基于内模控制的滤波方法改进及参数优化实施

针对实际工业控制中出现的系统的随机噪声和量测噪声会严重影响现场生产的控制效果,传统的内模控制方式无法很有效地解决这一问题。将Kalman滤波器引入到传统的内模控制原理中,通过Kalman滤波器来减小甚至消除噪声对控制系统的影响,提高系统的控制精度。同时,利用NLJ算法在考察系统性能指标的情况下,对传统内模原理中的低通滤波器的滤波参数进行自动寻优。通过对滤波环节的改善,充分发挥Kalman滤波和NLJ自动寻优的特点,使得控制系统的鲁棒性和快速性都得到了提高。仿真结果表明提出的设计方法能较好解决单变量和多变量被控对象的实时性和时滞性,并且具有良好的抗噪性,该方法参数调节容易,易于实施。     

Parameter and state estimation in nonlinear stochastic continuous‐time dynamic models with unknown disturbance intensity

Approximate Maximum Likelihood Estimation (AMLE) is an algorithm for estimating the states and parameters of models described by stochastic differential equations (SDEs). In previous work (Varziri et al., Ind. Eng. Chem. Res., 47 (2), 380‐393, (2008); Varziri et al., Comp. Chem. Eng., in press), AMLE was developed for SDE systems in which process‐disturbance intensities and measurement‐noise variances were assumed to be known. In the current article, a new formulation of the AMLE objective function is proposed for the case in which measurement‐noise variance is available but the process‐disturbance intensity is not known a priori. The revised formulation provides estimates of the model parameters and disturbance intensities, as demonstrated using a nonlinear CSTR simulation study. Parameter confidence intervals are computed using theoretical linearization‐based expressions. The proposed method compares favourably with a Kalman‐filter‐based maximum likelihood method. The resulting parameter estimates and information about model mismatch will be useful to chemical engineers who use fundamental models for process monitoring and control.     

Nonlinear stochastic modeling to improve state estimation in process monitoring and control

State estimation from plant measurements plays an important role in advanced monitoring and control technologies, especially for chemical processes with nonlinear dynamics and significant levels of process and sensor noise. Several types of state estimators have been shown to provide high‐quality estimates that are robust to significant process disturbances and model errors. These estimators require a dynamic model of the process, including the statistics of the stochastic disturbances affecting the states and measurements. The goal of this article is to introduce a design method for nonlinear state estimation including the following steps: (i) nonlinear process model selection, (ii) stochastic disturbance model selection, (iii) covariance identification from operating data, and (iv) estimator selection and implementation. Results on the implementation of this design method in nonlinear examples (CSTR and large dimensional polymerization process) show that the linear time‐varying autocovariance least‐squares technique accurately estimates the noise covariances for the examples analyzed, providing a good set of such covariances for the state estimators implemented. On the estimation implementation, a case study of a chemical reactor demonstrates the better capabilities of MHE when compared with the extended Kalman filter. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Estimation of time-varying time delay and parameters of a class of jump Markov nonlinear stochastic systems

It is a challenging problem to estimate time-varying time delay and parameters, especially for systems subject to disturbances with unknown statistics in measurements. The desirable filter should be sensitive to unmodeled dynamics caused by random changes in time delay and parameters, and also be robust to disturbances. Recently, we proposed a finite-horizon robust Kalman filter (RKF) through designing and simultaneously minimizing the upper bounds of unknown covariances of prediction errors, filtering residuals and estimation errors. Unfortunately, unmodeled dynamics and disturbances must be hypothesized to be zero-mean white noises in the RKF. To cope with more general unmodeled dynamics and/or disturbances, a class of jump Markov stochastic systems (JMSS) subject to unmodeled dynamics and disturbances is considered in this article so that a priori system information, such as the value range of unknown and/or randomly changing parameters, can be introduced. Through combining the RKF with the interacting multiple model (IMM) estimation technique, a RKF/IMM algorithm is proposed for such JMSS. Then it is applied to estimate time-varying time delay and parameters of a continuous stirred tank reactor (CSTR) with sensors subject to Gaussian disturbances with unknown means and/or covariances. The RKF/IMM algorithm is compared with the extended Kalman filter (EKF), the strong tracking filter (STF) and the RKF through computer simulations. The results show that, in the case that measurement disturbances are zero-mean noise with unknown covariances, the RKF/IMM and RKF achieve almost the same accurate estimates, which are superior to those of the STF and EKF; in the case that such disturbances have unknown covariances and time-varying means, only the RKF/IMM remains the ability to estimate time-varying time delay and parameters. Furthermore the RKF/IMM has unique ability to identify the disturbance mean no matter whether it is constant or time-varying. Moreover, the RKF/IMM algorithm is shown having strong robustness against the a priori filter parameters, this may be attractive in practical applications.     

