MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

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.     

A nested online scheduling and nonlinear model predictive control framework for multi-product continuous systems

In the pursuit of integrated scheduling and control frameworks for chemical processes, it is important to develop accurate integrated models and computational strategies such that optimal decisions can be made in a dynamic environment. In this study, a recently developed switched system formulation that integrates scheduling and control decisions is extended to closed-loop operation embedded with nonlinear model predictive control (NMPC). The resulting framework is a nested online scheduling and control loop that allows to obtain fast and accurate solutions as no model reduction is needed and no integer variables are involved in the formulations. In the outer loop, the integrated model is solved to calculate an optimal product switching sequence such that the process economics is optimized, whereas in the inner loop, an NMPC implements the scheduling decisions. The proposed scheme was tested on two multi-product continuous systems. Unexpected large disturbances and rush orders were handled effectively.     

变增益的非线性预测控制算法

采用变增益策略,用输入与稳态输出的映射表示系统的静态非线性,用一个增益为1的ARX模型表示系统的动态模型,代替多数文献中常用的分段线性多模型方法进行非线性系统的预测控制.文中通过对连续搅拌釜反应器(CSTR)的仿真,验证了本算法的有效性.     

Model based robust control approach for batch crystallization product design

The paper presents a novel control approach for crystallization processes, which can be used for designing the shape of the crystal size distribution to robustly achieve desired product properties. The approach is based on a robust optimal control scheme, which takes parametric uncertainties into account to provide decreased batch-to-batch variability of the shape of the crystal size distribution. Both open-loop and closed-loop robust control schemes are evaluated. The open-loop approach is based on a robust end-point nonlinear model predictive control (NMPC) scheme which is implemented in a hierarchical structure. On the lower level a supersaturation control approach is used that drives the system in the phase diagram according to a concentration versus temperature trajectory. On the higher level a robust model-based optimization algorithm adapts the setpoint of the supersaturation controller to counteract the effects of changing operating conditions. The process is modelled using the population balance equation (PBE), which is solved using a novel efficient approach that combines the quadrature method of moment (QMOM) and method of characteristics (MOC). The proposed robust model based control approach is corroborated for the case of various desired shapes of the target distribution.     

Nonlinear model predictive control for dividing wall columns

Dividing wall columns (DWCs) are practical, effective, and promising among distillation process intensification technologies. Nonlinear model predictive control (NMPC) schemes are developed in this study to control the three-product DWCs. As these systems are intensely interactive and highly nonlinear, NMPC may be more suitable than the traditional PI control. The model is established based on Python and Pyomo platforms. As the original mathematical model of the column section is ill-posed, index reduction is used to avoid a high-index differential-algebraic equation (DAE) system. The well-posed index-1 system after index reduction is employed for the steady-state simulation and dynamic control in this study. Case studies with three DWC configurations to separate the mixture of ethanol (A), n-propanol (B), and n-butanol (C) show that the NMPC performs very well with small maximum deviations and short settling times. This demonstrates that the NMPC is a feasible and very effective scheme to control three-product DWCs.     

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.     

Dynamic optimization oriented modeling and nonlinear model predictive control of the wet limestone FGD system

Nonlinear model predictive control (NMPC) scheme is an effective method of multi-objective optimization control in complex industrial systems. In this paper, a NMPC scheme for the wet limestone flue gas desulphurization (WFGD) system is proposed which provides a more flexible framework of optimal control and decision-making compared with PID scheme. At first, a mathematical model of the FGD process is deduced which is suitable for NMPC structure. To equipoise the model's accuracy and conciseness, the wet limestone FGD system is separated into several modules. Based on the conservation laws, a model with reasonable simplification is developed to describe dynamics of different modules for the purpose of controller design. Then, by addressing economic objectives directly into the NMPC scheme, the NMPC controller can minimize economic cost and track the set-point simultaneously. The accuracy of model is validated by the field data of a 1000 MW thermal power plant in Henan Province, China. The simulation results show that the NMPC strategy improves the economic performance and ensures the emission requirement at the same time. In the meantime, the control scheme satisfies the multiobjective control requirements under complex operation conditions (e.g., boiler load fluctuation and set point variation). The mathematical model and NMPC structure provides the basic work for the future development of advanced optimized control algorithms in the wet limestone FGD systems.     

