Economic performance analysis in the design of on-line batch optimization systems

In this paper, the on-line optimization of batch reactors under parametric uncertainty is considered. A method is presented that estimates the likely economic performance of the on-line optimizer. The method of orthogonal collocation is employed to convert the differential algebraic optimization problem (DAOP) of the dynamic optimization into a nonlinear program (NLP) and determine the nominal optimum. Based on the resulting NLP, the optimization steps are approximated by neighbouring extremal problems and the average deviation from the true process optimum is estimated dependent on the measurement error and the parametric uncertainty. The true process optimum is assumed to be represented by the optimum of the process model with the true parameter values. A back off from the active path and endpoint inequality constraints is determined at each optimization step which ensures the feasible operation of the process. Based on the analysis results the optimal structure of the optimizer in terms of measured variables and estimated parameters can be determined. The method of the average deviation from optimum is developed for the fixed terminal time case and for time optimal problems. In both cases, the theory is demonstrated on an example.     

Suboptimal nonlinear predictive control based on multivariable neural Hammerstein models

This paper describes a computationally efficient nonlinear Model Predictive Control (MPC) algorithm in which the neural Hammerstein model is used. The Multiple-Input Multiple-Output (MIMO) dynamic model contains a neural steady-state nonlinear part in series with a linear dynamic part. The model is linearized on-line, as a result the MPC algorithm requires solving a quadratic programming problem, the necessity of nonlinear optimization is avoided. A neutralization process is considered to discuss properties of neural Hammerstein models and to show advantages of the described MPC algorithm. In practice, the algorithm gives control performance similar to that obtained in nonlinear MPC, which hinges on non-convex optimization.     

Optimization-based tuning of nonlinear model predictive control with state estimation

Nonlinear model predictive controllers determine appropriate control actions by solving an on-line optimization problem. A nonlinear process model is utilized for on-line prediction, making such algorithms particularly appropriate for the control of chemical reactors. The algorithms presented in this paper incorporates an extended Kalman filter, which allows operations around unstable steady-state points. The paper proposes a formalization of the procedure for tuning the several parameters of the control algorithm. This is accomplished by specifying time-domain performance criteria and using an interactive multi-objective optimization package off-line to determine parameters values that satisfy these criteria. Three reactor examples are used to demonstrate the effectiveness of the proposed on-line algorithm and off-line tuning procedure.     

工业大系统双层结构预测控制的集中优化与分散控制策略

为降低工业大系统模型预测控制(Model predictive control,MPC)在线计算复杂度,同时保证系统的全局优化性能,提出一种集中优化、分散控制的双层结构预测控制策略.在稳态目标计算层(Steady-state target calculation, SSTC),基于全局过程模型对系统进行集中优化,将优化结果作为设定值传递给动态控制层;在动态控制层,将大系统划分为若干个子系统,每个子系统分别由基于各自子过程模型的模型预测控制进行控制,为减少各子系统之间的相互干扰,在各个子系统之间添加前馈控制器对扰动进行补偿,提高系统的总体动态控制性能.该策略的优点在于能确保系统全局最优性的同时降低了在线计算量,提高了工业大系统双层结构预测控制方法的实时性.仿真实例验证该方法的有效性.     

Steady-state target optimization designs for integrating real-time optimization and model predictive control

In industrial practice, the optimal steady-state operation of continuous-time processes is typically addressed by a control hierarchy involving various layers. Therein, the real-time optimization (RTO) layer computes the optimal operating point based on a nonlinear steady-state model of the plant. The optimal point is implemented by means of the model predictive control (MPC) layer, which typically uses a linear dynamical model of the plant. The MPC layer usually includes two stages: a steady-state target optimization (SSTO) followed by the MPC dynamic regulator. In this work, we consider the integration of RTO with MPC in the presence of plant-model mismatch and constraints, by focusing on the design of the SSTO problem. Three different quadratic program (QP) designs are considered: (i) the standard design that finds steady-state targets that are as close as possible to the RTO setpoints; (ii) a novel optimizing control design that tracks the active constraints and the optimal inputs for the remaining degrees of freedom; and (iii) an improved QP approximation design were the SSTO problem approximates the RTO problem. The main advantage of the strategies (ii) and (iii) is in the improved optimality of the stationary operating points reached by the SSTO-MPC control system. The performance of the different SSTO designs is illustrated in simulation for several case studies.     

