Vision-based adaptive control system for fluidized bed reactors

Vision-based adaptive control system for fluidized bed reactors Stanisław Anweiler a,* , Marek Krok b , Szymon Kołodziej c , Ricardo Chacartegui d , Jose Antonio Becerra Villanueva d , Małgorzata Sikora e , Barbara Wasilewska f , Dawid Przysię˙ zniuk g a Faculty of Mechanical Engineering, Department of Process and Environmental Engineering, Opole University of Technology, ul. Pr´ oszkowska 76, 45-758 Opole, Poland b Faculty of Electrical Engineering, Automatic Control and Informatics, Department of Control Science and Engineering, Opole University of Technology, ul. Pr´ oszkowska 76, 45-758 Opole, Poland c Faculty of Mechanical Engineering Department of Vehicles, Opole University of Technology, ul. Pr´ oszkowska 76, 45-758 Opole, Poland d Department of Energy Engineering, Escuela T´ ecnica Superior de Ingenieros de Sevilla, University of Seville, Camino Descubrimientos, s/n.- Isla Cartuja, 41092 Seville, Spain e Faculty of Mechanical Engineering, Koszalin University of Technology, ´ Sniadeckich 2 Street, 75-453 Koszalin, Poland f Faculty of Production Engineering and Logistics, Department of Production Management and Engineering, Opole University of Technology, ul. Pr´ oszkowska 76, 45-758 Opole, Poland g Faculty of Mechanical Engineering, Opole University of Technology, ul. Pr´ oszkowska 76, 45-758 Opole, Poland ARTICLE INFO Keywords: Two-phase Fluidization Visualization Image analysis Pneumatic valve control PLC Automatic control ABSTRACT In process engineering, precise, automatic, and dynamic identification of two-phase structures remains a challenging yet essential task, particularly for effectively controlling pneumatic systems handling solid particles. Complex interactions between gas and solid phases and variable flow geometries complicate the precise control of fluidized beds. This study evaluates an adaptive, vision-based flow control system designed for fluidized bed reactors, using real-time image analysis to characterize flow structures. A self-developed air flow valve regulator system, combined with a programmable logic controller (PLC) and dynamic image feedback, enables this innovative control approach. By analyzing grey-level signals within specified regions of interest (ROIs), the system accurately differentiates between critical fluidization regimes: bubbling, plugging, and turbulent flow. The control algorithm dynamically adjusts the flow rate, achieving a mean square error of 6.98 m 3 /h, underscoring the system’s reliability and potential for further optimization. Additionally, safeguards were implemented to prevent material loss at high airflow thresholds, enhancing system stability and safety. The findings demonstrate the potential of adaptive vision-based control for fluidized bed automation, offering an advanced solution for real-time monitoring and precise flow regulation in complex two-phase processes. 1. Introduction Fluidized bed reactors are extensively utilized across industries due to their high efficiency in mass and heat transfer processes, pivotal for applications in chemical processing, combustion, and material handling. However, achieving precise and stable control over two-phase (gas–solid) flow structures within these systems remains challenging due to their inherently complex and dynamic nature. Conventional measurement and control methods, primarily based on pressure drop analysis, often provide limited resolution for distinguishing specific flow regimes, such as bubbling, plugging, or turbulent fluidization and especially the transition between them. This paper introduces a novel adaptive control system that leverages real-time image analysis of grey-level signals to effectively identify and manage distinct fluidization regimes. The proposed vision-based system integrates advanced imaging technology with a programmable logic controller (PLC) to dynamically adjust airflow, significantly improving the accuracy and stability of the fluidization process. Initial results from experimental validation demonstrate that the developed adaptive algorithm maintains desired flow conditions reliably, highlighting its * Corresponding author. E-mail addresses: [email protected] (S. Anweiler), [email protected] (M. Krok), [email protected] (S. Kołodziej), [email protected] (R. Chacartegui), [email protected] (J.A.B. Villanueva), [email protected] (M. Sikora), [email protected] (B. Wasilewska), [email protected] (D. Przysię˙ zniuk). Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement https://doi.org/10.1016/j.measurement.2025.118046 Received 18 March 2025; Received in revised form 15 May 2025; Accepted 30 May 2025 Measurement 255 (2025) 118046 Available online 1 June 2025 0263-2241/© 2025 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). potential for industrial applicability and enhanced operational efficiency. Along climate emergency and the ambitious objective of gas emissions reduction by 43 % by 2030, reforming industry presents a formidable challenge [1]. This includes optimizing combustion methodologies, augmenting heat recovery, advancing the capturing of carbon, storage, and utilization technologies, and refining heat transfer mechanisms and heat exchangers [2]. Researchers still not fully understand and are able to predict the behaviour of these complex systems. The importance to measure different parameters, such as fluid and particle velocity profiles, particle size distribution and voidage during operation, etc. is crucial and currently no single technique available enables the measurement of all these parameters [3,4]. The approach based on computer vision and machine learning methods to identify two-phase flow with complex flow patterns is becoming popular [5]. The fluidizing particulate solids with gas represents a prevalent twophase flow procedure in industrial applications. [6]. The utility of fluidization systems is experiencing expansion across a spectrum of scales [7], encompassing large-scale operations for the conveyance of granular substances [8], the gasification and combustion of solids in diverse configurations of fluidized bed boilers [9], intermediate-scale systems for separation or clustering tasks [10], to small-scale applications such as granulation, drying, and coating in the pharmaceutical sector [11]. The array of fluidization applications is extending from microscale interactions in both liquids [12], and gas phases [13] to the nanoscale [14]. Within the solids processing sector, for instance, the market for pneumatic conveying systems is projected to reach a valuation of approximately $30 billion by 2025 [15]. This causes interest in automating the control of fluidized processes to keep growing. Automating the control process for two-phase flow presents a challenging problem due to the vast diversity of these systems. Despite their origins tracing back to the mid-20th century, contemporary designs represent modifications of those earlier models [16]. Adaptive control aims to manage uncertain dynamic systems in real-time by employing adaptation and learning mechanisms [17]. An adaptive vision control system is a scientific approach to controlling the operation of a process using computer vision techniques. The term adaptive can refer to both the optical and control systems. Adaptive optics, though a nascent discipline, is experiencing swift proliferation and enables the posing of novel inquiries into the organisation of the visual system [18]. Within science and engineering, adaptive control systems hold a prominent position and have been thoroughly investigated by the control community. Addressing the challenge of unknown control gains remains a crucial technical concern that continues to captivate the attention of numerous scholars [19]. Conversely, the multiphase flow patterns observed in these systems continue to be the subject of intense investigation [20]. Computational Fluid Dynamics (CFD) simulations are implemented to scrutinize the process with finer detail and aid in engineering novel apparatuses, with simulation outcomes corroborating against empirical data [21]. Through a synergistic methodology, existing and newly formulated models can delineate the dynamics of atomization, combustion, and the genesis of pollutants [22]. Numerical simulations facilitate forecasting particle dispersion effects on the continuous phase and the interplay among particles within the two-phase flow, thereby characterizing heat transfer [23]. Advancing toward process automation involves embracing visualization techniques, specifically through imaging and image recognition. Different methods are used for visualizing multiphase flows, including standard photography and video recordings [24]. Those methods include image analysis [25], photogrammetry [26] and videogrammetry [27]. This study applies a smart camera for image acquisition and analysis. While imaging-derived signals are excellent for process control, they require characterization and calibration to be interpretable by control systems. This is still an emerging research area and has a limited presence in the literature on two-phase flow advancements, specifically in fluidization applications concerning valve operation [28] or measurement and imaging systems used to determine two-phase flow [29]. Considering the existing knowledge on automatic fluidization control, a notable research gap involves automatic recognition of two-phase flow structures and identification of quantifiable characteristics suitable for control algorithm interpretation. This paper explores various properties of the image’s grey level signal to assess if any can distinctly indicate the current state of the fluidized bed. This approach is novel in process engineering and aligns with investigations into the potential performance of energy technology equipment and systems. Addressing this topic requires an interdisciplinary approach, incorporating modelling, experimentation, analysis, optimization, and proper result verification [30–33]. The extensive use of fluidization processes has attracted significant interest in different methods of control and regulation. One of the primary purposes is process intensification, which significantly enhances efficiency and directly reduces energy intensity, pollutant emissions, and overall negative environmental impact, aligning with current priorities in sustainable development [34]. Automation plays a crucial role in achieving these objectives, and dynamic image analysis represents an innovative step forward in controlling fluidization processes. The results from the experiments demonstrated that the designed system can effectively maintain the state of the fluidized bed by using the image’s grey level to regulate the airflow. 