Implementation of a control loop for a continuous powder mixing process X.J. Zhao a, C. Gatumel a, J.L. Dirion a, H. Berthiaux a, M.

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1 Implementation of a control loop for a continuous powder mixing process X.J. Zhao a, C. Gatumel a, J.L. Dirion a, H. Berthiaux a, M. Cabassud b a Université de Toulouse ; Mines Albi ; UMR CNRS 5302 ; Centre RAPSODEE, Campus Jarlard, F Albi Cedex 09, France b Laboratoire de Génie Chimique, UMR 5503 CNRS/INPT/UPS, 5 rue P.Talabot, Toulouse Cedex 01, France 1. Introduction Powder mixing is a crucial unit operation in a variety of industrial sectors like the pharmaceuticals, food, cement and polymer manufacturing. The ultimate goal of this operation is to obtain a homogenous mixture of ingredients distributed among each other as uniformly as possible. Powder mixing can be carried out either in continuous or batch mode. Continuous mixing process is considered as an advantageous choice in many of these industries. The main advantages are smaller equipment size, reduced process inventory and less solid handling such as filling and emptying of mixers. However, continuous process has some limitations. The pharmaceutical industry, due to the strict quality constraints on expensive products, has so far remained largely focused on batch manufacturing. Recent researches on the feasibility of continuous mixing for pharmaceutical powder illustrated different process constraints, such as mixture quality control, time-stability of this quality, sensitivity of the process to disturbances. All of these indicate a control strategy for the continuous powder mixing needs to be developed for stabilizing the process efficiently and enhancing productivity. However, so far, few studies have been directed at developing a control strategy because of the lack of sufficient understanding of process behavior. Prior to this, it is important to know where the process can be controlled and what parameters govern the process. In other words, for an effective implementation of continuous powder mixing manufacturing, it requires (1) the identification of the critical factors, (2) the on-line and real-time measurement of mixing performance and (3) a control strategy based on a single variable or multiple variables. Consequently, the effects of different process and design parameters on the powder flow and mixing behavior in the continuous mixers were also studied. Most of these studies did attempt to draw correlation between the mixing performance and various operating parameters. In addition, to assess the homogeneity of powder mixtures, different online and real-time monitoring techniques for continuous mixing have been recently developed, including image analysis, near infrared (NIR) and Raman spectroscopy, and so on. Powder mixers can be classified into two main categories: convective blenders (e.g., ribbon or screw cone blenders) and tumbling blenders (e.g., double-cone or V-mixers). The convective mixers, which generally consist of a static shell in which the powder is circulated around by rotating blades, paddles or screws, are commonly used in the food and pharmaceutical industries. In contrast to enclosed tumbler mixers, convective mixers can be readily designed to accommodate continuous operation. Most of the existing technologies for continuous powder mixing are of the convective type. The performance of several convective continuous mixers has been investigated for powders with different flow properties. Current researches have been mainly focused on the effects of different geometric designs (mixer size, mixer angle, impeller types, etc.) and operating conditions (feed rate, impeller speed, etc.) on the mixing performance. In recent research literature, the commercial mixers utilized are mainly manufactured by GEA in England and Gericke in Germany. The continuous mixers

