Continuous Fluidized Bed Spray Granulation Research Articles

Parallel compensator for zero dynamics stabilization in fluidized bed spray granulation

This contribution is concerned with the stabilization of continuous fluidized bed spray granulation processes with external sieve mill cycle. To keep the overall mass of particles inside the granulation chamber in well-defined bounds these processes are in general operated with a mass controller. This configuration is well-known to become unstable for certain ranges of the milling diameter. Here, the instability results in a nonlinear limit cycle of the particle size distribution. As has been shown in a previous contribution the stability problem is not inherent to the process, which is open-loop stable over a wide range of operating conditions. In fact, the root cause for the instability is the mass controller, which interacts with the unstable zero dynamics of the granulation process. To overcome this problem a parallel compensator will be designed, which allows to stabilize the process zero dynamics and thus solves the problem of control induced instabilities.

Gender-Based Eye Movement Differences in the Ilab-X Platform Using: An Eye-Tracking Study

Continuous fluidized bed spray granulation processes are known to be prone to non-linear oscillations, which requires a stabilizing controller design. In this article, a purely data-driven Koopman-based system linearization and control is proposed, which does not need any prior model knowledge and uses only systems input-output measurements. The linearization achieved by the Koopman embedding allows for linear-quadratic control design, which does not depend on the operating point. The proposed method was validated in a simulation study of a fluidized bed granulation process and was able to stabilize the particle size distribution in different operating points.

Koopman-based data-driven control for continuous fluidized bed spray granulation with screen-mill-cycle

Continuous fluidized bed spray granulation processes with external screen-mill cycle are known to be susceptible to nonlinear oscillations. As has been shown recently, mass control may induce periodical oscillation of the particle size distribution in fine grinding regimes, which requires the design of additional stabilizing control. In this contribution a data-driven control approach is investigated. It is based on the identification of the Koopman-based linear representation of the system and does not require any manual system modeling as it is based purely on input–output measurements. The resulting representation makes possible a linear–quadratic control design, that does not depend on a specific operational point. The proposed approach was successfully validated in a numerical study.

Koopman-based data-driven control for continuous fluidized bed spray granulation

Abstract Continuous fluidized bed spray granulation processes are known to be prone to non-linear oscillations, which requires a stabilizing controller design. In this article, a purely data-driven Koopman-based system linearization and control is proposed, which does not need any prior model knowledge and uses only systems input-output measurements. The linearization achieved by the Koopman embedding allows for linear-quadratic control design, which does not depend on the operating point. The proposed method was validated in a simulation study of a fluidized bed granulation process and was able to stabilize the particle size distribution in different operating points.

Control induced instabilities in fluidized bed spray granulation

This contribution is concerned with the stability problems occurring during the operation of continuous fluidized bed spray granulation processes with external sieve mill cycle. These processes are in general operated by a mass controller, which guarantees that the overall mass of particles in the granulation chamber stays in well-defined bounds. It is well-known that, depending on the milling diameter, instabilities may occur, which result in a nonlinear limit cycle of the particle size distribution. To overcome this problem two approaches have been proposed in the literature, constrain the admissible parameter space to exclude regions of instability and design additional stabilizing control loops. In the present contribution, the cause of this instability phenomenon will be studied. It will be shown that the instability is not inherent to the process, which turns out to be open-loop stable over the studied parameter range, but due to the mass controller. More specifically, it will be demonstrated that the zero dynamics of the granulation process become unstable for certain parameter ranges resulting in closed-loop unstable process behavior. To point out, that this behavior does not depend on the specific mass controller design procedure, three prototypical mass controllers of practical relevance are designed and analyzed.

Control of Multi-Chamber Continuous Fluidized Bed Spray Granulation

Abstract This paper is concerned with control of multi-chamber continuous fluidized bed spray granulation processes with external sieve-mill cycles. The process is described by a population balance equation for the particle size distribution in each chamber, resulting in a system of nonlinear partial integro-differential equations. Therefore, control design is challenging. In order to overcome these difficulties the control problem is formulated using a generalized distance measure, the discrepancy. It is shown that discrepancy based control allows to design a simple and effective nonlinear control law for multi-chamber continuous fluidized bed spray granulation processes with external sieve-mill cycles.

