State and parameter estimation plays an important role in many different engineering fields. Estimation of systems described by linear and nonlinear differential equations has been very well studied in the literature. Work in the past decade has been geared toward efficiently extending these algorithms to constrained systems. Of recent interest is the evaluation of state estimation techniques for differential-algebraic equation (DAE) systems. The algebraic equations in these studies are exact, an example being the mole fractions adding to unity. However, there are situations where algebraic equations can be of both certain and uncertain types. In this paper, we propose a modified extended Kalman filter (EKF) approach that can handle uncertainties in both differential and algebraic equations, and equality constraints. We also show the importance of this work in estimation of mole fraction, temperature, and pressure profiles in a water gas shift reactor. The impact of location and type of measurements on the estimation accuracy is also studied. (Figure Presented). © 2016 American Chemical Society.

Raghunathan Rengaswamy

Department Of Chemical Engineering

Parham Mobed

Sudhakar Munusamy

Debangsu Bhattacharyya

Algebra

Differential equations

Extended Kalman filters

Kalman filters

Nonlinear control systems

Nonlinear equations

Water gas shift

Differential algebraic equations

DIFFERENTIAL AND ALGEBRAIC EQUATIONS

Equality constraints

ESTIMATION TECHNIQUES

EXTENDED KALMAN FILTERING

Nonlinear differential equation

State and parameter estimations

Water gas shift reactors

Parameter estimation

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Industrial and Engineering Chemistry Research

Growing complexity of processes necessitates the use of information from sensors along with first-principles mathematical models to ensure safe and optimal operations. Use of sensors in complex processes requires identifying optimal location of sensors that can maximize information from a process. Classical sensor placement approaches for nonlinear systems that use state estimation schemes usually incorporate linearized models around the steady-state operating point. However, such approaches face difficulties when abnormalities or disturbances drift the system away from the normal operating point. Therefore, use of models that can appropriately track the behavior of the system in the sensor placement framework are of interest. However, the computational complexity of the detailed models makes such approaches intractable. In this work, we develop a sensor placement framework that combines genetic algorithms and the extended Kalman filter to obtain optimal sensor locations. Within this framework, we have investigated the applicability of simplified models by comparing the results of sensor placement for simplified and detailed models. The effect of the simplified models on the estimation accuracy and the optimal sensor network is further evaluated by analyzing the sensitivity to different parameters. Results show that an appropriate simplified model can not only significantly reduce the computational time of the sensor placement algorithm, but also yield a senor network with similar characteristics as the sensor network obtained using the detailed model. Further, information loss in using simplified models in sensor placement may be partially compensated through tuning of the filter parameters, resulting in acceptable, optimal sensor placement solutions. (Graph Presented). © 2016 American Chemical Society.

State and parameter estimation in distributed constrained systems. 2. GA-EKF based sensor placement for a water gas shift reactor

Kalman filter and its variants have been used for state estimation of systems described by ordinary differential equation (ODE) models. While state and parameter estimation of ODE systems has been studied extensively, differential algebraic equation (DAE) systems have received much less attention. However, most realistic chemical engineering processes are modelled as DAE systems and hence state and parameter estimation of DAE systems is a significant problem. Becerra et al. (2001) proposed an extension of the extended kalman filter (EKF) for estimating the states of a system described by nonlinear differential-algebraic equations (DAE). One limitation of this approach is that it only utilizes measurements of the differential states, and is therefore not applicable to processes in which algebraic states are measured. In this paper, we address the state estimation of constrained nonlinear DAE systems. The novel aspects of this work are: (i) development of a modified EKF approach that can utilize measurements of both algebraic and differential states, (ii) development of a recursive approach for the inclusion of constraints, and (iii) development of approaches that utilize unscented sampling in state and parameter estimation of nonlinear DAE systems; this has not been attempted before. The utility of these estimators is demonstrated using electrochemical and reactive distillation processes. © 2010 Elsevier Ltd.

Chemical Engineering Science

Recursive state estimation techniques for nonlinear differential algebraic systems

In any modern chemical plant or refinery, process operation and the quality of product depend on the reliability of data used for process monitoring and control. The_task_of improving the quality of data to be consistent with material and energy balances is called reconciliation. Because chemical processes often operate dynamically in nonlinear regimes, techniques such as extended-Kalman filter (EKF) and nonlinear dynamic data reconciliation (NDDR) have been developed for reconciliation. There are various issues that arise with the use of either of these techniques. EKF cannot handle inequality or equality constraints, whereas the NDDR has high computational cost. Therefore, a more efficient and robust method is required for reconciling process measurements and estimating parameters involved in nonlinear dynamic processes. Two solution techniques are presented: recursive nonlinear dynamic data reconciliation (RNDDR) and a combined predictor-corrector optimization (CPCO) method for efficient state and parameter estimation in nonlinear svstems. The proposed approaches combine the efficiency of EKF and the ability of NDDR to handle algebraic inequality and equality constraints. Moreover, the CPCO technique allows deterministic parameter variation, thus relaxing another restriction of EKF where the parameter changes are modeled through a discrete stochastic equation. The proposed techniques are compared against the EKF and the NDDR formulations through simulation studies on a continuous stirred tank reactor and a polymerization reactor. In general, the RNDDR performs as well as the two traditional approaches, whereas the CPCO formulation provides more accurate results than RNDDR at a marginal increase in computational cost. © 2005 American Institute of Chemical Engineers.

AIChE Journal

Recursive estimation in constrained nonlinear dynamical systems

Industrial & Engineering Chemistry Research

Data Reconciliation and Dynamic Modeling of a Sour Water Gas Shift Reactor

IET Control Theory & Applications

Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Matrix Mathematics

State and parameter estimation in distributed constrained systems. 1. Extended Kalman filtering of a special class of differential-algebraic equation systems

Journal	Data powered by TypesetIndustrial and Engineering Chemistry Research
Publisher	Data powered by TypesetAmerican Chemical Society
ISSN	08885885
Open Access	No