2 provided by the first manufacturer GEA were studied in three different sizes: a mixer of 0.74 m long and 0.15 m radius [1], a mixer of 0.31 m long and 0.05 m radius [2], and a mixer of 0.24 m long and m radius [3]. Two different sizes of the Gericke continuous mixers were examined: a GCM 250 continuous mixer of 0.3 m long and 0.1 m in diameter [4,5,6,7], and a GCM 500 of 0.5 m long and 0.2 m in diameter [8,9,10]. The influences of different types of stirrer on the hold-up and quality of mixtures have been examined [1,8], demonstrating that blade design has a significant effect on altering flow patterns, thereby affecting mixing performance. Experimental investigations using PEPT (Positron Emission Particle Tracking), relevant to pharmaceutical powder, have provided better physical understanding of the influence of operating parameters on the flow behavior within a continuous mixer [3]. The residence time distribution (RTD) and powder hold-up measurement have been defined to characterize the flow behavior in a continuous mixer studied [7]. And the rotational speed was found to be the most significant process parameter affecting mixing performance. The theory of Markov chains has been applied [11,12] to model and simulate the residence time distribution (RTD) obtained from tracer experiments in this powder continuous mixer. Recently, a Markov chain model has been reported by Ammarcha et al. [10] to describe the macroscopic behavior of bulk powder flow in this continuous mixer during transitory regimes in terms of hold-up weight and outflow rate with operating conditions. This paper is concerned with the simulation and experimental control of the powder mixing process. The aim of the present work is as follows: To design a straightforward control strategy, including selection of the controlled variables and design of the control structure. To assess the performance of the proposed controllers via a set of simulation and experimental control studies. All of the above provide a basic review of control of this process and they are useful for the future research on this topic. 2. Process description and modeling 2.1 Experimental setting The mixture studied here is made of two powder ingredients: fine-grain couscous colored in black (component A) and medium-grain couscous (component B). The schematic diagram of experimental set-up is shown in Fig. 1(a). It mainly consists of two gravimetric feeders, a continuous mixer, and a real-time monitoring of concentration of powder mixture using on-line image analysis at the outlet of the mixer. Each gravimetric feeder consists of a hopper, a feeding device (screw) and a weight system (balance). The mixer used in this study is a pilot-scale Gericke GCM 500 continuous mixer as shown in Fig. 1(b). A detailed description can also be found [12]. The stirrer in Fig. 1(c) installed in the mixer consists of a rectangular frame with five blades on each long side and two blades at each end, which ensure radial particle dispersion inside the mixer, and an internal screw that promotes the powder s axial transport to transfer the material out of the mixer. The feeders and mixer engines are controlled by an automated system linking to a Personal Computer (PC). At the mixer outlet, a powder layer of constant width and thickness is continuously filmed by a numerical camera (14 images per second). The mixture layer is simultaneously analyzed in surface and determined in mass by the proper calibration, using the Labview software package. All this data permit to characterize the homogeneity of the powder mixture on-line by successive windows, where each window consists of n consecutive images (or samples). For each packet (or window) of n samples, the mean X,

3 the standard deviation σ and the relative standard deviation (RSD) can be defined by the following Eq. (1), Eq. (2) and Eq. (3). X 1 = n k x i n i= 1 (1) σ k = 1 n n i= 1 ( x X ) i k 2 (2) RSD k = σ k X k (3) Where x i is the concentration of each sample in key component, k is the order number of the window acquired at the time t k. In this study, n is defined as 14. Fig. 1. Experimental set-up: (a) schematic of the studied continuous mixing system, (b) pilot-scale continuous mixer Gericke, (c) stirrer device. 2.2 Model simulation This continuous mixer is modeled via a Markov chain model of which the transition probabilities depend on the local holdup in the mixer, and the hold-up weight is determined by feed rates and rotational speed of the stirrer in the mixer. The mixer model has also been experimentally validated and reported [13]. In this study, a simulator based on the proposed Markov chain model is programmed using Labview. This simulator can be used to predict mixing behavior of two powders input mass flow rates, Q A and Q B, in the continuous mixer under a specified range of operating conditions. In other words, this modeling relates the output concentration x to the inputs, such as Q A, Q B, and the rotational speed of the mobile N m, which is expressed by the frequency of the motor N. The conversion between N m and N has been done by empirical calibration: N m (rpm) = 2.6N(Hz). Therefore, the simulator can be presented by a simplified function as:

4 x k = f (Q A,k,Q B,k, N k, k t) (4) In practice, the rotation speed N depends on the operating voltage of the motor E. A linear relationship is described by Eq. (5), where E is the provided voltage in volts. N= (E ) / (5) 3. Control design As a first step of control strategy, a single-input-single-output (SISO) architecture was considered. The proportional-integral-derivation controller (PID controller) is chosen because of its robustness and simplicity in tuning parameters. A block diagram of the closed-loop control system is show in Fig. 2. It mainly consists of a setpoint (SP), a process variable (PV), a manipulated variable (MV) as the controller output and a disturbance input, where t is the sampling time. In this control study, the mixture quality is taken as PV, which is defined as the average output concentration of the powder mixture X. The disturbance input is represented by the input mass flow rate fluctuation, where the feeding fluctuation investigated is so high that it can t be ignored. The rotational speed (N) should have been as MV, since N is a most important factor influencing mixing performance without perturbations in the feeding system. It is must be stated here that the operating voltage (E) is used as MV and it is directly adjusted by the PID controller in order to regulate the rotation speed N. Fig. 2. Closed-loop PID control scheme of the continuous powder mixing process. The controller is designed to minimize the time to reach and maintain within the new setpoint when there is a step change in setpoint generated by a step change of one powder feed rate. The PID Control Toolkit in Labview is applied, where MV(k) is computed as follows: e(k)= SP PV(k) k 1 e( i) + e( i 1) T d MV ( k) = KC e( k) + t ( PV ( k) PV ( k 1)) Ti i= 1 2 t (6) (7) where e is the error between the desired setpoint and the measured process variable, K c is the controller gain, T i is the integral time in minutes, T d is the derivative time in minutes, t is the sampling period, and k is the current sample. In this work, the sampling period t is set to 1 second. The actual controller output is limited to the range specified for control output. A series of tests in