1.1. Motivation Significant progress has been made in understanding and describing the mixed flow of solid particles and gas. However, managing complex gas–solid interactions in a reactor is still an open challenge. Complex gas–solid interactions in fluidized bed reactors involve diverse transient phenomena, including bubble formation, growth, coalescence, and bursting, slugging, vortex structures, particle agglomeration, and clustering. The motivation for this work is the need to improve the control of fluidization processes, therefore increasing their energy efficiency and precision. As shown in the introduction, traditional methods based on pressure drop measurements are often insufficient. Technologies, such as adaptive image analysis and control, is expected to improve process stability and accuracy. This work presents an approach to enhance the automation of fluidized bed reactors through an adaptive control system based on vision analysis. By integrating image analysis from a smart industrial camera with a self-designed airflow valve controller, we aim to effectively identify and regulate two-phase flow regimes. Using a programmable logic controller (PLC), the system analyses visual data to adjust the flow rate dynamically, maintaining optimal fluidization conditions. 1.2. Novelties and contributions of the paper •Signals were studied, and software was designed that works for different states of the deposit •Using dynamic image analysis to control the fluidization process. •The creation of an algorithm that maintains a preset fluidized bed state based on feedback between visual data and flow measurements. •Integrating a decision-making system using a PLC to manage gas–solid two-phase flow based on grey-level image analysis is a novel approach that enables dynamic and precise real-time adjustment of fluidization conditions. Developing an algorithm to maintain preset fluidization conditions based on feedback between visual data and flow measurements is a new scientific contribution. Designed to evolve through machine learning, the algorithm has the potential to increase its accuracy and efficiency as data is acquired. S. Anweiler et al. Measurement 255 (2025) 118046 2 2. Materials and methods In the field of process engineering, dense phase flow control is one of the critical elements in pneumatic solids handling and processing. Complex geometry and interactions between the gas and solid phases make it challenging to control the flow precisely. This paper details a study on applying an automated flow control system, featuring experiments that utilized a self-engineered feedback system for an airflow control valve, incorporating image analysis from an industrial smart camera. This process is regulated based on visual data, which is analyzed and interpreted by a decision-making system implemented on a Programmable Logic Controller (PLC). The experiments focused on twophase gas–solid flow in a vertical riser, with the flow regime being determined based on grey-scale image analysis. The layout of the experimental setup is depicted in Fig. 1. In this study, millet groats were utilized as the particulate material. The bulked bed was positioned within a two-dimensional channel, a setup frequently employed by researchers to train vision systems during experiments [35], and simulations [36]. The channel is 200 mm in width, 30 mm in thickness (gap), and 1200 mm in height and was aerated using an air jet with velocities ranging from 0.69 to 2.55 m/s. The height-to-width ratio of the stacked bed is 1 [37]. However, when recalculated using the channel’s equivalent diameter, the bed’s heightto-diameter ratio (H/D) is approximately 4. There may be some uncertainty about the rare slotted character of the reactor. A simplified model was chosen so that even the smallest bubbles in the bed could be observed, avoiding 3D effects obscuring the structures in the initial stage of the study. The properties of the fluidized bed are detailed in Table 1. It should be noted that the simplified vertical pseudo-2D geometry and the selected millet groats particles serve as a demonstrative setup enabling detailed visualization and accurate characterization of two-phase flow phenomena. Additional attention is being paid to the lighting system. The light source significantly affects the greyscale values and measurement accuracy in a fluidized bed system, as variations in lighting can cause fluctuations that misrepresent particle distribution. Consistent and uniform lighting ensures that the