Nonlinear model predictive control of a batch fluidized bed dryer for pharmaceutical particles

The availability of reliable online moisture content measurements exploiting near-infrared (NIR) spectroscopy and chemometric tools allows the application of online control strategies to a wide range of drying processes in the pharmaceutical industry. In this paper, drying of particles with a pilot-scale batch fluidized bed dryer (FBD) is studied using a in-line NIR probe. A consolidated phenomenological state-space model of an FBD based on mass and energy balances is calibrated applying a nonlinear least-square identification to experimental data (grey-box modeling). Then, relying on the calibrated model, a nonlinear model predictive controller and a moving horizon state estimator are designed. The objective is to reach a specific particle moisture content setpoint at the end of the drying batch while decreasing cycle time and limiting particle temperature. A penalty term on the energy consumption can also be added to the usual tracking control cost function. Compared to a typical FBD operation in industry (mostly open-loop), it is shown that the drying time and the energy consumption can be efficiently managed on the pilot-scale process while limiting various operation problems like under drying, over drying, or particles overheating.     

Comparison of three control strategies for optimization of spray dryer operation

Spray drying is the preferred process to reduce the water content of many chemicals, pharmaceuticals, and foodstuffs. A significant amount of energy is used in spray drying to remove water and produce a free flowing powder product. In this paper, we present and compare the performance of three controllers for operation of a four-stage spray dryer. The three controllers are a proportional-integral (PI) controller that is used in industrial practice for spray dryer operation, a linear model predictive controller with real-time optimization (MPC with RTO, MPC-RTO), and an economically optimizing nonlinear model predictive controller (E-NMPC). The MPC with RTO is based on the same linear state space model in the MPC and the RTO layer. The E-NMPC consists of a single optimization layer that uses a nonlinear system of ordinary differential equations for its predictions. The PI control strategy has a fixed target that is independent of the disturbances, while the MPC-RTO and the E-NMPC adapt the operating point to the disturbances. The goal of spray dryer operation is to optimize the profit of operation in the presence of feed composition and ambient air humidity variations; i.e. to maximize the production rate, while minimizing the energy consumption, keeping the residual moisture content of the powder below a maximum limit, and avoiding that the powder sticks to the chamber walls. We use an industrially recorded disturbance scenario in order to produce realistic simulations and conclusions. The key performance indicators such as the profit of operation, the product flow rate, the specific energy consumption, the energy efficiency, and the residual moisture content of the produced powder are computed and compared for the three controllers. In this simulation study, we find that the economic performance of the MPC with RTO as well as the E-NMPC is considerably improved compared to the PI control strategy used in industrial practice. The MPC with RTO improves the profit of operation by 8.61%, and the E-NMPC improves the profit of operation by 9.66%. The energy efficiency is improved by 6.21% and 5.51%, respectively.     

Dynamic Neural-Network-Based Model-Predictive Control of an Industrial Baker's Yeast Drying Process

This paper presents dynamic neural-network-based model-predictive control (MPC) structure for a baker's yeast drying process. Mathematical model consists of two partial nonlinear differential equations that are obtained from heat and mass balances inside dried granules. The drying curves that are obtained from granule-based model were used as training data for neural network (NN) models. The target is to predict the moisture content and product activity, which are very important parameters in drying process, for different horizon values. Genetic-based search algorithm determines the optimal drying profile by solving optimization problem in MPC. As a result of the performance evaluation of the proposed control structure, which is compared with the model based on nonlinear partial differential equation (PDE) and with feedforward neural network (FFN) models, it is particularly satisfactory for the drying process of a baker's yeast.      

An experimentally validated simulation model for a four-stage spray dryer

In this paper, we develop a dynamic model of an industrial type medium size four-stage spray dryer. The purpose of the model is to enable simulations of the spray dryer at different operating points, such that the model facilitates development and comparison of control strategies. The dryer is divided into four consecutive stages: a primary spray drying stage, two heated fluid bed stages, and a cooling fluid bed stage. Each of these stages in the model is assumed ideally mixed and the dynamics are described by mass- and energy balances. These balance equations are coupled with constitutive equations such as a thermodynamic model, the water evaporation rate, the heat transfer rates, and an equation for the stickiness of the powder (glass transition temperature). Laboratory data is used to model the equilibrium moisture content and the glass transition temperature of the powder. The resulting mathematical model is an index-1 differential algebraic equation (DAE) model with 12 states, 9 inputs, 8 disturbances, and 30 parameters. The parameters in the model are identified from well-excited experimental data obtained from the industrial type spray dryer. The simulated outputs of the model are validated using independent well-excited experimental data from the same spray dryer. The simulated temperatures, humidities, and residual moistures in the spray dryer compare well to the validation data. The model also provides the profit of operation, the production rate, the energy consumption, and the energy efficiency. In addition, it computes stickiness of the powder in different stages of the spray dryer. These facilities make the model well suited as a simulation model for comparison of the process economics associated to different control strategies.     

