State Estimation in Nonlinear Processes. Application to pH Process Control

Abstract

In the field of process engineering, there are many factors that demand the knowledge of one part of the state vector, if not the full one. Among others, the implementation of nonlinear control methods as well as monitoring of some relevant process variables can be mentioned. The purpose of this paper is to introduce a nonlinear state observer of full order (i.e., the order of the observer matches the order of the nonlinear system observed) in order to estimate all of the state variables of the process. Though the estimated states can be used for many purposes, in this work we aim at using the estimations for output reference tracking. In particular, we deal with the pH neutralization process, which is widely recognized as a difficult problem for the purpose of control. To achieve the pH control goal, a simple algorithm is proposed which lies on a stable reference error dynamics model. Finally, computer simulations are developed for showing the performance of both the nonlinear observer and the control strategy based on pH measurement. For this purpose, a neutralization reaction between a strong acid and a strong base in the presence of a buffer agent is dealt with.

Unscented Kalman Filtering of a Simulated pH System

“…To illustrate this phenomenon, the titration curve of the process is given in Figure 2 for q B from 0 L/min to 5 L/min, which is the region of very pronounced nonlinearity. The reader is referred elsewhere 31 for the titration curve for a wider range of the inlet flow rates.…”

“…Expression 23 was rewritten as a third-order polynomial, 31 from which the value of the output may be derived by introducing the following auxiliary variables: Solving for pH,…”

“…Expression 23 was rewritten as a third-order polynomial, from which the value of the output may be derived by introducing the following auxiliary variables: Solving for pH, The output equation (eq 25) clearly exhibits a very strong nonlinear behavior. To illustrate this phenomenon, the titration curve of the process is given in Figure for q B from 0 L/min to 5 L/min, which is the region of very pronounced nonlinearity.…”

Optimizing autocatalysis with uncertainty by derivative‐free estimators

“…There is a variety of nonlinear estimators based on Kalman filter method 22 . In chemical engineering processes for an example, the extended Kalman filter (EKF) is one of the most commonly used nonlinear estimator 23 due to its derivative‐free solution to the estimation problem.…”

An identification-based state estimation method for a class of non-linear systems

“…In addition, since linearization techniques are employed, convergence and speed of convergence are local properties, which in turn implies that while the estimation error converges in a given time interval, it may diverge in another one. The speed of the convergence is also dependent on the initial value of the covariance matrix, which is assumed to start the algorithm [6]. The approximation issues of the EKF method are handled in the unscented Kalman filter method but this brings additional computational burden and complication.…”