greyscale values accurately reflect the actual state of the fluidized bed, minimizing noise and artefacts. The lighting setup consists of a flat panel with an array of 2000 pieces of DCpowered LEDs designed to provide stable and uniform illumination across the observation area. The light intensity is equivalent to a 3,000watt incandescent light. Multiple LEDs ensure an even light distribution, minimizing shadows and reflections that could affect the greyscale values. Initially, we experimented with AC-powered halogen bulb scenic spotlight reflectors but found that the LEDs offered more stable and consistent lighting conditions. The theoretical Minimum Fluidization Velocity (U mf ) for millet groats (Panicum miliaceum) was initially calculated based on grain properties and standard correlations (Wen and Yu correlation [42]), yielding approximately 0.203 m/s. However, the practical U mf , determined empirically through real-time image analysis, was substantially higher (0.69 m/s). This discrepancy primarily results from factors such as particle shape irregularity, non-uniform size distribution, surface roughness, and particle agglomeration effects, typically not accounted for by theoretical models. A comprehensive analysis of these factors is beyond the scope of this paper. The U mf measurements, shown in Table 1, correspond to the latest tests done by [43]. In this stage of research, typical fluidization process issues, such as the classification of bed particles into Geldart groups [44], pressure drops, Reynolds and Archimedes numbers, detailed bed height analyses [45] or the flow maps are not as relevant as the control system itself. It consists of an open-loop controller, depending on the greyscale value the camera returns. In this application, the camera data is transmitted using TCP/IP protocol for robustness and reliability of communication against disturbances. The camera has dedicated software (Banner Vision Manager), which allows operation configuration, including the Region of Interest (ROI), performed calculations, and communication methods. Then, the smart camera executes the calculations in real-time. The greyscale calculation for defined ROIs and the TCP/IP communication protocol have been chosen. The camera provides new calculation results to the network depending on the computational load, so the number of ROIs should be reduced. When analyzing six different ROIs simultaneously, the camera can perform the necessary calculations in 20 ms on average, which gives about 45 frames per second. The camera sends the greyscale values to the PLC, which reads and writes them into an integer variable. Based on the greyscale analysis and flow measurement, the controller calculates a new control value, i.e. valve value. For the physical implementation of the 0–20 mA signal interpreted by the valve controller, the 15-bit output register contains set content, physically realized by the analogue output (AO) module, and sent to the valve positioner. The value of a 15-bit output register can range from 0 to 32767. This is because a 15-bit number in binary counting can represent 215 different values, starting from 0 (all bits off) to 32,767 (all bits on). The 15-bit value is calculated proportionally to the set valve opening degree in connection with the above. The valve opening, which results from the algorithm, controls the whole process, Fig. 1. Overview of the test bench highlighting essential components. Table 1 Details of the tested fluidised bed components. Feature Symbol Value Unit Height of the fluidized chamber h 1200 mm Width of the fluidized chamber a 200 mm The gap of the fluidized chamber b 30 mm The cross-sectional area of the chamber A 0.006 m 2 Average particle diameter d p 2 mm Bulk density of the bed ρ 827 kg/m 3 Geldart’s classification of the particles −B-D − Minimum fluidization velocity U mf 0.69 m/s Gas flow rate for U mf V 15 m 3 /h Lift (transportation) velocity U t 2.55 m/s Gas flow rate for U t V 55 m 3 /h Electropneumatic valve [38,39]− − − Smart camera [40]− − − Process controller TX500 HMI/PLC Series [41]− − − S. Anweiler et al. Measurement 255 (2025) 118046 3 and the control algorithm is to evolve later via machine learning. The schematic representation of the measurement and control system is depicted in Fig. 2. Fig. 3 shows general flow regime diagram for the whole range of gas–solid contacting, from percolating packed beds to lean pneumatic transport of solids; adapted from [46] along with an example of the visualization. Industrial practice shows a need to create and maintain a proper two-phase flow regime. Whether it will be bubbling or turbulent fluidized bed, one usually wants to avoid certain phenomena, e.g. plug pulsation, which may lead to structure vibrations, assuring an adequate mass transfer (and heat transfer if applicable). For this purpose, the authors propose a feedback system that detects the flow structure in realtime and, based on the algorithm developed, decides on the operation of the air valve. The decision to open the valve is determined by analyzing the grey level within