Irrigation control based on model predictive control (MPC): Formulation of theory and validation using weather forecast data and AQUACROP model

This research proposes A THEORETICAL FRAMEWORK based on model predictive control (MPC) for irrigation control to minimize both root zone soil moisture deficit (RZSMD) and irrigation amount under a limited water supply. We (i) investigate means to incorporate direct measurements to MPC (ii) introduce two Robust MPC techniques – Certainty Equivalence control (CE) and Disturbance Affine Feedback Control (DA) – to mitigate the uncertainty of weather forecasts, and (iii) provide conditions to obtain two important theoretical aspects of MPC – feasibility and stability – in the context of irrigation control. Our results show that system identification enables automation while incorporating direct measurements. Both DA and CE minimize RZSMD and irrigation amount under uncertain weather forecasts and always maintain soil moisture above wilting point subject to water availability. The theoretical results are compared against the model AQUACROP, weather data and forecasts from Shepparton, Australia. We also discuss the performance of Robust MPC under different water availability, soil, crop conditions. In general, MPC shows to be a promising tool for irrigation control.     

Optimizing model predictive control of an industrial distillation column

The main scope of this work is the implementation of an MPC that integrates the control and the economic optimization of the system. The two problems are solved simultaneously through the modification of the control cost function that includes an additional term related to the economic objective. The optimizing MPC is based on a quadratic program (QP) as the conventional MPC and can be solved with the available QP solvers. The method was implemented in an industrial distillation system, and the results show that the approach is efficient and can be used, in several practical cases.     

Price-driven coordination method for solving plant-wide MPC problems

In large-scale model predictive control (MPC) applications, such as plant-wide control, two possible approaches to MPC implementation are centralized and decentralized MPC schemes. These represent the two extremes in the “trade-off” among the desired characteristics of an industrial MPC system, namely accuracy, reliability and maintainability. To achieve optimal plant operations, coordination of decentralized MPC controllers has been identified as both an opportunity and a challenge. Typically, plant-wide MPC problem can be formulated as a large-scale quadratic program (QP) with linking equality constraints. Such problems can be decomposed and solved with the price-driven coordination method and on-line solutions of these structured large-scale optimization problems require an efficient price-adjustment strategy to find an “equilibrium price”. This work develops an efficient price-adjustment algorithm based on Newton’s method, in which sensitivity analysis and active set change identification techniques are employed. With the off-diagonal element abstraction technique and the enhanced priced driven coordination algorithm, a coordinated, decentralized MPC framework is proposed. Several case studies show that the proposed coordination-based decentralized MPC scheme is an effective approach to plant-wide MPC applications, which provides a high degree of reliability and accuracy at a reasonable computational load.     

Profile control in distributed parameter systems using lexicographic optimization based MPC

Process equipment that exhibits significant spatial variation of system properties, such as temperature or concentration in a fixed bed reactor, are typically modeled as distributed parameter systems. While some properties of the final product exiting the equipment may depend on the states concerning the endpoint, others may be a function of the history of processing within the equipment. In such instances, control of the spatial property profile may be beneficial. In this work, we explore the idea of profile control using extended MPC and outline the additional challenges that must be addressed in this context. In case that the target profile is unachievable, we present an MPC formulation that uses lexicographic optimization to prioritize the different sections of the profile. Simulation of a simple representative system namely a hypothetical plug flow reactor is used to demonstrate that the lexicographic optimization based MPC provides a systematic approach to profile control and spans between the endpoint control strategy and the whole profile control strategy. The benefits of lexicographic optimization based MPC were also demonstrated on a large-scale distributed parameter system of industrial size, namely the continuous pulp digester.     

Tuning SISO offset-free Model Predictive Control based on ARX models

In this paper, we present a tuning methodology for a simple offset-free SISO Model Predictive Controller (MPC) based on autoregressive models with exogenous inputs (ARX models). ARX models simplify system identification as they can be identified from data using convex optimization. Furthermore, the proposed controller is simple to tune as it has only one free tuning parameter. These two features are advantageous in predictive process control as they simplify industrial commissioning of MPC. Disturbance rejection and offset-free control is important in industrial process control. To achieve offset-free control in face of unknown disturbances or model-plant mismatch, integrators must be introduced in either the estimator or the regulator. Traditionally, offset-free control is achieved using Brownian disturbance models in the estimator. In this paper we achieve offset-free control by extending the noise model with a filter containing an integrator. This filter is a first order ARMA model. By simulation and analysis, we argue that it is independent of the parameterization of the underlying linear plant; while the tuning of traditional disturbance models is system dependent. Using this insight, we present MPC for SISO systems based on ARX models combined with the first order filter. We derive expressions for the closed-loop variance of the unconstrained MPC based on a state space representation in innovation form and use these expressions to develop a tuning procedure for the regulator. We establish formal equivalence between GPC and state space based off-set free MPC. By simulation we demonstrate this procedure for a third order system. The offset-free ARX MPC demonstrates satisfactory set point tracking and rejection of an unmeasured step disturbance for a simulated furnace with a long time delay.     

