A SOFT APPROACH SOFT SENSOR TECHNOLOGY FOR EXTRUSION AND OPPORTUNITIES FOR MONITORING, CONTROL AND FAULT DIAGNOSTICS

Transcription

1 A SOFT APPROACH SOFT SENSOR TECHNOLOGY FOR EXTRUSION AND OPPORTUNITIES FOR MONITORING, CONTROL AND FAULT DIAGNOSTICS M. McAfee 1 *, S.Thompson 2 1 Queen s Univ. Belfast. m.mcafee@qub.ac.uk; 2 Queen s Univ. Belfast. steve.thompson@qub.ac.uk This paper highlights a novel technique for monitoring viscosity in polymer extrusion. The device represents a noninvasive technique based on Soft Sensor technology; involving sophisticated process modelling and the integration of available on-line data to correct and adjust the model in response to errors and disturbances. The Soft Sensor measurements show excellent performance relative to a rheometric die; accurately tracking fluctuations in the bulk viscosity of the melt at the die due to changing operating conditions and changes in feed material in real-time. The potential to detect changes in feed material properties and to update model parameters accordingly is explored, representing an exciting development for implementation of advanced control schemes to continually optimise the operating conditions to achieve higher quality tolerances, reduce set-up and downtime and consequently reduce energy and material wastage. The technology enables a much more holistic approach to optimisation of settings, disturbance rejection and self-tuning ability than previously attempted in extrusion control. Introduction Extrusion is the fundamental polymer process; inherent to the production of the vast majority of polymer and composite products. Unfortunately, it is an unpredictable process and highly prone to disturbances. Historically, long set-up times have been required to identify suitable operating conditions to achieve satisfactory product quality. Considerable energy and raw material is wasted during change-over and start-up, and difficulty in identifying and responding to process disturbances during a production a run often results in off-specification product and further downtime. Trends towards co-extrusion (requiring machines to handle broad material and melt throughput ranges), non-homogeneous starting materials (e.g. recyclate), and an ever-widening range of materials available, further demand greater flexibility in process control. The use of polymers in many high-end applications means that quality specifications for extruded products are often critical. Dimensional tolerances, functional properties and surface finish are subject to increasingly stringent demands. However, due to instabilities inherent in polymer extrusion, achieving precision tolerances can be extremely challenging in practice. The delivery of a fully plasticized, homogenous melt, as characterized by a consistent melt viscosity, is paramount in order to prevent many defects. Existing control schemes for extrusion attempt to regulate the viscosity indirectly through control of the melt temperature/pressure as these parameters are much easier to monitor than viscosity itself. A major shortcoming of temperature and pressure control is that these variables are not directly correlated to performance or quality indicators in extrusion. If the properties of the feed material vary then a constant melt temperature is not synonymous with steady flow and actually conflicts with the requirement of constant pressure. There are therefore many advantages in measuring viscosity directly. This would allow clear detection of the homogeneity of the melt and furthermore would prove useful to producers in identifying a viscosity range corresponding to optimum product quality. Unfortunately, in-process viscosity monitoring is difficult to achieve. Side-stream rheometers (usually referred to in the industry as on-line rheometers) are commercially available to measure the in-process melt viscosity; these instruments typically involve a gear pump to draw off a side stream of polymer melt from the extruder barrel for continuous sampling. This sample is fed through a narrow capillary and the viscosity is derived from the pressure drop along the capillary. However these instruments are associated with a significant measurement lag and distortion of the melt stream [1]. In-line instruments provide an alternative to side-stream rheometers. These are located between the extruder screw and the die and incorporate the entire melt stream for sampling. The use of pressure drop measurements along an in-line capillary or slit die to determine the viscosity has been investigated by many authors e.g. [2]-[5]. However, such instruments require small die cross-sections rendering them impractical in large-scale production. Dielectric measurements have also been used to investigate mechanical viscosity in polymer melts [6], however at present this technology is only capable of measuring viscosity over a very small cross-section and has a lag in the order of several minutes. This work highlights a new concept in viscosity monitoring for control of polymer extrusion. A Soft Sensor technique is described whereby viscosity is tracked via inferential modelling of more readily available process measurements. Soft Sensor Design The viscosity of the melt at the exit of an extruder may be estimated as function of the shear rate and temperatures to which the polymer is subject as a result of the screw speed and barrel temperature settings. Such a model will be