specific image areas, called detection probes – image areas (ROIs). One needs to determine representative place detection probes that can easily recognize the structure or the pulsation. This study will answer whether one image area is sufficient for regime characterization and valve operation or to get information for the fluidized bed-based designs. An interesting approach for the future would be to compare the processing of more information (several areas) with one or two, show the differences in control and results, and expect that with more control of the visualization, you could get more accurate control and results but with more time necessary to calculate. The representative Region of Interest (REP ROI) was determined by analyzing various areas within the fluidized bed to identify the most indicative section for capturing the fluidization dynamics. Initially, all areas above the deposit during fluidization were rejected as they were only helpful during pneumatic transport phases. The bottom area of the deposit was also excluded because the observed values were too proportional to the airflow, failing to capture different bed conditions. The selected ROI partially coincided with an area that showed a linearly increasing grey level during the early phases of fluidization, making it suitable for detecting initial particle movements. This ROI stabilized during turbulent fluidization, providing consistent data that effectively indicated transitions between different fluidization states. For further discussion, see Section III. The pressure drop on the fluidized bed is often examined, which helps distinguish the fluidized state from the fixed bed and the pneumatic transport. This allows the determination of the fluidized bed’s general state for an opaque apparatus. However, it is nearly impossible to differentiate between the two-phase flow regime and structure solely based on the pressure drop. Fig. 4 illustrates the pressure drop in a fluidized bed relative to gas velocity. In Fig. 4, during section A, the fluidized bed’s pressure drop (ΔP) Fig. 2. Conceptual diagram of the automatic two-phase flow control system, highlighting the image analysis and decision-making framework. S. Anweiler et al. Measurement 255 (2025) 118046 4 increases linearly with the flow velocity (u), indicating a solid bed stage where the gas filters through and the bed particles remain stationary. In section B-C, as the flow velocity increases to point B, ΔP matches the total gravitational force of the bed. At this juncture, the bed begins to loosen and expand slightly. As the flow velocity rises past point B, the bed particles start to float, and the bed expands. Despite the increasing velocity (u), ΔP remains nearly constant, marking the desired fluidized bed stage from a control perspective. Beyond point C in section C-later, the flow velocity further escalates, transitioning the bed into the pneumatic transport stage. In sections B-C, the pressure drop remains constant; however, as shown in Fig. 3, there is a significant variation in the two-phase flow structures and patterns. These differences can be identified by analyzing changes in the grey level of the image, which is schematically depicted in Fig. 5. The considerable measurement and control capabilities of the developed automatic fluidization process control system are highlighted. Future research will enhance this system by integrating it into a closed-loop configuration utilizing a proportional-integral-derivative (PID) controller. However, before implementing this closed-loop control scheme, it is essential to identify different fluidized bed structures and their associated grey levels. This paper, therefore, explores various bed types and their specific grey levels within certain bed areas. A PID-like incremental controller was used to open the valve with too-low flow rates and close it with too-high flow rates. Δu(k) = Kpe(k) + Ki∑e(k) + KdΔe(k)(1) The proportional gain was initially chosen to achieve slow but stable control at a specific flow rate and then fine-tuned to optimise settling time performance. However, it was noted that the proportional gain, when selected for one operating point, led to oscillations at a different flow rate setpoint. Consequently, the single-valued proportional gain was replaced by an adaptive gain characteristic, which varies according to the desired flow rate. Seven operating points were identified to implement this adaptive gain, and their corresponding parameters were determined experimentally. Since fluidization is a nonlinear system the gains were experimentally determined for a number of operating points. Based on the selected operating points the gains were approximated for other flow rates shown in Table 2. During nominal operation of the bed such an approach proved to be sufficient for stabilization of gas flow rate. Based on this observation, a 4th-order polynomial approximation was utilized to determine the gains for all possible setpoints. To prevent the system from stalling due to near-zero gain or becoming unstable due to excessively high