to control the process active constraints and the NMPC the self-optimizing variables. The well-known self-optimizing control methodology has been applied, considering the most important measurements of the process. This methodology provides the optimum combination of measurements to keep constant with minimum economic loss. In order to avoid nonfeasible dynamic operation, a preselection of the measurements has been performed, based on the nonlinear model of the process and evaluating the possibility of keeping their values constant in the presence of typical disturbances.     

Model based control of a liquid swelling constrained batch reactor subject to recipe uncertainties

This work presents the application of nonlinear model predictive control (NMPC) to a simulated industrial batch reactor subject to safety constraint due to reactor level swelling, which can occur with relatively fast dynamics. Uncertainties in the implementation of recipes in batch process operation are of significant industrial relevance. The paper describes a novel control-relevant formulation of the excessive liquid rise problem for a two-phase batch reactor subject to recipe uncertainties. The control simulations are carried out using a dedicated NMPC and optimization software toolbox OptCon which implements efficient numerical algorithms. The open-loop optimal control problem is computed using the multiple-shooting technique and the arising nonlinear programming problem is solved using a sequential quadratic programming (SQP) algorithm tailored for large-scale problems, based on the freeware optimization environment HQP. The fast response of the NMPC controller is guaranteed by the initial value embedding and real-time iteration technologies. It is concluded that the OptCon implementation allows small sampling times and the controller is able to maintain safe and optimal operation conditions, with good control performance despite significant uncertainties in the implementation of the batch recipe.     

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.     

基于全局正交配置的非线性预测控制算法

针对非线性预测控制(NMPC)在线优化计算量大这一关键问题,提出一种基于全局正交配置的非线性预测控制算法。该算法以高阶插值正交多项式为基函数同时配置优化时域内的状态变量和控制变量,将连续动态优化问题转化为非线性规划问题(NLP)求解。全局正交配置可以使用较少的配置点而获得较高的逼近精度,这样即使NMPC使用很长的优化时域,离散化后得到的NLP问题的规模也比较小,能够有效地降低在线优化计算量。最后,以连续聚合反应过程为例验证了算法的有效性。     

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.     

Nonparametric nonlinear model predictive control

Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impeded by linear models due to the lack of a similarly accepted nonlinear modeling or databased technique. Aimed at solving this problem, the paper addresses three issues: (i) extending second-order Volterra nonlinear MPC (NMPC) to higher-order for improved prediction and control; (ii) formulating NMPC directly with plant data without needing for parametric modeling, which has hindered the progress of NMPC; and (iii) incorporating an error estimator directly in the formulation and hence eliminating the need for a nonlinear state observer. Following analysis of NMPC objectives and existing solutions, nonparametric NMPC is derived in discrete-time using multidimensional convolution between plant data and Volterra kernel measurements. This approach is validated against the benchmark van de Vusse nonlinear process control problem and is applied to an industrial polymerization process by using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University.     

APPLICATION OF FUZZY ADAPTIVE CONTROLLER IN NONLINEAR PROCESS CONTROL

In general, physical processes are usually nonlinear and control system design based on the linearization technique cannot control the process well for a wide range of operation. Use of the variable transformation method may not always solve the problem. In this paper, a fuzzy adaptive controller is proposed to control the nonlinear process. The CSTR control problem has also been considered. The results are compared with the method of nonlinear model predictive control (NMPC) with constrained and unconstrained control variables. A fuzzy model-following control system scheme is also proposed. The results show that the proposed controller is a feasible control structure for a nonlinear or parameter-variations process control.     

Dynamic Optimization and Non‐linear Model Predictive Control to Achieve Targeted Particle Morphologies

An event‐driven approach based on dynamic optimization and nonlinear model predictive control (NMPC) is investigated together with inline Raman spectroscopy for process monitoring and control. The benefits and challenges in polymerization and morphology monitoring are presented, and an overview of the used mechanistic models and the details of the dynamic optimization and NMPC approach to achieve the relevant process objectives are provided. Finally, the implementation of the approach is discussed, and results from experiments in lab and pilot‐plant reactors are presented.     

On‐Line PEMFC Control Using Parameterized Nonlinear Model‐Based Predictive Control

In this work, a fast nonlinear model‐based predictive control (NMPC) strategy is designed and experimentally validated on‐line on a real fuel cell. Regarding NMPC strategies, the most challenging part remains to achieve on‐line implementation, especially when dealing with fast dynamic systems. As previously demonstrated in a recent work, the proposed control strategy is ideally suited to address this problem. Indeed, it is 30 times faster than classical NMPC controllers. This strategy relies on a specific parameterization of the control actions to reduce the computational time and achieve on‐line implementation. Due to its short computational time compared to mechanistic models, an artificial neural network model is designed and experimentally validated. This model is employed as internal model in the NMPC controller to predict the system behavior. To confirm the applicability and the relevance of the proposed NMPC controller varying control scenarios are investigated on a test bench. The built‐in controller is overridden and the NMPC controller is implemented externally and executed on‐line. Experimental results exhibit the outstanding tracking capability and robustness against model‐process mismatch of the proposed strategy. The parameterized NMPC controller turns out to be an excellent candidate for on‐line applications.     

