Achieving state estimation equivalence for misassigned disturbances in offset‐free model predictive control

Integrated white noise disturbance models are included in advanced control strategies, such as Model Predictive Control, to remove offset when there are unmodeled disturbances or plant/model mismatch. These integrating disturbances are usually modeled to enter either through the plant inputs or the plant outputs or partially through both. There is currently a lack of consensus in the literature on the best choice for the structure of this disturbance model to obtain good feedback control. We show that the choice of the disturbance model does not affect the closed‐ loop performance if appropriate covariances are used in specifying the state estimator. We also present a data based autocovariance technique to estimate the appropriate covariances regardless of the plant's true unknown disturbance source. The covariances estimated using the autocovariance technique and the resulting estimator gain are shown to compensate for an incorrect choice of the source of the disturbance in the disturbance model. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

自适应广义一般模型控制

针对一般模型控制的缺点,提出了两种改进的自适应广义一般模型控制方法.它们把传统的一般模型控制推广到相对阶大于1 同时又具有时变参数的复杂非线性过程.第1种控制策略主要利用强跟踪滤波器直接在线估计时变参数,来修正过程模型;另一种方法是将所有干扰因素归结为输入等价干扰,通过估计它来实现对过程的前馈控制.仿真实验结果验证了所提出方法的有效性.     

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     

基于ILC&EKF的PM SM转矩脉动最小化方法的仿真研究

提出一种新型的将频域中的迭代学习控制算法(ILC)和扩展卡尔曼滤波器(EKF)相结合来抑制永磁同步电动机(PMSM)转矩脉动的方法。迭代学习算法用来抑制电机运行过程中产生的周期性的转矩脉动。由于在电机终端安装传感器会提高系统的成本、引入噪声等,提出使用扩展卡尔曼滤波器作为观测器来估计系统参数,从电机输出终端根据电机的定转子的电流和电压值准确估计出电机的速度值、转矩值和转子位置角的大小。通过matlab/simulink工具箱仿真结果证明了该方法的可行性和有用性。     

Estimation of void boundaries in flow field using expectation–maximization algorithm

Phase distribution in the flow field provides an insight into the hydrodynamics and heat transfer between the fluids. Void fraction, which is one of the key flow parameters, can be determined by estimating the phase boundaries. Electrical impedance tomography (EIT), which has high temporal characteristics, has been used as an imaging modality to estimate the void boundaries, using the prior knowledge of conductivities. The voids formed within the process vessel are not stable and their movement is random in nature, thus dynamic estimation schemes are necessary to track the fast changes. Kalman-type estimators like extended Kalman filter (EKF) assume the knowledge of model parameters, such as the initial states, state transition matrix and the covariance of process and measurement noise. In real situations, we do not have the prior information of the model parameters; therefore, in such circumstances the estimation performance of the Kalman-type filters is affected. In this paper, the expectation–maximization (EM) algorithm is used as an inverse algorithm to estimate the model parameters as well as non-stationary void boundary. The uncertainties caused in Kalman-type filters, due to the inaccurate selection of model parameters are overcome using an EM algorithm. The performance of the method is tested with numerical and experimental data. The results show that an EM has better estimation of the void boundary as compared to the conventional EKF.     

Applying a dual extended Kalman filter for the nonlinear state and parameter estimations of a continuous stirred tank reactor

The extended Kalman filter (EKF) provides an efficient method for generating approximate maximum-likelihood estimates of the states or parameters of discrete-time nonlinear dynamical systems. In this paper, we consider the dual-estimation problem, the so-called dual EKF, in which both the states of a dynamical system and its parameters are estimated simultaneously, given only noisy observations. The main contribution of this paper is to show the efficacy of a proposed simplified dual-EKF technique (which in this work will be referred to as the dual EKF-2) in comparison with the conventional joint EKF. This has been demonstrated by conducting simulation studies on a CSTR which has been dynamically simulated using the HYSYS simulation package. Extensive analysis revealed that, not only the dual-EKF approach can achieve optimal state- and parameter-estimation performances comparable to the joint EKF, but also it has the main advantage of carrying out separate estimations of the states and parameters.     