gain, the final gain calculation was constrained to a range from 0.2 to 10. During this development phase, it was noted that the operating point should not solely depend on the desired flow rate, as this approach led to prolonged settling times when dealing with significant setpoint changes. Consequently, the operating point is determined based on a weighted sum of the setpoint and the current flow rate, facilitating a smoother transition between the current and desired flow rates. The final characteristic of the proportional gain (K p ) is depicted in Fig. 6. The proportional incremental term without the mentioned boundaries is: Kp=0.000009919849564x4−0.001137249409024x3 +0.045167168175658x2−0.751123215768367x +4.997462947486267 where x=3V(k)+Vref (k) 4 denotes the current operating point used for the determination of proportional gain. The integration component, as in the previously mentioned classical PID controller, can be added to minimize control error. The integral gain was determined experimentally to be Ki=0.002Vref , which allows it to adjust to the current operational point. The sum of the control errors is calculated and applied under specific conditions for the process. The integration result is reset to zero if the control error exceeds a pre-set threshold to counteract overshooting due to wind-up and non-linear effects. In this scenario, the integration part is deactivated if the disparity between the desired and actual flow rates exceeds 5 %. The accumulated control error is also capped at 400 m 3 /h, ensuring that the control error will approach zero near the flow rate setpoint. A third controller component based on error difference was incorporated into the PLC algorithm to leverage the PID framework’s advantages fully. The differential gain was set to Kd=10, enhancing Fig. 3. General flow regime diagram for the entire spectrum of gas–solid interactions, from fixed beds to pneumatic transport. The map is constructed as a function of the Archimedes number and the dimensionless superficial gas velocity u G *. Flow regimes are divided into: I – bubbling fluidization, II – turbulent fluidization, III – fast fluidization, and IV – pneumatic transport. The boundaries of fluidization (minimum fluidization velocity u mf and transport velocity u t are marked. The horizontal axis denotes Geldart’s powder classification (C, A, B, D) indicating particle behavior under gas flow. The red-framed area highlights the experimental research range conducted in this study, covering transitional regimes between bubbling, turbulent, and fast fluidization. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 4. Relationship between pressure drop (ΔP) and flow velocity (u) in a fluidised bed, adapted from source [47]. S. Anweiler et al. Measurement 255 (2025) 118046 5 control speed without compromising system stability or robustness. This study uses an adaptive concept, which involves adjusting the controller settings so that the resulting flow structure matches the expected structure as closely as possible. This structure is then maintained within an appropriate range of classification parameters, such as pressure, temperature, gray level and the nature of the changes in the gray level signal. The programmable logic controller does not directly control the valve in the current hardware setup. Instead, the PLC sends a reference value to an internal valve controller with specific parameters. A dead band of 0.5 % was established to minimize wear on the valve actuator, meaning the controller only adjusts the valve position if the difference exceeds this threshold. This functionality can be monitored through a dedicated interface, which allows adjustments to the internal valve controller. Future research will focus on expanding this system by integrating it with a closed-loop system based on a proportional-integral–differential (PID) controller. However, before a closed-loop control system can be fully implemented, it is necessary to accurately identify the various fluidized bed structures and their characteristic gray levels. Therefore, this paper focuses on the analysis of different bed types and their specific gray levels in selected areas, which provides a basis for future precise regulation using a PID controller. Notably, the valve setpoint range (0–100 %) corresponds to an analogue output of 4–20 mA, achieved by setting the appropriate 15-bit register value, which spans from 0 to 32768. Additionally, a new procedure was introduced to enhance stability, reduce actuator wear, and improve reliability. If the control error remains below 3 % for at least three consecutive seconds (150 steps of 20 ms each), the setpoint for the control valve remains unchanged until the error exceeds 3 %. This hysteresis approach mitigates issues like those observed with valve behavior in Fig. 7. The primary goal was to achieve stable steady-state performance across various flow rate setpoints, verified through testing on an actual fluidized bed. 3. Results and discussion The results presented below demonstrate the effectiveness of the developed control system under experimental laboratory conditions. Examples of the process visualization results showing changes in the two-phase structure were gathered in Fig. 3. 