NOTE ON THE KALMAN FILTER WITH ESTIMATED PARAMETERS

Abstract. State estimation and prediction problems are considered for a stochastic process represented by a state space form which involves unknown parameters. We first study the stability of the Kalman filter corresponding to the state space form without assuming the stationarity of the process. Second, we consider the state estimation and prediction when the process is stationary, and show some asymptotic properties of the state estimates and predicted values obtained by the Kalman filter with estimated parameters which converge to the true parameters or to the equivalent classes of the true parameters with probability one.     

Calorimetric estimation for a batch-loop emulsion polymerisation reactor

To facilitate the online monitoring and control of a pilot-scale polymerisation reactor, state estimation techniques are investigated. Specifically, a batch-loop reactor is employed for the emulsion polymerisation of methyl methacrylate. The reactor consists of jacketed tubular sections fitted with in-line static mixers, thus providing mixing homogeneity and improved temperature control. A direct estimation of the reaction rate is attained through measurements of process and jacket side temperatures, and thus a calorimetric method of estimation. This is compared with a Kalman filter based calorimetric approach, in which there is compensation for model uncertainties and measurement noise. For both estimation methods, no knowledge of the kinetic model for polymerisation is needed. Experimental results indicate that with an accurate model of the process energy balance, in which, for example, the recycle pump energy input is described, the Kalman filter approach is found to provide excellent prediction of conversion, for both high and low conversions, for this pilot-plant reactor system. The approach does not require any (approximate) kinetic knowledge, and is thus considerably easier in implementation than the extended Kalman filter approaches.     

AN OPTIMAL EXTENDED KALMAN FILTER DESIGNED BY GENETIC ALGORITHMS

A Geno-Kalman filter is utilized for state estimation of a bench-scale batch reactor that handles an exothermic reaction between H₂O₂ and Na₂S₂O₃. This reaction system includes three different states including the concentration of reactants as well as the temperature of the reactor. All of the states are measured during the process. The proposed procedure is to run an optimal extended Kalman filter by which the Kalman design parameters, Q and R, are obtained by genetic algorithms. The extended Kalman filter is initially designed by trial and error and used as a baseline in this study. Then an optimal white-bound extended Kalman filter design is obtained through an optimization on the baseline estimator, using genetic algorithms. The results show a significant improvement in the performance of the estimator. Moreover, a color-bound extended Kalman filter was also designed to allow a dynamic linear trend for the change in nonzero elements of the process noise covariance matrix.     

Distributed parameter estimation and identification for system with fast and slow dynamics: A tubular,fixed-bed catalytic reactor to form styrene

A simple and efficient on-line scheme is developed to estimate temperature and compositions along a packed bed reactor in which styrene is being produced by the dehydrogenation of ethylbenzene. Slowly varying catalyst activity is also identified. The system is distributed in time and axial position and is nonlinear in the states: temperature and nine compositions. The dehydrogenation rate is augmented with a catalyst activity parameter which is assumed to undergo a long-term exponential decay.Since the decline in catalyst activity is slow when compared to state dynamics, a quasi-steady-state approach is used to derive a state filter equation neglecting process state dynamics and assuming spatially uncorrelated measurements and model uncertainty. For this filter, temperature measurements are available from four locations along the reactor and compositions are measured only at the reactor exit. A second dynamic, Kalman filter is used to identify the slowly varying catalyst activity.The two filters, one for distributed, steady-state, state estimation and the other for dynamic catalyst activity identification, are tested by computer simulation using measurements with added white noise. Several cases for numbers of sensors and noise levels are studied. The overall scheme is efficient and useable for on-line implementation. The steady-state filter is readily extended to distributed systems in more than one spatial variable such as reactor models with axial and radial dependencies. For steady-state or static models, multiple measurements yield significant improvements in the quality of the optimal estimates. Internal measurement locations allow for the subdivision of the spatial domain for the problem and improved profile estimates.     

STATE ESTIMATION IN THE BATCH DRYING OF FOODS

ABSTRACT

Measurement of material moisture content is necessary for the control of product quality in batch drying. However, this variable cannot be measured on-line, and state estimation techniques are proposed. A non-linear dynamic model is developed for batch drying of foods. Process disturbances and measurement errors are modeled as stochastic processes and a hybrid extended Kalman filter is employed for state estimation. This filter is based on the local linearization of the process model around the suboptimal filter estimates. The moisture estimation approach was applied to experimental points obtained in a laboratory dryer with quite satisfactory results.     

