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

Abstract

ontinuous crystallizers are widely used to produce bulk commodity materials such as potassium chloride, ammonium sulfate, and C sodium chloride. Due to the economical significance of the process, control of crystallizes has been the subject of many research work.Important properties of crystals are crystal size distribution (CSD), purity, and shape. From manufacturer's point of view, the crystallizer needs to be operated at high productivity. Crystals with small mean size and wide size distribution can result in caking of dried product leading to problems in storage and handling. Poorly shaped crystals often need compaction and recrystallization. In many applications, purity is more important than the CSD. Low purity product negatively affects the marketability of the product.Majority of investigations in the area of crystallization control are focused on the CSD and its oscillatory behaviour that may be observed in industrial continuous crystallizers. A theoretical study of a complex crystallizer is carried out by Randolph et al., (1977) to identify the CSD instability observed in industrial crystallizers. A feedback control scheme to overcome the problem is proposed by Randolph and Low (1 982) and Randolph et al., (1987). A feedforward algorithm to control the CSD is also used by Han (1967). Rohani (1986) proposes the magma density in the fines loop as the measured variable rather than the crystallizer nuclei density used by Randolph et al., (1 977). The controllers in these studies are single input-single output (SISO) and the main issue is to select an appropriate measured variable to control the CSD. In the 1990s, with the availability of faster computers, advanced controllers and estimation algorithms are employed for the multi-input multi-output (MIMO) control of crystallizers. Eek et al. (1995) report a dynamic model for a suspension crystallizer using pilot plant data. A closed loop identification algorithm and a model predictive controller (MPC) are developed by Eek (1995). Rohani et al. (1999a, b) conduct a theoretical study of a nonlinear MPC to control the size distribution, crystal purity, and productivity in a KCI crystallizer. Tadayyon and Rohani (2000) develop a MIMO nonlinear QDMC to control a pilot plant KCI crystallizer. It is assumed that the online measurements of the CSD and impurity are available. However, these assumptions are not realistic as the online and robust measurement of crystal size distribution is still a formidable task. A study of various currently available CSD sensors indicates that the majority of these instruments still impose some limitations. A back light scattering technique, patented by Laser Sensor Technology Inc. (Redmond, WA, USA), makes the online monitoring of chord length distribution (CLD) possible.An extended Kalman filter (EKF)-based nonlinear quadratic dynamic matrix control (EQDMC) for an evaporative cooling draft-tube baffled (DTB) KCI crystallizer is developed. The controller is used to maintain the productivity, crystal mean size and impurity of crys...

Nonlinear model predictive control for the polymorphic transformation of L‐glutamic acid crystals

“…With advances in sensor technologies, another control strategy developed to provide improved robustness to model uncertainty is C‐control, which follows an optimal or nearly optimal concentration‐temperature trajectory 9, 13–16. Despite the high impact of model predictive control (MPC)17–23 in academic research and industrial practice, its application to solution crystallization processes has been rather limited 24–29. One contribution considered the effects of uncertainties on the closed‐loop performance of nonlinear model predictive control (NMPC) applied to crystallization processes 27.…”

Application of state estimation based NMPC to an unstable nonlinear process

“…Note that this particular approach of the EKF uses the knowledge of the nonlinear model to update the state of the process. This is an improved version of the EKF with respect to the most diffused approach in which both the predicted states and the covariance matrix are calculated using the linearized model (Bastin and Dochain, 1990;Tadayyon and Rohani, 2001). It must be noticed that for the Kalman filter as a linear unbiased minimum variance estimator, the parameters P K , R K and Q K have all physical meaning.…”

“…Depending on the obtainable information about the process, there exist many possible kinds of estimators to be used depending on the mathematical structure of the process model (Wang et al, 1997). In this sense, the standard extended Kalman filter (EKF) is one of the most (if not the most) widely diffused observer among other nonlinear observers based on linearization techniques (Stephanopoulos and San, 1984;Tadayyon and Rohani, 2001). For instance, Lee and Ricker (1994) proposed a state observer based MPC strategy using successive linearization.…”

Use of Calorimetry Model and Batch Control Technique for Scale-Up of Unseeded Batch Cooling Crystallization of Poly(hydroxybenzophenone)

“…With the evolution of control theory and measurement techniques, advanced control strategies for crystallization processes have become an important research topic. For example, sophisticated optimal criterion-based nonlinear control − has been investigated mainly in academia because of the intricate nonlinear characteristics of crystallization processes. Because this research involves only temperature control, an ILC technique is considered more appropriate for our purposes, as it is simpler and its ultimate performance is not dependent on model accuracy unless divergent.…”