Latent‐variable Nonlinear Model Predictive Control Strategy for a pH Neutralization Process

Linear model predictive control (MPC) is a widely‐used control strategy in chemical processes. Its extension to nonlinear MPC (NMPC) has drawn increasing attention since many process systems are inherently nonlinear. When implementing the NMPC based on a nonlinear predictive model, a nonlinear dynamic optimization problem must be calculated. For the sake of solving this optimization problem efficiently, a latent‐variable dynamic optimization approach is proposed. Two kinds of constraint formulations, original variable constraint and Hotelling T² statistic constraint, are also discussed. The proposed method is illustrated in a pH neutralization process. The results demonstrate that the latent‐variable dynamic optimization based the NMPC strategy is efficient and has good control performance.     

PS转炉造渣过程的动态优化控制

建立了Pierce-Smith(PS)转炉造渣过程的非线性状态空问模型,并提出了基于生产质量指标反馈校正的铜锍造渣过程的动态优化控制方案.该方案首先基于最优模型求得最优控制律.为消除吹炼过程中的扰动以及其他不确定因素所带来的影响,再引入基于生产质量指标的反馈调整机制.其中反馈信息由软测量模犁根据进出转炉的物料计算得到,智能控制单元根据反馈的质量信息和期望的质量目标间的偏差对最优控制律进行补偿修正.并在该动态优化控制方案基础上,设计并开发了铜锍吹炼过程的优化控制指导决策系统.实际运行结果表明该系统优化了产品的质量,同时也实现了铜锍生产过程的节能.     

基于稳态非线性模型和线性ARX模型组合的非线性预测控制

通过点集映射来表示非线性系统的稳态模型,用系统的稳态增益来修正具有外界输入的线性自回归（AutoRegressive with eXternal input, ARX）模型的动态增益,提出了一种基于稳态非线性模型和线性ARX模型组合的非线性预测控制算法．该算法用递归最小二乘法在线辨识系统的动态模型参数,用序列二次规划算法求解目标函数．最后通过对典型化工非线性对象pH中和过程的仿真对本算法进行了验证．结果表明,本算法比广义预测控制算法具有更好的设定值跟踪性能和抗干扰能力．     

Distributed economic MPC: Application to a nonlinear chemical process network

In the present work, we focus on the development and application of Lyapunov-based economic model predictive control (LEMPC) designs to a catalytic alkylation of benzene process network, which consists of four continuously stirred tank reactors and a flash separator. We initially propose a new economic measure for the entire process network which accounts for a broad set of economic considerations on the process operation including reaction conversion, separation quality and energy efficiency. Subsequently, steady-state process optimization is first carried out to locate an economically optimal (with respect to the proposed economic measure) operating steady-state. Then, a sequential distributed economic model predictive control design method, suitable for large-scale process networks, is proposed and its closed-loop stability properties are established. Using the proposed method, economic, distributed as well as centralized, model predictive control systems are designed and are implemented on the process to drive the closed-loop system state close to the economically optimal steady-state. Extensive simulations are carried out to demonstrate the application of the proposed economic MPC (EMPC) designs and compare them with a centralized Lyapunov-based model predictive control design, which uses a conventional, quadratic cost function that includes penalty on the deviation of the states and inputs from their economically optimal steady-state values, from computational time and closed-loop performance points of view.     

Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems

In this work, we propose a conceptual framework for integrating dynamic economic optimization and model predictive control (MPC) for optimal operation of nonlinear process systems. First, we introduce the proposed two-layer integrated framework. The upper layer, consisting of an economic MPC (EMPC) system that receives state feedback and time-dependent economic information, computes economically optimal time-varying operating trajectories for the process by optimizing a time-dependent economic cost function over a finite prediction horizon subject to a nonlinear dynamic process model. The lower feedback control layer may utilize conventional MPC schemes or even classical control to compute feedback control actions that force the process state to track the time-varying operating trajectories computed by the upper layer EMPC. Such a framework takes advantage of the EMPC ability to compute optimal process time-varying operating policies using a dynamic process model instead of a steady-state model, and the incorporation of suitable constraints on the EMPC allows calculating operating process state trajectories that can be tracked by the control layer. Second, we prove practical closed-loop stability including an explicit characterization of the closed-loop stability region. Finally, we demonstrate through extensive simulations using a chemical process model that the proposed framework can both (1) achieve stability and (2) lead to improved economic closed-loop performance compared to real-time optimization (RTO) systems using steady-state models.     