5 the pilot mixer demonstrate that the stirrer rotational speed N can be adjusted between 25 and 55 Hz, which means the operating voltage E is between 2.94 and 6.61Volts. 4. Results and discussion To demonstrate the effectiveness of the proposed control scheme, both simulation and experimental results are presented. The average concentration of component A (represented by X) at the outlet of the mixer is kept at 50% operating with Q A = Q B = 3.5 g/s and N = 30 Hz in the initial stage (t = 0 second). The setpoint (SP) is changed from 50% to the new value 63.16% as a result of a step change in Q A from 3.5 to 6 g/s. In the simulation study, it is supposed that two powders are fed under ideal feeding conditions. Whereas, in the experimental research as presented in Fig. 3, the measured feed rate Q A is changed from 3.5 to 6 g/s and then remained at 6 g/s with random fluctuations and the measured feed rate Q B is maintained at 3.5 g/s with random fluctuations, although the feeders are continuously controlled based on the principle of loss-in-weight. Fig. 3. Experimental response for a step change to Q A of the feeding system. The PID control simulation is performed in Labview by using the Markov chain Model described in Section 2. The PID parameters are: K c = 35, T i = 0.08, T d = 0.008, found from the Labview PID Autotuning toolkit with fast response. The sample period Δt for the PID controller is set to 1 second. The behavior of the continuous mixer is simulated respectively without and with the proposed PID closed-loop control. As well, experimental studies are carried out for two cases. Simulation and experimental closed-loop response curves of both the process variable X (or the average concentration of component A) and the indirect manipulated variable N (or the rotational speed) are shown in Fig. 4 and Fig. 5, comparing to the corresponding results without PID control, which means the rotational speed N will remain constant at its initial value 30 Hz.

6 Fig. 4. Simulation results without and with PID closed-loop control: (a) Evolution of the process variable X, (b) Evolution of the indirect manipulated variable N. As shown in Fig. 4(a), compared with the simulation result without PID control, the simulated PID control allows a faster response of the process variable X at the beginning. This effect occurs due to a rapid rise of the indirect manipulated variable N demonstrated in Fig. 4(b). However, the following intense reduction of the rotation speed command leads to poor performance. The process variable X continues to increase but at a relatively slow rate, compared with that obtained when there is no change in the rotational speed N. The N varies rarely when X is very close to the setpoint. As the PID parameters have a great influence on the stability and performance of the control system, optimal

7 PID parameters may be found for slowing down the decreasing rate of the rotation speed command so as to keep its best performance. The PID parameters applied above is still not bad in control performance and they are used in the following experimental investigations. Fig. 5. Experimental results without and with PID closed-loop control: (a) Evolution of the process variable X, (b) Evolution of the indirect manipulated variable.

