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.     

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.     

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.     

EFFECTS OF ALUMINUM/FLUORIDE CHEMISTRY IN WET LIMESTONE FLUE GAS DESULFURIZATION

In wet limestone flue gas desulfurization (FGD), elevated fly ash loadings can initiate the formation of liquid phase aluminum/fluoride (A1F _n ) complexes which inhibit limestone dissolution, causing depressed slurry pH and reduced SO₂ removal. This phenomenon was examined in a bench-scale pilot FGD scrubber system, and in batch reactor experiments, under conditions similar to those in full-scale utility FGD systems. It was shown that leachability of aluminum from fly ash is a critical factor, and depends on pH, fluoride concentration, and solid material properties. Reductions in limestone dissolution rate of more than an order of magnitude were measured at soluble aluminum concentrations as low as l0ppm. The implications for full-scale FGD systems reinforce the importance of maintaining efficient particulate removal upstream of the FGD scrubber.     

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.     

烟气脱硫率的选择及其影响因素的探讨

烟气脱硫率是石灰石/石膏湿法烟气脱硫系统的重要性能指标,它综合反映了脱硫系统的工作状况。文章针对金陵石化热电联合车间4×220 t/h煤粉炉增设烟气脱硫装置运行过程中出现的烟气脱硫率低进行分析探讨,并提出了解决方案、运行控制措施等,为该装置今后能够良好运行提供了依据。     

Optimum Values of Process Parameters of the “Wet Limestone Flue Gas Desulfurization System”

In this article the method of cost optimization of the “Wet Limestone Flue Gas Desulfurization System” is presented. The optimization calculations include process and cost models. The process model describes the most important stage of SO₂ removal that runs in the absorber and in the holding tank. It includes absorption of sulfur dioxide, oxidation of SO^2–₃, dissolution of limestone, and crystallization of gypsum. The model was applied to calculate indispensable parameters for estimating costs and then to minimize capital and operating costs. Costs of all important equipment were estimated, such as SO₂ removal systems with the absorber and the holding tank, reagent feed system with the ball mill and dewatering gypsum slurry system. Optimum values of the process parameters for different conditions of running flue gas desulfurization system were found. The process and cost model can be useful when designing the wet limestone FGD systems and carrying out economic analysis of the flue gas desulfurization plants.     

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.     

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.     

Optimization-based strategies for the operation of low-density polyethylene tubular reactors: nonlinear model predictive control

In this work, we present a general nonlinear model predictive control (NMPC) framework for low-density polyethylene (LDPE) tubular reactors. The framework is based on a first-principles dynamic model able to capture complex phenomena arising in these units. We first demonstrate the potential of using NMPC to simultaneously regulate and optimize the process economics in the presence of persistent disturbances such as fouling. We then couple the NMPC controller with a compatible moving horizon estimator (MHE) to provide output feedback. Finally, we discuss computational limitations arising in this framework and make use of recently proposed advanced-step MHE and NMPC strategies to provide nearly instantaneous feedback.     

火电厂烟气脱硫工程设计

在石灰石/石膏湿法脱硫工程实际应用中,影响脱硫效率的因素很多,主要问题包括结垢堵塞、设备和管道的腐蚀等,正确处理这些问题是保证烟气脱硫(FGD)系统长期稳定可靠运行的关键。相应的技术措施需综合考虑技术上的可行性和经济上的合理性等诸多因素,设计、设备选型、营运等各个阶段各个因素之间互相影响。如何优化设计方案,降低投资和运行检修费用,需要综合加以考虑。提出的方案是根据已运行项目的工程实际结果得出的结论,具有一定的实用和参考价值。     

Integrated nonlinear model predictive fault tolerant control and multiple model based fault detection and diagnosis