Adaptive discrepancy based control of continuous fluidized bed spray granulation with external sieve-mill cycle

Abstract In this contribution control design for continuous fluidized bed spray granulation with external sieve-mill cycle in the presence of uncertain mill behavior is presented. It is well-known that this specific particulate process becomes unstable in certain parameter regions. Being described by a population balance model, a nonlinear partial integro-differential equation, control design is challenging. To overcome this problem control design is studied in terms of a generalized stability theory, i.e. stability with respect to two discrepancies. The resulting discrepancy based control can be extended by additional parameter adaptation to cope with the present uncertainties.

Influence of separation properties and processing strategies on product characteristics in continuous fluidized bed spray granulation

The realization of continuous operation in fluidized bed spray granulation raises issues of process stability and product specification. It requires an appropriate process control strategy and a suitable granulator design. In previous work, a two-zone population balance (PB) model was developed and simulated product size distributions were evaluated by experiments in a Wurster granulator with external straight-duct air classification, however only regarding the process stability. The present contribution extends this population balance model with further equations for the purpose of product size control whereby the parameter setting of the former investigation serves as basis of the shown simulation study. Three process control strategies have been developed, implemented into the PB-model and investigated for diverse desired particle growth ratios and various separation sharpnesses. The simulation results show that only one of these strategies is able to provide the targeted requirements of both, process stability and product specification, but only for sufficiently good separation performance.

Non-identifier-based adaptive control of continuous fluidized bed spray granulation

This paper is concerned with stabilizing control for continuously operated fluidized bed spray granulation with internal product classification. It is well-known that these processes may become unstable for certain operating conditions giving rise to nonlinear oscillations in the particle size distribution. In contrast to previous works, in this contribution a model-free adaptive control is proposed. It is shown that the given fluidized bed spray granulation process fulfills the required structural assumptions. The designed control schemes, universal adaptive and λ-tracking control, are tested in a noise-free scenario and including measurement noise.

Influence of process conditions on the product properties in a continuous fluidized bed spray granulation process

This work focuses on continuously operated spray granulation processes in horizontal fluidized beds highlighting the influence of process conditions on the particle properties of the resulting product granules. The drying process has a decisive influence on the kinetics of the growth rate and thus also on the properties of the particles, such as the morphological structure, particle moisture content and porosity as well as density, compression strength and the wetting behavior. This influence has been considered in this study in more detail on the basis of the model material sodium benzoate. In order to compare the produced granules at different drying conditions and spray rates of the suspension an external product classification was used to achieve a certain product granule size. The obtained experimental results show a deep influence of the thermal conditions onto granule morphology and structural properties, which is in qualitative agreement with recent experimental observations (Rieck et al., 2015; Hoffmann et al., 2015a; Schmidt et al., 2017b). The overall trend of the results reveal smoother product granules with decreasing spray rates of the suspension and increasing drying temperatures. These smoother surface morphologies lead to a more homogeneous layering which has as a consequence that the internal particle porosity is decreasing while the solids density and the compression strength of the particles are increasing at the same time. In this study the purely qualitative classification of the surface texture from previous experimental studies was extended by the topographic analysis of the product granules, giving the possibility to quantify the morphological structure by means of roughness measurements. This makes the morphological design accessible as product property and permits the utilization of models that describe the morphology according to the process conditions.

Auto-tuning Control Systems for Improved Operation of Continuous Fluidized Bed Spray Granulation Processes with External Product Classification

In this contribution control of continuous fluidized bed spray granulation processes with external product classification is studied. From a practical point of view control schemes being easy to implement and maintain using standard process control systems are preferable. Hence, the focus will be on standard PI control structures. In order to account for variations and uncertainties in the process an additional tuning procedure should be included. Here, an optimization based online controller adaptation scheme called iterative feedback tuning (ITF) will be investigated.

Entropy-based control of continuous Fluidized bed spray granulation processes

This paper is concerned with control of a continuous fluidized bed spray granulation. On the basis of an entropy function a control Lyapunov function will be derived. In order to facilitate the control design procedure this entropy-based control Lyapunov function will be approximated by its second order Taylor expansion.