基于经济模型预测控制的金氰化浸出过程动态实时优化

针对金氰化浸出过程时间常数大、不确定性强等问题,提出了一种基于经济模型预测控制（EMPC）的动态实时优化方法。不同于传统的模型预测控制,EMPC将经济指标直接作为滚动优化的目标函数,在每个采样时刻求解滚动窗口内的最优操作序列。和稳态优化方法相比,基于EMPC的方法能保证动态最优性,提高经济收益。此外,金氰化浸出过程受随机噪声、未知参数可变等不确定性影响,提出使用扩展卡尔曼滤波（EKF）,通过构造增广系统对状态变量及不确定参数进行在线同步估计,加强EMPC的准确性和可靠性。仿真结果表明,提出的EMPC+EKF策略能有效提高金氰化浸出过程的经济性能。     

STATE ESTIMATION IN THE BATCH DRYING OF FOODS

Measurement of material moisture content is necessary for the control of product quality in batch drying. However, this variable cannot be measured on-line, and state estimation techniques are proposed. A non-linear dynamic model is developed for batch drying of foods. Process disturbances and measurement errors are modeled as stochastic processes and a hybrid extended Kalman filter is employed for state estimation. This filter is based on the local linearization of the process model around the suboptimal filter estimates. The moisture estimation approach was applied to experimental points obtained in a laboratory dryer with quite satisfactory results.     

基于改进差分进化算法-径向基神经网络的电热水浴串级控制系统研究

针对电热水浴装置温度控制中被控对象存在的大惯性、非线性、大延迟等特点,设计了一种基于改进差分进化(improved differential evolution, IDE)算法的径向基（radial basis function, RBF）神经网络串级控制系统。采用IDE算法对RBF神经网络的初始参数进行优化,采用优化后的RBF神经网络辨识主控制回路被控对象的Jacobian信息,进而实现主控制回路PID(proportional integration differentiation)控制器参数的在线调整。针对主控制回路控制器包含输出噪声,导致控制性能下降的问题,引入Kalman 滤波器对串级控制的主回路进行重新设计,控制对象的输出值经过Kalman 滤波算法处理后再返回闭环控制系统。以微化工领域常用电热水浴装置为对象,对IDE-RBF-PID-PI串级控制系统进行仿真实验,结果表明,IDE-RBF-PID-PI串级控制系统相较于常规串级控制,大大提高了控制性能,主控制回路引入的Kalman滤波算法有效消减控制系统的输出噪声,控制效果接近于无噪声的理想状态。     

Dynamic synergistic modelling for cobalt removal process in zinc hydrometallurgy and the research of parameter estimation based on unscented Kalman filter

The cobalt removal process with arsenic salt of zinc hydrometallurgy has serious non-linearity, uncertainty, and mutual coupling. Its accurate dynamic modelling has always been a challenging problem. On the basis of in-depth analysis of cobalt removal process and reaction mechanism, considering the cascade relationship between the reactors, a dynamic synergistic continuously stirred tank reactor (SCSTR) mechanism model of the cobalt removal process was constructed. Aiming at the unknown parameters in the SCSTR model, the idea of the Kalman filter was introduced, and the unknown parameters were characterized as unknown states; a method of estimating the unknown model parameters was developed using the augmented state equation and the unscented Kalman filter (UKF) algorithm. Simulation results with industrial data of a zinc smeltery showed that the parameter estimation model has high accuracy, and the estimated parameters can be used in the SCSTR model. An intensive simulation analysis of the dynamic characteristics of the complete SCSTR model was carried out to verify the influence of different input disturbances on the output ion concentration of each reactor, which demonstrated the excellent dynamic performance and potential of the model. Ultimately, according to the industrial calculation analysis, the SCSTR model has a guiding effect on the addition of zinc powder in the reactors, overcomes the blindness in the production process, and provides a momentous basis for the optimization control of the cobalt removal process.     

基于改进Kalman滤波算法的多模型融合建模方法

针对聚合物生产过程重要质量控制指标或状态变量的软测量问题,提出了一种基于改进Kalman滤波算法的多模型融合建模方法。将混合核函数主元分析(K₂PCA)与人工神经网络(ANN)相结合,建立一种基于K₂PCA-ANN的数据驱动模型;利用改进Kalman滤波算法实现K₂PCA-ANN模型与机理模型融合,构建一种并联结构的混合模型;协调二次滤波(线性滑动平滑)和方差更新对混合模型进行优化处理,使混合模型的估计性能尽可能地达到最优,使混合模型的预测稳定性得到有效改善。将该多模型融合建模方法应用于氯乙烯聚合过程聚合速率软测量中,应用研究结果表明:与单一的机理模型或K₂PCA-ANN数据驱动模型的预测性能相比,该建模方法建立的聚合速率模型具有更佳的预测性能。该建模方法的运用为进一步开展聚合物生产过程优化与控制等研究提供基础条件。     