Tube-based robust sampled-data MPC for linear continuous-time systems

This note extends to the continuous-time case the “tube-based” approach for the design of discrete-time robust model predictive control (MPC) algorithms developed in Mayne, Seron, and Rakovi? (2005). This extension is of interest in view of the simplicity and popularity of the method as well as of the industrial relevance of continuous-time implementations of MPC. The proposed robust control law is composed of two terms: (1) a sampled-data MPC control law and (2) a continuous-time state feedback term.     

Performance evaluation of two industrial MPC controllers

This paper presents case studies of the performance evaluation of two industrial multivariate model predictive control (MPC) based controllers at the Mitsubishi chemical complex in Mizushima, Japan: (1) a 6-output, 6-input para-xylene (PX) production process with six measured disturbance variables that are used for feedforward control; and (2) a multivariate MPC controller for a 6-output, 5-input poly-propylene splitter column with two measured disturbances. A generalized predictive controller-based MPC algorithm has been implemented on the PX process. Data from the PX unit before and after the MPC implementation are analyzed to obtain and compare several different measures of multivariate controller performance. The second case study is concerned with performance assessment of a commercial MPC controller on a propylene splitter. A discussion on the diagnosis of poor performance for the second MPC application suggests significant model-plant-mismatch under varying load conditions and highlights the role of constraints.     

Closed-loop stable model predictive control of integrating systems with dead time

Model predictive control (MPC) applications in the process industry usually deal with process systems that show time delays (dead times) between the system inputs and outputs. Also, in many industrial applications of MPC, integrating outputs resulting from liquid level control or recycle streams need to be considered as controlled outputs. Conventional MPC packages can be applied to time-delay systems but stability of the closed loop system will depend on the tuning parameters of the controller and cannot be guaranteed even in the nominal case. In this work, a state space model based on the analytical step response model is extended to the case of integrating time systems with time delays. This model is applied to the development of two versions of a nominally stable MPC, which is designed to the practical scenario in which one has targets for some of the inputs and/or outputs that may be unreachable and zone control (or interval tracking) for the remaining outputs. The controller is tested through simulation of a multivariable industrial reactor system.     

闪速熔炼气流干燥优化控制系统的设计与实现

针对气流干燥过程水分难以稳定的问题，设计了一个由水分软测量模型和氮气专家控制器组成的双反馈控制系统．通过智能协调得到软测量的输出，结合约束条件，采用遗传算法搜索燃油量的最优值；由氮气专家控制器来调节氮气量，从而改变回转窑窑头含氧率，使精矿不着火．通过这两个反馈调节，使得耗氮量和燃油量同时达到最小．工业数据验证表明，累计平均耗氮量和燃油量分别下降了1.4%和0.3%．     

近红外技术监测流化喷雾制粒水份的研究

流化床喷雾制粒是一种较复杂的生产过程，实现生产过程中物料含水量实时监测，对提高产品质量、实现生产装置自动化意义重大。本文探索利用近红外测试分析技术．实现对流化床喷雾制粒生产过程颗粒含水量的实时监测。根据现代NIR理论和不同含水率颗粒光谱特点，采用双光路4波段8光束反射式近红外测试装置，进行含水率测试实验，实现了颗粒含水量在线监测，实验表明本文方法具有较高的测量精度和抗干扰性，为实现产品颗粒含水量自动测控提供了一种新的方法。     

双层结构预测控制研究进展

现代工业大系统的优化控制采用递阶结构,其中以预测控制为代表的先进过程控制已经成为重要的一级.目前,主流的工业预测控制技术均采用双层结构,即包含稳态优化层和动态控制层.双层结构预测控制技术可以有效解决复杂工业过程常见的多目标优化、多变量控制的难点问题.本文简要总结了双层结构预测控制的算法,并从控制输入与被控输出稳态关系入手分析了多变量预测控制稳态解的相容性和唯一性,说明了稳态优化的重要性.针对双层结构预测控制与区间预测控制的性能比较、稳态模型的奇异性以及闭环系统动态特性等提出了一些见解,并指出了需要重点研究的主题.     