3.1. Gray level analysis for characteristic bed structures This part of the study analyzed how air velocity affects the formation of structures in selected bulk materials, what gray levels it generates in the image, and how this should affect the regulation of the process. Fig. 8 shows the analysis of gray level changes for selected areas of interest (ROIs), and Fig. 9 shows the average gray level for these areas to determine a representative ROI for distinguishing flow structures. The objective of the above analysis was to determine: (a) The representative area for measuring grey levels (ROI) as shown for subsequent flow rates in Fig. 9. (b) The average grey level for a specific two-phase flow structure corresponding to a particular airflow made it possible to establish a setpoint for the subsequent automatic flow rate adjustment. 3.2. Application of the PID controller Based on the above analysis, Fig. 10 shows the result of the response of automatic airflow control for the pre-set two-phase structure. On the flow chart, imperfections of the regulation waveform (disturbances and fluctuations) can be noticed, especially in the initial Fig. 5. Grey level fluctuations over time for the image in selected regions of interest (ROI) for the single flow pattern (gas flux V =39 m 3 /h). Table 2 Flow Rates and Corresponding Desired Controller Gains. Flowrate 0 15 20 25 30 35 50 Gain 5 0.5 0.65 0.5 0.4 0.2 0.2 Fig. 6. Adaptive gain profile. S. Anweiler et al. Measurement 255 (2025) 118046 6 stages of changes in the flow rate values. This is due to the adaptation of the automatic control algorithm to the actual state of the bed and the adaptation of the algorithm to the current operating point. Further work will gradually eliminate these disturbances and improve the system’s response. The mean square error of the flow control was measured at 6.98 m3/h, indicating potential for further improvement; however, the primary objective of achieving static accuracy was met. The control algorithm introduced has its advantages and disadvantages. A significant downside is a nonzero steady-state error and relatively prolonged transient states. This issue stems from the algorithm’s design. On the other hand, the advantages include maintaining the flowrate reference value stably across all considered ranges, with a maximum steady state error limited to 3 % of the setpoint value, as shown in Fig. 11. While the transient states are longer than ideal, they are not the primary focus of this study, as improvements can be achieved using the inverse static characteristic developed here. The fit obtained is a 5th-order polynomial, demonstrating that the considered control system exhibits significant nonlinearity. Thus, the adoption of an adaptive control algorithm is fully justified. Given this characteristic, plans include the implementation of an inverse-based control algorithm, which is expected to yield significantly improved control performance. Currently, intensive development efforts are focused on this inverse approach. To address the nonlinear nature of the control system, steady-states were determined for various flow rates to gather ample data for addressing all associated peculiarities related to the grey-level scale. Additionally, the camera aperture and focus were adjusted using zero flow as a reference. An example illustrating the registered grey levels for different regions of interest was earlier depicted in Fig. 9. The term “nonlinear system” can be used in a broader context that includes a variety of complex or chaotic mechanisms. In this case, the use of a polynomial control system refers to a specific type of nonlinearity arising from the characteristics of the fluidization process, rather than to complex or chaotic mechanisms. Fig. 7. Relationship between valve position and setpoint. Fig. 8. Variation in grey level for selected Regions of Interest (ROIs) over time. S. Anweiler et al. Measurement 255 (2025) 118046 7 3.3. Correlation of pressure drop with gray level for identifying fluidization conditions This subsection discusses the relationship between fluidized bed pressure drop and image gray level analysis. How these two metrics reflect changes in flow pattern and bed condition is presented. The pressure drop over the same air velocity range was then measured, as shown in Fig. 12, and compared with the characteristic pressure drop for the fluidization process previously shown in Fig. 4. The similarity of the waveform is clear, and despite the apparent variability of the measured pressure drop in the fluidized bed section (BC), the differences are less than 0.1 kPa, which disqualifies it from being a process estimator in this regard. Therefore, in general diagrams, the BC section is represented as a straight line, and consequently, a method must be found to map this variability. The solution may be to combine several inputs of information, which are presented later in the article. From