Improving scenario decomposition algorithms for robust nonlinear model predictive control

This paper deals with the efficient computation of solutions of robust nonlinear model predictive control problems that are formulated using multi-stage stochastic programming via the generation of a scenario tree. Such a formulation makes it possible to consider explicitly the concept of recourse, which is inherent to any receding horizon approach, but it results in large-scale optimization problems. One possibility to solve these problems in an efficient manner is to decompose the large-scale optimization problem into several subproblems that are iteratively modified and repeatedly solved until a solution to the original problem is achieved. In this paper we review the most common methods used for such decomposition and apply them to solve robust nonlinear model predictive control problems in a distributed fashion. We also propose a novel method to reduce the number of iterations of the coordination algorithm needed for the decomposition methods to converge. The performance of the different approaches is evaluated in extensive simulation studies of two nonlinear case studies.     

汽油在线优化调合模型设计

汽油在线调合具有非线性和大纯滞后等不易控制的特点.提出采用非线性PID控制模型的约束条件和基本公式,以及对调合模型中采用的非线性PID 鲁棒优化 Smith预估进行了较深入的分析,解决了调合过程最棘手的辛烷值混合的非线性问题.经二个实际项目工程的实施验证,很好地解决了调合过程的辛烷值优化控制的精度和稳定性问题.     

Nonlinear model predictive control of an industrial polymerization process

Nonlinear model predictive control (NMPC) is used to maintain and control polymer quality at specified production rates because the polymer quality measures have strong interacting nonlinearities with different temperatures and feed rates. Polymer quality measures that are available from the laboratory infrequently are controlled in closed-loop using a NMPC to set the temperature profile of the reactors. NMPC results in better control of polymer quality measures at different production rates as compared to using the nonlinear process model with reaction kinetics to implement offline targets for reactor temperatures.     

Automated reformulation of disjunctive constraints in MINLP optimization

In this paper, a general method for handling disjunctive constraints in a MINLP optimization problem is presented. This method automates the reformulation of an, in a abstract modeling language given, optimization problem into a mathematical problem that is solvable with existing optimization tools. This implementation can use common MILP solvers for linear problems and nonlinear methods for quasi-convex optimization problems. It also includes the possibility to use the logics in the system and solve the system logically using subproblems.     

Nonlinear model predictive control: current status and future directions

Linear model predictive control (LMPC) is well established as the industry standard for controlling constrained multivariable processes. A major limitation of LMPC is that plant behavior is described by linear dynamic models. As a result, LMPC is inadequate for highly nonlinear processes and moderately nonlinear processes which have large operating regimes. This shortcoming coupled with increasingly stringent demands on throughput and product quality has spurred the development of nonlinear model predictive control (NMPC). NMPC is conceptually similar to its linear counterpart except that nonlinear dynamic models are used for process prediction and optimization. The purpose of this paper is to provide an overview of current NMPC technology and applications, as well as to propose topics for future research and development. The review demonstrates that NMPC is well suited for controlling multivariable nonlinear processes with constraints, but several theoretical and practical issues must be resolved before widespread industrial acceptance is achieved.     

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.     

SIMOP: Efficient reactive distillation optimization using stochastic optimizers

A methodology to improve the efficiency of stochastic methods applied to the optimization of chemical processes with a large number of equality constraints is presented. The methodology is based on two steps: (a) the optimization of the simulation step, which involves the optimum choice of design variables and subsystems to be simultaneously solved; (b) the optimization of the nonlinear programming (NLP) problem using stochastic methods. For the first step a flexible tool (SIMOP) is used, whereby different numerical procedures can be easily obtained, taking into account the problem formulation and specific characteristics, the need for specific initialization schemes and the efficient solution of systems of nonlinear equations. This methodology was applied to the optimization of a reactive distillation process for the production of ethylene glycol. Due to the complexity of the mathematical model, several different numerical procedures were generated, and their influence on the computational burden and on the reliability and accuracy of the optimization to reach the global optimum were studied. The results obtained suggest that in addition to the choice of design variables, the structure of subsystems associated to numerical procedures has a considerable impact on the performance of the optimizers.     

NMPC of an industrial crystallization process using model-based observers

This paper illustrates the benefits of a nonlinear model-based predictive control (NMPC) approach applied to an industrial crystallization process. This relevant approach proposes a setpoint tracking of the crystal mass. The controlled variable, unavailable, is obtained using an extended Luenberger observer. A neural network model is used as internal model to predict process outputs. An optimization problem is solved to compute future control actions taking into account real-time control objectives. The performances of this strategy are demonstrated via simulation in cases of setpoint tracking and disturbance rejection. The results reveal a significant improvement in terms of robustness and energy efficiency.