A survey of industrial model predictive control technology

This paper provides an overview of commercially available model predictive control (MPC) technology, both linear and nonlinear, based primarily on data provided by MPC vendors. A brief history of industrial MPC technology is presented first, followed by results of our vendor survey of MPC control and identification technology. A general MPC control algorithm is presented, and approaches taken by each vendor for the different aspects of the calculation are described. Identification technology is reviewed to determine similarities and differences between the various approaches. MPC applications performed by each vendor are summarized by application area. The final section presents a vision of the next generation of MPC technology, with an emphasis on potential business and research opportunities.     

Detecting near-surface moisture stress in Sphagnum spp.

Estimating near-surface moisture conditions from the reflectance spectra (400-2500 nm) of Sphagnum moss offers great opportunities for the use of remote sensing as a tool for large-scale detailed monitoring of near-surface peatland hydrological conditions. This article investigates the effects of changes in near-surface and surface moisture upon the spectral characteristics of Sphagnum moss. Laboratory-based canopy reflectance data were collected from two common species of Sphagnum subjected to drying and subsequent rewetting. Several spectral indices developed from the near infra-red (NIR) and shortwave infra-red (SWIR) liquid water absorption bands and two biophysical indices (REIP and the chlorophyll index) were correlated with measures of near-surface moisture. All spectral indices tested were significantly correlated with near-surface moisture (with r between 0.27 and 0.94). The strongest correlations were observed using indices developed from the NIR liquid water absorption features (fWBI₉₈₀ and fWBI₁₂₀₀). However, a hysteretic response was observed in both NIR indices when the canopies were re-hydrated, a finding which may have implications for the timing of remote sensing image acquisition. The Moisture Stress Index (MSI), developed from the SWIR liquid water absorption feature also showed strong correlations with near-surface wetness although the range of moisture conditions over which the index was able to detect change was highly dependent on Sphagnum species. Of the biophysical spectral indices tested (REIP and the chlorophyll index), the most significant relationships were observed between the chlorophyll index and near-surface wetness. All spectral indices tested were species specific, and this is attributed to differences in canopy morphology between Sphagnum species. The potential for developing estimations of surface and near-surface hydrological conditions across northern peatlands using remote sensing technology is discussed.     

分散式MPC经济性能评估

近年来,学术界对集中式模型预测控制 (Model predictive control, MPC) 性能评估进行了广泛的研究. 对于大规模化工过程, 工业现场通常采用分散式MPC的控制结构. 由于各子系统间存在复杂的耦合关系, 针对集中式MPC 的性能评估方法不能客观反映分散式MPC的性能. 本文基于线性矩阵不等式(Linear matrix inequality, LMI)的方法对分散式MPC进行经济性能评估. 首先提出了一种迭代方法求解分散式线性二次型调节器(Linear quadratic regulator, LQR)问题, 该方法显著降低了已有求解方法的保守性. 再利用LQR基准建立了一组随机优化命题对MPC进行经济性 能评估, 评估方法对集中式MPC与分散式MPC均适用, 评估结果可以指导MPC参数调整, 也可以为集中式与分散式MPC结构选择提供重要参考. 通过对重油分馏塔控制问题的仿真验证了本文方法的有效性与应用价值.     

烟叶复烤区温度与排潮率的解耦控制仿真研究

烟叶复烤是香烟生产中的一个重要的环节,复烤过程中温度、水分直接影响了复烤后的烟叶指标和后续烟叶的制丝、打包等工序,复烤干燥区是一个复杂多变量强耦合系统。为了获得较好的控制效果,针对云南某复烤厂仅控制温度而未考虑与湿度的耦合性,并且其控制效果不佳的问题,通过采集大量现场数据,在获得干燥区排潮率软测量模型和温湿度动态模型的基础上,采用前馈解耦控制方法进行了干燥区温度与排潮率的控制仿真研究。仿真研究结果表明,干燥区温度与排潮率的前馈解耦控制与未解耦PID控制相比,具有较好的控制效果。     

Hybrid Fuzzy Modelling for Model Predictive Control

Model predictive control (MPC) has become an important area of research and is also an approach that has been successfully used in many industrial applications. In order to implement a MPC algorithm, a model of the process we are dealing with is needed. Due to the complex hybrid and nonlinear nature of many industrial processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed. A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between the proposed modern intelligent (fuzzy) approach and a classic (linear) approach was made. It was established that the MPC algorithm employing the proposed hybrid fuzzy model clearly outperforms the approach where a hybrid linear model is used, which justifies the usability of the hybrid fuzzy model. The hybrid fuzzy formulation introduces a powerful model that can faithfully represent hybrid and nonlinear dynamics of systems met in industrial practice, therefore, this approach demonstrates a significant advantage for MPC resulting in a better control performance.