遗传算法优化的Fuzzy+变论域自适应Fuzzy-PID复合控制策略研究

提出了一种用遗传算法优化的Fuzzy+变论域Fuzzy-PID复合控制器的新方法。该控制器由Fuzzy控制和变论域Fuzzy-PID控制两部分组成。在系统的动态阶段,采用Fuzzy控制使其具有最优的动态性能;当系统进入稳态阶段,采用变论域自适应Fuzzy-PID控制使其具有最优的稳态性能。用遗传算法离线搜索出一组最优的PID参数作为在线调节的初始值,在在线部分,以离线搜索出的PID参数为基础,通过变论域的模糊推理在线调整系统瞬态响应的PID参数,使系统具有良好的自适应能力。 采用加权平滑切换的方式,保证两种不同控制过渡的平稳性。将提出的复合控制策略应用于变风量空调系统的室温串级控制中,计算机仿真结果表明,该方法使系统具有良好的动、稳态性能,抗干扰性和鲁棒性好。     

自适应在线稳态优化方法及其在丙烯腈装置上的应用

介绍了一种自适应优化方法,通过机理分析和模型结构辨识确定系统的模型结构, 采用在线运行数据拟合过程动态模型参数,并依此计算目标函数相对于各操作参数的梯度, 最终确定优化的方向.根据算法设计的计算机软件ANOPT在一个丙烯腈装置上得到实际应 用.结果表明,本方法具有适应性好,抗干扰能力强,寻优速度快等特点,并且不需在线组分分 析仪表,非常适用于实际工业过程.     

Theoretical analysis of unconstrained nonlinear model predictive control

Model predictive control (MPC) is a well-established controller design strategy for linear process models. Because many chemical and biological processes exhibit significant nonlinear behaviour, several MPC techniques based on nonlinear process models have recently been proposed. The most significant difference between these techniques is the computational approach used to solve the nonlinear model predictive control (NMPC) optimization problem. Consequently, analysis of NMPC techniques is often connected to the computational approach employed. In this paper, a theoretical analysis of unconstrained NMPC is presented that is independent of the computational approach. A nonlinear discrete-time, state-space model is used to predict the effects of future inputs on future process outputs. It is shown that model inverse, pole-placement, and steady-state controllers can be obtained by suitable selection of the control and prediction horizons. Moreover, the NMPC optimization problem can be modified to yield nonlinear internal model control (NIMC). The computational requirements of NIMC are considerably less than NMPC, but the NIMC approach is currently restricted to nonlinear models with well-defined and stable inverses. The NIMC controller is shown to provide superior servo and regulatory performance to a linear IMC controller for a continuous stirred tank reactor.     

A Directional Modifier-Adaptation Algorithm for Real-Time Optimization

The steady advances of computational methods make model-based optimization an increasingly attractive method for process improvement. Unfortunately, the available models are often inaccurate. The traditional remedy is to update the model parameters, but this generally leads to a difficult parameter estimation problem that must be solved on-line. In addition, the resulting model may not represent the plant well when there is structural mismatch between the two. The iterative optimization method called Modifier Adaptation overcomes these obstacles by directly incorporating plant measurements into the optimization framework, principally in the form of constraint values and cost and constraint gradients. However, the number of experiments required to estimate these gradients increases linearly with the number of process inputs, which tends to make the method intractable for processes with many inputs. This paper presents a new algorithm, called Directional Modifier Adaptation, that overcomes this limitation by only estimating the plant gradients in certain privileged input directions. It is proven that plant optimality with respect to these privileged directions can be guaranteed upon convergence. A novel, statistically optimal, gradient estimation technique is developed. The algorithm is illustrated through the simulation of a realistic airborne wind-energy system, a promising renewable energy technology that harnesses wind energy using large kites. It is shown that Directional Modifier Adaptation can optimize in real time the path followed by the kite.     

Economics-based NMPC strategies for the operation and control of a continuous catalytic distillation process

Process profitability is an yes or no criterion for the successful long-term operation of industrial processes. This article describes the use of dynamic online economic process optimization to improve the performance of chemical processes. Different model-predictive control techniques have progressively been applied to coupled multivariable control problems and in many cases, especially in the petrochemical industry, the reference values are adjusted infrequently by stationary optimization based upon a rigorous nonlinear stationary plant model (real-time optimization, RTO). In between these optimizations, however, the process may be operated suboptimally due to the presence of disturbances. Nonlinear dynamic model-based optimization has been proposed recently to combine optimal operation and feedback control. In this paper, a model of the complex dynamics of a pilot-scale continuous catalytic distillation process is used to explore the potential benefits of online economics optimizing control strategies. We compare the direct economic optimization scheme with a compromise scheme, the economics-oriented tracking controller. The outcome of this work indicates that by using direct economics optimizing NMPC the plant economics can be handled better while guaranteeing the product specifications which are formulated as explicit constraints.     