8 For the experimental validations, Fig. 5(a) shows the response of the average concentration X under the proposed PID control compared to that obtained without PID control. The PID control makes X attain around its new steppoint 63.16% after less than 20 seconds. Whereas, without PID control, for the average concentration X, there is a delay time of about 14 seconds before X starts to increase, and X is less than 63.16% when X trends to stabilize. All of these illustrates that the designed SISO closed-loop control algorithm is able to stabilize rapidly the controlled variable X. Fig. 5(b) shows that the indirect manipulated variable N rises quickly at the beginning and then declines rapidly, after that, it decreases slowly until it reaches its minimum value. The trend is roughly the same as that observed in simulation. Fig. 5 demonstrates the rise of X at the beginning is due to the increase of N, then the rapid decline of N causes X reduce to the value less than SP value, and finally X is returned around to the desired value until N varies slowly within 25 and 30 Hz. In conclusion, when there is a positive step change in Q A, an increase of the rotational speed at the beginning allows minimizing the time to reach the new desired value of the average concentration at the mixer outlet. The powder mixture is relatively stable although the rotational speed reduces to less than initial value. It is observed that the experimental results are somewhat different from the simulations. In the experiment, the controlled variable X is more dispersed and it reaches its new setpoint value faster. As it is mentioned above, theory (or ideal ) values are provided for two feed rates in simulation, while actual variability (or fluctuation) in the feed rate often contributes significantly to the variability of the final mixture [7]. It implies that all possible disturbances should be considered to ameliorate the existing modeling. Anyway, the simulated control here helps us to find rapidly the proper PID parameters avoiding a series of controller tuning in the pilot plant. Fig. 6. The relative standard deviation (RSD) observed experimentally As it is mentioned in Section 2, the homogeneity of the outlet mixture can also be characterized by the relative standard deviation (RSD), which is known as the coefficient of variability and commonly used in industry. Lower RSD values mean less variability between samples, which indicates better blend uniformity. Fig. 6 illustrates the experimental RSD curves for the case without PID control

9 and the case with PID control. It is can be seen that the RSD values vary within the range of 3% and 9%. In the pharmaceutical industry, it requires the RSD must be less than 6%. Therefore, to estimate the control effect on RSD, the percentage of points for RSD less than 6% can be quantified for each case: 49% obtained when there is no PID control and 69% obtained with PID control. It represents an improvement of 20% due to the proposed PID control. In conclusion, the regulation of the average concentration at the outlet allows minimizing slightly RSD on-line. To effectively optimize, the RSD should be taken as a process variable in further investigations on the regulation of the continuous mixer. 5. Conclusions A continuous powder mixing process consisting of two gravimetric feeders, a continuous mixer and an on-line analysis system for powder mixture at outlet of the mixer is recently studied and modeled by the theory of Markov chain. This work has demonstrated a closed-loop control design for this continuous powder mixing process, based on PID Control Toolkit in Labview software. This paper discussed the results obtained by both simulation and experimental implementation of PID controller. It demonstrates that the PID controller for adjusting the stirrer rotational speed N permits to regulate on-line the average concentration of the powder mixture at the mixer outlet when there is a step change in setpoint. From the experimental results, the proposed PID control was effective for the continuous mixer using a simple closed-loop control structure. However, it is noted that there is a little difference between real and simulated control. The Markov chain model for the mixer simulation should be optimized, because an efficient simulator will greatly benefit the process control design. On the other hand, the RSD is slightly regulated by the proposed control plan. It is interesting to study a control plan using RSD as the controlled variable or a more complicated control scheme in order to improve further the blender uniformity. Furthermore, the present work investigated the control when there is a step change in one powder feed rate at the mixer inlet. The proposed control will be examined in more cases including different fluctuations in feed rates of two powders. References [1] P.M. Portillo, M.G. Ierapetritou, F. Muzzio, Characterization of continuous convective powder mixing process, Powder Technology 182 (2008) [2] P.M. Portillo, M.G. Ierapetritou, F. Muzzio, Effects of rotation rate, mixing angle and cohesion in two continuous powder mixers A statistical approach, Powder Technology 194 (2009) [3] P.M. Portillo, A.U. Vanarase, A. Ingram, J.K. Seville, M.G. Ierapetritou, F. Muzzio, Investigation of the effect of impeller rotation rate, powder flow rate, and cohesion on powder flow behavior in a continuous blender using PEPT, Chemical Engineering Science 65 (2010) [4] Y. Gao, F. Muzzio, M. Ierapetritou, Characterization of feeder effects on continuous solid mixing using fourier series analysis, AIChE Journal 57 (2010) [5] A.U. Vanarase, M. Alcala, J.I. Jerez Rozo, F. Muzzio, R.J. Romanach, Real-time monitoring of drug concentration in a continuous powder mixing using NIR spectroscopy, Chemical Engineering Science 65 (2010)

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