基于自适应EKF算法的输出融合软仪表设计

在化工过程中,作为观测关键质量参数的重要手段,软仪表技术受到了广泛的关注。目前,关于软仪表的研究主要集中在建模技术上。然而,化工过程复杂多样,仅使用软测量模型进行质量变量的估计易出现预估效果不稳定、随机偏差大等现象。为此,文献提出了一系列的改进算法,但仍存在计算复杂、算法抗干扰能力差等问题。本文提出一种基于自适应扩展Kalman滤波(EKF)的输出融合软仪表设计方法,利用Kalman滤波算法对软测量模型预估数据和现场观测进行数据融合,校正软测量模型预估偏差;并在输出融合软仪表背景下,设计了一种含衰减因子的观测噪声统计估计器,将其与滤波算法相结合,构成自适应EKF算法,以提高融合软仪表的输出精度及抗干扰性能。通过仿真实验对所提出的算法进行了全面分析,并将该算法应用于小型实验装置,验证了算法的实用性及有效性。     

DESIGN AND IMPLEMENTATION OF STATE OBSERVERS IN REACTIVE DISTILLATION

This study demonstrates that state observers can be developed and applied to infer the composition profiles of reactive distillation columns from noise-contaminated temperature measurements. The design and implementation of a Kalman filter (KF) and a Luenberger observer (LO) are carried out, and their performances are quantitatively assessed. The reliability, accuracy, and robustness of the two designs method are examined and compared quantitatively. The design and implementation of a Luenberger observer are simpler and easier to carry out than those of a Kalman filter. On the other hand, a Kalman filter is found to be more robust to a noisy measurements, erroneous initial estimates, and model uncertainties. A Luenberger observer could be used for composition estimation of reactive distillation when an ideal model of the system can reasonably approximate the real system; otherwise, a Kalman filter is recommended to be applied in more practical situations.     

DESIGN AND IMPLEMENTATION OF STATE OBSERVERS IN REACTIVE DISTILLATION

This study demonstrates that state observers can be developed and applied to infer the composition profiles of reactive distillation columns from noise-contaminated temperature measurements. The design and implementation of a Kalman filter (KF) and a Luenberger observer (LO) are carried out, and their performances are quantitatively assessed. The reliability, accuracy, and robustness of the two designs method are examined and compared quantitatively. The design and implementation of a Luenberger observer are simpler and easier to carry out than those of a Kalman filter. On the other hand, a Kalman filter is found to be more robust to a noisy measurements, erroneous initial estimates, and model uncertainties. A Luenberger observer could be used for composition estimation of reactive distillation when an ideal model of the system can reasonably approximate the real system; otherwise, a Kalman filter is recommended to be applied in more practical situations.     

一类线性系统卡尔曼滤波器自适应算法

为了解决实际线性系统中系统噪声方差和观测噪声方差未知的问题,提出了一种新的卡尔曼滤波自适应算法,利用新息序列的方差,可以在系统的自身计算过程中逐步估计并校正系统噪声方差和观测噪声方差.系统模拟显示,估计的系统噪声方差和观测噪声方差均收敛于实际的系统噪声方差和观测噪声方差,而且收敛速度比传统卡尔曼滤波要快.     

基于多目标优化的两段提升管重油催化裂解自优化控制

针对两段提升管重油催化裂解过程经济运行要求和工艺特点,从多目标优化角度出发,提出一种自优化控制方法。首先,基于过程稳态模型,考虑操作约束条件,构造同时最大化丙烯产量和最小化干气产量的多目标操作优化问题,并采用标准化法向约束方法求解获得完整、均匀分布的Pareto最优解;然后,根据多目标优化结果所揭示的最优操作条件与积极约束之间的关系,提出了一种基于串级控制的自优化控制策略。仿真结果表明,与传统的提升管出口温度设定值跟踪控制相比,本文方法在干扰作用下能够及时调整操作条件,降低干扰对过程优化运行的不利影响。     

On the robustness of the soft sensors used to monitor a vial freeze-drying process

Process monitoring is a key issue in pharmaceutical freeze-drying to evaluate if the limit product temperature is approached, to identify the ending point of the main drying stage, and to estimate the value of some parameters of a mathematical model of the process so that it can be used for cycle optimization. Soft sensors can be used for this purpose: three algorithms, based on the extended Kalman filter and on product temperature measurement, have been compared in this study; they differ on the number of estimated parameters and on the way used to set their initial estimates. Results evidence that the accuracy of estimates is strongly dependent on the initial values of model parameters, and soft sensors #1 and #2 require a preliminary investigation to get accurate initial estimates of the heat and mass transfer coefficients. Soft sensor #2 should be preferred as it just requires an initial estimate of the heat transfer coefficient. Significant advantages are obtained with soft sensor #3: accurate estimates are obtained whichever values of the parameters are used to start the calculations (provided that reasonable values are used) and, thus, it can be effectively used to monitor the freeze-drying cycle without any preliminary investigation. Soft sensor #3 should thus be preferred to the other tools for freeze-drying monitoring.