Experimental Investigation of Continuous Fluidized Bed Spray Granulation with Internal Classification

Free flowing and dust free granules with defined properties can be produced from solid-containing liquids like suspensions, solutions or melts by means of fluidized bed spray granulation. In the presented work, granules are produced from a 30 w-% solution of sodium benzoate by layering. The granules are discharged through a classifying tube installed centrally in the distributor plate of the fluidized bed. New nuclei for the granulation are produced solely internally through overspray. The presented experiments investigate the influence of the classifying, drying and fluidizing parameters on nucleation, product properties and process stability.

Discrepancy based control of particulate processes

This article deals with a new approach to particulate process control. The model system under investigation, the continuous fluidized bed spray granulation with external product classification, is described by a nonlinear partial integro-differential equation, the population balance equation for the particle size distribution. This process exhibits interesting dynamical behavior, i.e. a change of the stability behavior and the occurrence of limit cycles. In addition, the zero dynamics with respect to moment measurements frequently used in practice are unstable in certain parameter regions. In order to stabilize these types of systems in this contribution the use of a generalized distance measure, the discrepancy, is proposed. Applying, the associated stability theory, i.e. stability theory with respect to two discrepancies, a stabilizing control law can be derived. One of the main advantages of the proposed discrepancy based control method is that no model reduction is required.

Adaptive discrepancy based control of continuous fluidized bed spray granulation with internal classification

This paper is concerned with adaptive stabilization of open loop unstable uidized bed spray granulation with internal product classication by means of nonlinear feedback control. Since the process model is represented by a nonlinear partial integro-dierenti al equation, direct stabilization of the particle size distribution in a Lp or L1 norm is dicult. To overcome this problem a stability notion using two generalized distance measures, the discrepancies, is used. It is shown that the adaptive version of the resulting discrepancy based control law is able to cope with uncertainties present in industrial applications.

H∞Loop Shaping Control for Continuous Fluidized Bed Spray Granulation with Internal Product Classification

This paper is concerned with stabilizing open loop unstable fluidized bed spray granulation with internal product classification by means of feedback control. Using the results of a detailed model analysis, that is, numerical bifurcation, controllability and observability analysis and a study of the gap metric, an appropriate combination of manipulated and control variables is proposed. Using a reduced transfer function model a robust controller is designed by means of H∞ loop shaping methods. The controller is validated by simulation of the nonlinear plant model using an appropriate start-up strategy.

Discrepancy based control of continuous fluidized bed spray granulation with internal product classification

This paper is concerned with stabilizing open loop unstable fluidized bed spray granulation with internal product classification by means of nonlinear feedback control. The process dynamics are described by a population balance model, i.e. a nonlinear partial integro-differential equation. Therefore a direct stabilization in a classical Lp-norm is at least very difficult. To overcome this problem a stability concept using two generalized distance measures, called discrepancies, is used. In order to show that the discrepancy based control approach presented in this contribution also guarantees stability in the sense of a Lp-norm or L∞-norm additional conditions are stated and verified.

Stabilization of continuous fluidized bed spray granulation with external product classification

This paper is concerned with stabilizing open loop unstable fluidized bed spray granulation with external product classification by means of feedback control. Using the linearization of the discretized population balance model of the process a transfer function is derived and reduced by its normalized coprime factor representation. For the simplified model a PI controller is developed and validated by simulating with the nonlinear plant model using an appropriate start-up strategy. As this controller does not achieve stability over the full range of operating conditions a robust control law is designed by H ∞ loop shaping.

Stabilization of continuous fluidized bed spray granulation - a Lyapunov approach

This article deals with the stabilization of continuous fluidized bed spray granulation with external product classification. Using Lyapunov stability theory a control law is derived guaranteeing exponential convergence of the error particle size distribution in a norm associated to the second moment. In contrast to other approaches popular for particle process control no model reduction is used.

A numerical bifurcation analysis of continuous fluidized bed spray granulation with external product classification

Nonlinear oscillations in continuous fluidized bed spray granulation with external product classification are analyzed. Using methods from numerical bifurcation analysis the size and location of the instability regions in the space of the design parameters and the adjustable operating parameters are predicted and discussed. The analysis is based on a new relatively simple population balance model, which is formulated on a mass basis, and provides first qualitative insights into the nonlinear dynamic behavior of continuous fluidized bed spray granulation processes.