Model predictive control for the reactant concentration control of a reactor

The reactant concentration control of a reactor using Model Predictive Control (MPC) is presented in this paper. Two major difficulties in the control of reactant concentration are that the measurement of concentration is not available for the control point of view and it is not possible to control the concentration without considering the reactor temperature. Therefore, MIMO control techniques and state and parameter estimation are needed. One of the MIMO control techniques widely studied recently is MPC. The basic concept of MPC is that it computes a control trajectory for a whole horizon time minimising a cost function of a plant subject to a dynamic plant model and an end point constraint. However, only the initial value of controls is then applied. Feedback is incorporated by using the measurements/estimates to reconstruct the calculation for the next time step. Since MPC is a model based controller, it requires the measurement of the states of an appropriate process model. However, in most industrial processes, the state variables are not all measurable. Therefore, an extended Kalman filter (EKF), one of estimation techniques, is also utilised to estimate unknown/uncertain parameters of the system. Simulation results have demonstrated that without the reactor temperature constraint, the MPC with EKF can control the reactant concentration at a desired set point but the reactor temperator is raised over a maximum allowable value. On the other hand, when the maximun allowable value is added as a constraint, the MPC with EKF can control the reactant concentration at the desired set point with less drastic control action and within the reactor temperature constraint. This shows that the MPC with EKF is applicable to control the reactant concentration of chemical reactors.     

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.     

A novel online affine model identification of multivariable processes using adaptive neuro-fuzzy networks

This paper presents a novel systematic identification methodology for online affine modeling of multivariable processes using adaptive neuro-fuzzy networks. The proposed approach introduces an integrated procedure to simultaneously estimate a number of adaptive neuro-fuzzy networks with simple and compact dynamic structures to realize a multivariable affine model identification in real-time. A new fuzzy rule significance concept, based on a generic time-weighted rule activation record (WRAR), together with a measure of time-weighted root mean square (WRMS) error are incorporated to maintain efficient structural and parametric mechanisms for proper adaptation of the resulting neuro-fuzzy networks. An extended Kalman filter (EKF) algorithm is developed to adaptively adjust the neuro-fuzzy free parameters corresponding to the nearest created fuzzy rules. Extensive simulation test studies will be conducted to explore the capabilities of the proposed identification approach to adaptively develop online multivariable affine dynamic models for a highly nonlinear and time-varying continues stirred tank reactor (CSTR) and a highly nonlinear binary distillation column as two challenging benchmark problems.     

未知输入扩展卡尔曼滤波的收敛性分析及其非线性故障诊断

Unknown input observer is one of the most famous strategies for robust fault diagnosis of linear systems, but studies on nonlinear cases are not sufficient. On the other hand, the extended Kalman filter （EKF） is wellknown in nonlinear estimation, and its convergence as an observer of nonlinear deterministic system has been derived recently. By combining the EKF and the unknown input Kalman filter, we propose a robust nonlinear estimator called unknown input EKF （UIEKF） and prove its convergence as a nonlinear robust observer under some mild conditions using linear matrix inequality （LMI）. Simulation of a three-tank system “DTS200”, a benchmark in process control, demonstrates the robustness and effectiveness of the UIEKF as an observer for nonlinear systems with uncertainty, and the fault diagnosis based on the UIEKF is found successful.     

Extended kalman filter‐based nonlinear model predictive control of a continuous KCl‐NaCl crystallizer

An extended Kalman filter (EKF)‐based nonlinear quadratic dynamic matrix control (EQDMC) for an evaporative cooling draft‐tube baffled (DTB) KCl crystallizer is developed. The controller is used to maintain the productivity, crystal mean size and impurity of crystals. Since these controlled variables are not directly measurable, the EKF is used to estimate them. The nonlinear controller is a combination of an extended linear dynamic matrix control (EDMC) and the quadratic dynamic matrix control (QDMC). This combination provided good control of the system despite the process nonlinearity, constraints, and inadequate reliable online measurement of the controlled variables. The performance of the controller in the presence of plant/model mismatch, disturbance, wrong estimation and simultaneous step changes in the controller setpoints is discussed.     

Consensus-based approach for parameter and state estimation of agro-hydrological systems

The development of advanced closed-loop irrigation systems requires accurate soil moisture information. In this work, we address the problem of soil moisture estimation for the agro-hydrological systems in a robust and reliable manner. A nonlinear state-space model is established based on the discretization of the Richards equation to describe the dynamics of the agro-hydrological systems. We consider that model parameters are unknown and need to be estimated together with the states simultaneously. We propose a consensus-based estimation mechanism, which comprises two main parts: (a) a distributed extended Kalman filtering algorithm used to estimate several model parameters; and (b) a distributed moving horizon estimation algorithm used to estimate the state variables and one remaining model parameter. Extensive simulations are conducted, and comparisons with existing methods are made to demonstrate the effectiveness and superiority of the proposed approach. In particular, the proposed approach can provide accurate soil moisture estimate even when poor initial guesses of the parameters and the states are used, which can be challenging to be handled using existing algorithms.     