In this paper, a new fault-tolerant control approach is presented for a class of nonlinear systems, which preserves system stability despite a time delay in fault detection. The faults are assumed to occur in the actuators and are modeled for the general form of affine nonlinear systems. A fault detection and diagnosis (FDD) block is designed based on the multiple model method. The bank of extended Kalman filters (EKF) is used to detect predefined actuator faults and to estimate the unknown parameters of actuator position. The estimated parameters are then used to correct the model of the faulty system and to reconfigure the controller. The reconfigurable controller is designed based on the stabilizing nonlinear model predictive control (NMPC) scheme. On the other hand, in the duration between fault occurrence and fault detection, because of the mismatch between the process and the model, the system states may go off the attraction region. The proposed method is based on designing multiple local controllers for individual predefined faults. Depending on the value of a system variable at the moment of fault detection, one of these controllers will operate. This leads to a stability region of a set of auxiliary equilibrium points (AEPs), which is larger than the attraction region. Moreover, a framework for preserving system stability is presented. Finally, a practical chemical process example is presented to illustrate the effectiveness of this method.     

Passivity-based control of the phthalic anhydride fixed-bed reactor

The control of tubular fixed-bed reactors with highly exothermic reactions is approached from a passivity-based control perspective. The proposed controller solves dynamic tracking of the reactor exit conversion and stabilization of the reactor temperature by exploiting the passivity properties of the process. The model-based control structure proposed in this paper provides a suitable framework for developing the passivity-based control law and the state predictor. The integrated controller is designed and its performance in the face of parameter variation and model uncertainty is tested by numerical simulation. Digital simulation on an industrial phthalic anhydride fixed-bed reactor shows that the proposed control scheme can give satisfactory dynamic tracking ability and disturbance rejection performance, which is robust in the presence of process variation and model uncertainty. This paper provides a basic insight into the characterization and solution of control problems that are particular to tubular fixed-bed reactor systems and constitutes the application of passivity-based control theory to complex chemical processes.     

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.     

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.     

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 MPC for fed-batch multiple stages sugar crystallization

This paper addresses the issue of developing feasible advanced control strategies for the operation of industrial fed-batch multi-stage sugar crystallization processes. The operation of such processes poses very challenging problems mainly those inherent to its batch nature and also those due to the difficulties in measuring key process variables. Inadequate control policies lead to out-of-spec batches, with consequent losses resulting from the need of product recycling.In order to address these problems, a modification of the general Nonlinear Model Predictive Control (NMPC) is proposed in this paper, where the NMPC is executed only when the tracking error is outside a pre-specified bound α. Once the error converges towards the α-strip, the NMPC is switched off and the control action is kept constant. In order to further reduce the complexity of the control system, the proposed modification, termed Error Tolerant MPC (ETMPC), is provided with a Recurrent Neural Network (RNN) predictive model. The ETMPC + RNN control scheme was extensively tested on a crystallizer dynamic simulator, tuned with data from two industrial units, and compared with the classical NMPC and PI strategy. The results demonstrate that both NMPC and ETMPC controllers lead to improved end point process specifications, when compared with the PI controller. The explicit introduction of the error tolerance in the optimization relaxes the computational burden and can complement several other suggestions in the literature for feasible industrial real time control.     

Dissolution of a South African calcium based material using urea: An optimized process

The rate at which limestone dissolves is very important in wet flue gas desulfurization process (FGD). High dissolution rates provide better alkalinity, which is important for sulfur dioxide (SO₂) absorption. This study investigates the use of urea to improve the dissolution rate of limestone. The dissolution characteristics have been studied by using a pH-Stat method. The dissolution rate constant was measured according to the shrinking core model with surface control, i.e. (1−(1−X)^1/3)=k _r t. The effect of experimental variables such as temperature, amount of urea, solid to liquid ratio and stirring speed on the dissolution rate of limestone were investigated. Using a central composite design (CCD) of experiments variables, a mathematical model was developed to correlate the experimental variables to the dissolution rate constant. The experimental value was found to agree satisfactorily with predicted dissolution rate constant. The model shows that high temperature and low solid to liquid ratio improves the dissolution rate. The dissolution rate increased slightly with increase in the stirring speed. In the presence of urea the dissolution rate constant increased by 122%. The dissolution reaction follows a shrinking-core model with the chemical reaction control as the rate-controlling step.     

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.