the analysis of the waveforms depicting grey level variation, as illustrated in Fig. 9, a representative Region of Interest (ROI) was identified, as shown in Fig. 13. The area was selected by checking different test areas of interest in parallel. First, all areas located above the deposit during fluidization were rejected. These areas would work well in the pneumatic transport phase, but they do not provide the possibility of detecting the moving bed before fluidization begins. The area at the very bottom of the deposit was also eliminated, but the reason for this decision was different. The observed values were growing too proportionally to the value of the airflow. Hence, it will not allow the detection of other bed conditions. The selected area, which partially coincides with ROI 4, allowed the observation of a linearly increasing grey level in the early phases of Fig. 9. The average grey level distribution over increasing gas flux for the different ROIs (images show example flow patterns for selected gas flux). Fig. 10. Flowrate behavior under different setpoints. Fig. 11. Relationship between flow rate and required stable valve setpoint value. S. Anweiler et al. Measurement 255 (2025) 118046 8 fluidization, where the first movements of particles appear. When the bed enters the turbulent fluidization phase, the grey level stabilizes, which, combined with the constant pressure drop, may suggest that if the flow increases further, the pneumatic transport phase will occur. A summary of the (ideal and real) pressure drop and greyscale values is summarized in Fig. 14. From Fig. 14, it is clear that the support of the recognition of the flow structure for process control employing analysis of changes in the grey level is possible. Therefore, the variation characteristics for all airflow fluxes from 15 to 55 m 3 /h were studied in detail and presented in Figs. 15 to 17 and collectively for comparison in Fig. 18. Such a range was chosen because 0–15 is a stationary bed, and above 55, particles were lifted out of the apparatus, i.e. pneumatic transport. Hence, the grey-level signals regarding their PDF, histogram, and FFT analysis will now be examined. 3.4. Statistical analysis of gray level signal This section discusses statistical methods that support the analysis of brightness signals, which makes it possible to accurately distinguish flow states and identify moments of transition between different structures. Details on probability distributions, spectral analysis, and other techniques that enrich image analysis are provided. Fig. 17 visualizes all signals considered for a 47 m 3 /h flow. As with the previous increase in airflow, image brightness increased as more and more material was pneumatically tossed, allowing more light to reach the camera from the lamps directly downstream of the fluidized bed. The shift of the histogram towards the maximum value also indicates the state of high agitation of the bed and the appropriate phase of its fluidization. Frequency analysis shows that instead of single, clearly dominant components, the spectrum has significantly expanded, indicating the complexity of the ongoing process. Additionally, the control algorithm was equipped with a safeguard that prevented material from being blown out of the apparatus by restricting the airflow upon reaching a critical threshold. It was observed that on the steady states, the grey level tends to float around the average value. Therefore, a high-pass filter was applied to the original greyscale signal to eliminate the artifacts coming from the camera operation. Based on the Discrete Fourier Transform (DFT) given in the following manner: Xk=∑ N−1 n=0 xne−i2 π kn N,k=0,⋯,N−1 Where Xk is signal, xn is the power of components with different frequencies governed by e−i2 π kn N. DFT is a transformation that converts a signal from its original time domain to a representation in the frequency domain, however, computing directly from the definition is numerically inefficient. Therefore, this study used a Fast Fourier Transform (FFT) to determine frequencies concealed within the greyscale signal, reflecting the fluidized bed’s behavior. FFT is an algorithm that computes the DFT with lower computational complexity; hence, it is helpful in potential real-time applications. The sampling frequency used is 50 Hz, corresponding to a time of 20 ms. This frequency is sufficient to analyze all phenomena in the apparatus. In particular, according to the Shanon-Kotielnikov theorem [48], also called the Nyquist-Shannon Theorem [49]The highest frequency of change possible to capture is 25 Hz, as can be observed in Figs. 15-18, where the relevant range is up to 5 Hz. Anything above that is an artefact. It, therefore, shows that the sampling frequency used is Fig. 12. Comparison between measured pressure drop (blue line) and ideal pressure drop. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 13. Representative ROI (yellow) and the average grey level over gas flux. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) S. Anweiler et al. Measurement 255 (2025) 118046 9