基于EKF和UKF算法非均匀介质热物性参数重建

将无迹卡尔曼滤波技术(unscented Kalman filter, UKF)用于求解一维介质热物性参数反演问题;也对利用扩展卡尔曼滤波技术(extended Kalman filter, EKF)反演一维介质中热导率问题进行了研究。首先给出了正问题模型,然后详细介绍了EKF算法和UKF算法的基本原理。最后为了验证当前算法的可行性,采用UKF算法重建了介质内部随位置变化的热导率,并采用EKF算法重建了介质内部随时间变化的热导率。计算结果表明,UKF算法和EKF算法均能较为准确地反演介质的热导率。为了减小重建结果的时间滞后,建议使用较小的测量误差协方差R。     

Distributed semi-cooperative filter for a nonlinear multi-agent system with heterogeneous and homologous unknown inputs

In this study, the simultaneous estimation of the states and unknown inputs for a nonlinear multi-agent system with homologous and heterogeneous unknown inputs is performed. The decentralized sub-filter is used to estimate the states and heterogeneous unknown inputs, whereas the distributed sub-filter is used to estimate the homologous unknown inputs. The extended Kalman filter is used to solve the estimation problem for nonlinear systems. Compared with previous studies, the distributed solution is improved to relax the existence of the homologous unknown input sub-filter. Moreover, the updating method of the residual generator is improved to relax the heterogeneous unknown input sub-filter. The practical problem of estimating the state of charge and temperature of the battery pack is used to verify the effectiveness of the proposed filter.     

搅拌反应器中反应热的实时监测Ⅱ模拟放热反应过程的状态及参数估计

在自制的５Ｌ规模反应量热实验装置中，以热平衡为基础建立了搅拌反应器的动态热传递模型，应用扩展Ｋａｌｍａｎ参数估计和状态估计的方法在线得到模型参数和模拟反应的放热速率、累积反应热。实验数据和模型估计值比较，预测误差在±７％以内     

基于稳定Hammerstein模型的在线软测量建模方法及应用

针对复杂工业过程中由于存在未建模动态和不确定干扰,导致关键变量的软测量精度下降的问题,提出了一种基于稳定Hammerstein模型(H模型)的在线软测量建模方法。H模型的非线性增益采用带有时变稳定学习算法的小波神经网络模型,线性系统部分采用基于递推最小二乘的ARX模型,基于输入到状态稳定性理论证明了H模型辨识误差的有界性。其中小波神经网络具有表征强非线性的特性,稳定学习算法可抑制未建模动态和不确定干扰的影响,改善了模型的预测精度和自适应能力。以典型非线性系统和实际污水处理过程为例进行了仿真研究,结果表明,基于稳定H模型的软测量方法具有较高的在线软测量精度。     

基于Unscented卡尔曼滤波器的管道泄漏的快速检测与定位

针对扩展卡尔曼滤波器(EKF)对非线性模型进行状态估计时,需要将非线性模型进行线性化,而天然气管道模型的非线性程度十分严重的情况,提出一种基于无偏卡尔曼滤波器(UKF)估计的管道泄漏检测与定位方法.该方法是一类用采样策略逼近非线性模型的方法,避免了线性化,并且不需要计算Jacob矩阵,UKF的收敛速度明显优于EKF,能够快速地检测出泄漏.仿真结果说明UKF在泄漏检测中相对于EKF的优势.     

Observer-based control algorithms for a distillation column

This paper studies the synthesis of nonlinear observer-based globally linearizing control (GLC) algorithms for a multivariable distillation column. Two closed-loop observers/estimators, namely extended Kalman filter (EKF) and adaptive state observer (ASO), have been designed within the GLC framework to estimate the state variables along with the poorly known parameters. Exactly same basic model structure was used for developing the observers. The model structure is so simple that the estimator design was performed based on only two component balance equations around the condenser-reflux drum and the reboiler-column base systems of the distillation column. To construct these observers, the poorly known parameters, namely component vapor flow rate leaving top tray, component liquid flow rate leaving bottom tray and distribution coefficient in the reboiler, were considered as extra states with no dynamics. The comparative study has been carried out between the proposed GLC in conjunction with ASO (GLC-ASO) and that coupled with EKF (GLC-EKF). The GLC-ASO control scheme showed comparatively better performance in terms of set point tracking and disturbance as well as noise rejections. The control performance of GLC-ASO and a dual-loop proportional integral derivative (PID) controller was also compared under set point step changes and modeling uncertainty. The proposed GLC-ASO structure provided better closed-loop response than the PID controller.     

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。     

Online temperature estimation of Shell coal gasification process based on extended Kalman filter

Obtaining the temperature inside the gasifier of a Shell coal gasification process(SCGP) in real-time is very important for safe process operation. However, this temperature cannot be measured directly due to the harsh operating condition. Estimating this temperature using the extended Kalman filter(EKF)based on a simplified mechanistic model is proposed in this paper. The gasifier is partitioned into three zones. The quench pipe and the transfer duct are seen as two additional zones. A simplifi...