极值系统的在线辨识与稳态优化控制方法研究

研究一种基于非线性环节直接表示的ＳＩＳＯＨａｍｍｅｒｓｔｅｉｎ模型参数辨识方法，针对非线性环节呈极值特性的情况，研究一种由在线辨识得到的非线性环节的参数估计值进行稳态优化的控制方法。仿真结果验证了该方法的有效性。     

Nonlinear system identification using optimized dynamic neural network

In this paper, both off-line architecture optimization and on-line adaptation have been developed for a dynamic neural network (DNN) in nonlinear system identification. In the off-line architecture optimization, a new effective encoding scheme—Direct Matrix Mapping Encoding (DMME) method is proposed to represent the structure of neural network by establishing connection matrices. A series of GA operations are applied to the connection matrices to find the optimal number of neurons on each hidden layer and interconnection between two neighboring layers of DNN. The hybrid training is adopted to evolve the architecture, and to tune the weights and input delays of DNN by combining GA with the modified adaptation laws. The modified adaptation laws are subsequently used to tune the input time delays, weights and linear parameters in the optimized DNN-based model in on-line nonlinear system identification. The effectiveness of the architecture optimization and adaptation is extensively tested by means of two nonlinear system identification examples.     

Robust end-point optimizing feedback for nonlinear dynamic processes

The paper suggests two novel approaches to the synthesis of robust end-point optimizing feedback for nonlinear dynamic processes. Classically, end-point optimization is performed only for the nominal process model using optimal control methods, and the question of performance robustness to disturbances and model-plant mismatch remains unaddressed. The present contribution addresses the end-point optimization problem for nonlinear affine systems with fixed final time through robust optimal feedback methods. In the first approach, a nonlinear state feedback is derived that robustly optimizes the final process state. This solution is obtained through series expansion of the Hamilton-Jacobi-Bellman PDE with an active opponent disturbance. As reliable measurements or estimates of all states may not always be available, the second approach also robustly optimizes the process end-point, but uses output rather than state information. This direct use of measurement information is preferred since the choice of a state estimator for robust state feedback is non-trivial even when the observability issue is addressed. A linear time-variant output corrector is obtained by feedback parametrization and numerical optimization of a nonlinear H _∞ cost functional. A number of possible variations and alternatives to both approaches are also discussed. As model-plant mismatch is particularly common with chemical batch processes, the suitability of the robust optimizing feedback is demonstrated on a semi-batch reactor simulation example, where robustness to several realistic mismatches is investigated and the results are compared against those for the optimal open-loop policy and the optimal feedback designed for the nominal model.     

Nonlinear model predictive control using parameter varying BP-ARX combination model

A novel back-propagation AutoRegressive with eXternal input (BP-ARX) combination model is constructed for model predictive control (MPC) of MIMO nonlinear systems, whose steady-state relation between inputs and outputs can be obtained. The BP neural network represents the steady-state relation, and the ARX model represents the linear dynamic relation between inputs and outputs of the nonlinear systems. The BP-ARX model is a global model and is identified offline, while the parameters of the ARX model are rescaled online according to BP neural network and operating data. Sequential quadratic programming is employed to solve the quadratic objective function online, and a shift coefficient is defined to constrain the effect time of the recursive least-squares algorithm. Thus, a parameter varying nonlinear MPC (PVNMPC) algorithm that responds quickly to large changes in system set-points and shows good dynamic performance when system outputs approach set-points is proposed. Simulation results in a multivariable stirred tank and a multivariable pH neutralisation process illustrate the applicability of the proposed method and comparisons of the control effect between PVNMPC and multivariable recursive generalised predictive controller are also performed.     

基于阶段辨识的诺西肽发酵过程菌体浓度软测量

由于发酵过程中系统非线性特性与发酵阶段密切相关的实际特点,针对诺西肽发酵过程菌体浓度的估计问题,提出了一种基于阶段辨识的软测量方法.首先以分阶段的诺西肽发酵过程非结构模型为基础.根据隐函数存在定理进行辅助变量的合理选择;然后利用经数学推导得到的指示变量"伪比生长率"完成发酵阶段的在线辨识,并采用神经网络构建出对应于各阶段的局部软测量模型.实际应用结果表明,所提方法有效、预估精度较高.