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.     

Online machine learning modeling and predictive control of nonlinear systems with scheduled mode transitions

This work develops a model predictive control (MPC) scheme using online learning of recurrent neural network (RNN) models for nonlinear systems switched between multiple operating regions following a prescribed switching schedule. Specifically, an RNN model is initially developed offline to model process dynamics using the historical operational data collected in a small region around a certain steady-state. After the system is switched to another operating region under a Lyapunov-based MPC with suitable constraints to ensure satisfaction of the prescribed switching schedule policy, RNN models are updated using real-time process data to improve closed-loop performance. A generalization error bound is derived for the updated RNN models using the notion of regret, and closed-loop stability results are established for the switched nonlinear system under RNN-based MPC. Finally, a chemical process example with the operation schedule that requires switching between two steady-states is used to demonstrate the effectiveness of the proposed RNN-MPC scheme.     

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.     

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。     

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.     

模糊非线性内模控制算法及其在pH值控制中的应用

pH值控制过程具有较强的非线性,历来是过程控制研究的一大热点,本文针对pH值控制系统提出了一种基于模糊推理网的非线性内模控制算法（FNIMC）。模糊推理网用于辨识对象的模糊模型;FNIMC由一个逆模控制器和具有一个可调参数的鲁棒滤波器组成。仿真结果表明该算法优于非线性PID调节器,且计算效率高。     

Integrated batch‐to‐batch and nonlinear model predictive control for polymorphic transformation in pharmaceutical crystallization

Polymorphism, a phenomenon in which a substance can have more than one crystal form, is a frequently encountered phenomenon in pharmaceutical compounds. Different polymorphs can have very different physical properties such as crystal shape, solubility, hardness, color, melting point, and chemical reactivity, so that it is important to ensure consistent production of the desired polymorph. In this study, an integrated batch‐to‐batch and nonlinear model predictive control (B2B‐NMPC) strategy based on a hybrid model is developed for the polymorphic transformation of L ‐glutamic acid from the metastable α‐form to the stable β‐form crystals. The hybrid model comprising of a nominal first‐principles model and a correction factor based on an updated PLS model is used to predict the process variables and final product quality. At each sampling instance during a batch, extended predictive self‐adaptive control (EPSAC) is employed as a NMPC technique to calculate the control action by using the current hybrid model as a predictor. At the end of the batch, the PLS model is updated by utilizing the measurements from the batch and the above procedure is repeated to obtain new control actions for the next batch. In a simulation study using a previously reported model for a polymorphic crystallization with experimentally determined parameters, the proposed B2B‐NMPC control strategy produces better performance, where it satisfies all the state constraints and produces faster and smoother convergence, than the standard batch‐to‐batch strategy. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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.     

Rotary Dryer Control Using a Grey-Box Neural Model Scheme

The application of a Grey-box Neural Model (GNM) in a nonlinear model predictive control scheme (NMPC) of a direct rotary dyer is presented in this work. The GNM, which is based on the combination of phenomenological models and empirical artificial neural network (ANN) models, was properly developed and validated by using experimental fish-meal rotary drying information. The GNM was created by combining the rotary dryer mass and energy balances and a feed forward neural network (FFNN), trained off-line to estimate the drying rate and the volumetric heat transfer coefficient. The GNM results allowed us to obtain the relation between the controlled variable (solid moisture content) and the manipulated variable (gas phase entrance temperature) used in the predictive control strategy. Two NMPC control strategies, one with a fixed extended prediction horizon and another with an extended range prediction horizon, were applied to a simulated industrial fish-meal drying process. The results showed that a correct rotary dryer representation can be obtained by using a GNM approach. Due to the representation capability of the GNM approach, excellent control performances of the NMPCs were observed when the process variables were subject to disturbances. As analyzed in this work, the fixed extended prediction horizon MPC surpassed recognized control methodologies (quadratic dynamic matrix control).     

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.     

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.     

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。