2 specific to the properties of a particular material. The drawback of such a model is that it is open-loop in nature and will suffer in accuracy due to modelling errors and disturbances in the process. If the feed properties change, such as on the addition of a new batch of material, the model will no longer accurately describe the viscosity of the melt at the die, and as such it cannot be used as an indicator for controlling process disturbances. An alternative approach is to consider the effect of the melt viscosity on measurable extruder variables such as the torque exerted on the screw and the extruder barrel pressure. The relationships between these parameters depend on the extruder geometry, the die restriction, the frictional coefficient of the screw and barrel, and so on. In this Soft Sensor strategy, both of these approaches are combined to develop a robust and accurate viscosity indicator. Firstly, an open-loop model based on the material properties is used to obtain a viscosity estimate ( Prediction Model ); this predicted viscosity is then input to a second model which will estimate the resulting pressure/torque as a function of the melt viscosity ( Feedback Model ). These estimated values can then be compared against actual plant measurements and the error signal used as feedback into the prediction model to correct errors. A schematic of the proposed strategy is given by Figure 1. Inputs (N, T1,T2,..Tn) Extruder Plant Outputs (P,τ) N Prediction Model η Feedback Model - + error k N = S crew speed Ti = Temp in barrel zone i η = Viscosity τ = Screw torque/ motor power Figure 1. Structure of Soft Sensor The Feedback model is obviously critical to the accuracy of the Soft Sensor as it will drive the viscosity estimates such that the predicted extruder outputs match the actual plant measurements. The accuracy of the predicted model is less critical as it will be corrected by the feedback mechanism. This means that when the feed material properties change, resulting in inaccuracy of the predicted viscosity estimates, the errors will be corrected by the feedback mechanism giving the system viscosity tracking ability. The Prediction model may be based on the temperature and shear rate of the melt using a standard rheological model of the material if the relevant material properties are known (for example from laboratory tests). This is a suitable approach where the main objective of the soft sensor is as a device for monitoring the viscosity. Alternatively, where the main objective is to control the viscosity through manipulation of the extruder operating conditions, a dynamic model relating the extruder inputs to the output viscosity is a key requirement and is generally obtained from plant testing. The development of the Feedback model and alternative approaches to obtaining a Prediction model are outlined below. Experimental In order to generate and test the individual models and the Soft Sensor as a whole, plant data was obtained from trials on a Killion KTS-100 laboratory single-screw extruder. The extruder barrel is made up of three heating zones (solid feed, melting and melt conveying) which are controlled by Eurotherm 808 PID controllers. The plant was instrumented with a strain gauge type pressure transducer at the barrel exit and a Hioki /21 digital power meter to monitor the power consumption and current drawn by the motor driving the screw. An in-line rheometer die was fitted to the end of the extruder for measurement of viscosity; this incorporates three pressure transducers to calculate the pressure drop along the die length. Design and testing of this instrument is described in previous work [1], where it was noted that two of the pressure sensors suffered from offset errors. This was attributed to damage caused by repeated cycles of cooling and hardening of polymer in the transducer tappings between test runs, and is unfortunately an unforeseen feature of the die design. However, the sensitivity and response of the readings were unaffected, and as detection of fluctuation in viscosity is the primary aim here, uncertainty in the absolute value of viscosity was deemed acceptable. Two materials were used to investigate the development of models for the proposed Soft Sensor. Both were Low Density Polyethylene (LDPE) polymers of different grades, Exxon LD159AC (referred to as PE1 from this point) and Dow 300E (PE2). System Identification tests were carried out on the plant for the generation of data to use in model development and testing of the sensor. The inputs of interest; Screw Speed, N; set-point temperature in solid feed zone, T1; set-point temperature in melting zone, T2; and set-point temperature in melt conveying zone, T3, were excited by a

3 Gaussian input sequence. The sequence was executed in a random walk algorithm such that a wide operating range was covered whereas consecutive input changes were within practical operating limits. Barrel temperatures were varied by ±20 o C from the standard operating profile, while the screw speed was varied between 30 and 105rpm. The output variable measurements, motor power, E, pressure, P, and viscosity, η were captured at a rate of 10Hz and smoothed over every ten points resulting in a data sample rate of 1Hz. The system inputs and outputs are summarized in Figure 2. T1 T2 T3 N D.C. Mot o r 1 2 Extruder Zones 3 In-Line Rheometer η M E = M P Figure 2. Extrusion system variables Three data sets were produced for each material, two were used in training of models and one set remained unseen for validation purposes. Development of Feedback Model The feedback model is paramount to the success of the Soft Sensor in tracking viscosity and is required to be valid despite changes in the feed material or other process disturbances such as melting instability. Hence, this model is not related to specific material properties but rather on fundamental physical relationships which are a function of the machine design. For example, the build-up of back pressure in the extruder is a function both of the throughput rate of material and the melt viscosity. Maddock [7] proposed that this could be approximated by the Poiseuille equation: P = β Q η (1) where β = die resistance, Q= volumetric throughput. As Q was found to be directly proportional to screw speed for the plant and material used in this work, under these conditions the relationship would be: P = knη (2) where k is a constant dependent on extruder and die design. Motor power on the other hand is a function of the screw speed and torque, E = NT τ (3) Where T τ = torque The motor power constitutes an integral measurement of forces across the entire process as it is a function of the total shear stress acting on the barrel. It is subject to forces in the solids conveying zone as well as the melt viscosity along the melting and conveying zone. Hence it is not the most suitable indicator of melt viscosity at the die but it can indicate disturbances in the system such as feeding instability; fluctuations in channel fill; or jamming of an incompletely melted solid plug in the converging channel region at the end of the screw. As a much greater correlation exists between viscosity and pressure than between viscosity and motor power, it follows that prediction of pressure is a more appropriate feedback mechanism. However, the Poiseuille relationship is only theoretically valid for Newtonian fluids and applies to laminar flow in a pipe. The conditions in extrusion of polymer melts are quite different. Polymers are highly non-newtonian; the flow is unlikely to be laminar subsequent to the screw rotation and convergence in the die; and the pressure at this point is subject to transients in rate and flow. Elastic properties of the material may induce normal stresses due to converging and turbulent flow, also affecting the pressure. Disturbances such as blocking of the filter screen positioned between the barrel exit and the die will also affect the relationship. As the ability to capture these complex dynamic disturbances is required, a semi-empirical or grey-box approach to obtaining a dynamic Feedback model was adopted. This involves specifying a term pool of fundamental relationships based on physical mechanisms in the process. In this case terms were based on the coupling of screw speed and viscosity as per the poiseuille relationship but with additional terms to capture more complex phenomena: where, k n = constant. (i)n k1 (ii)η k2 (iii)e k3 (iv) N k4.η k5 (v) N k6.e k7 (vi) η k8.e k9 (vii) N k10.η k11.e k12

4 A Genetic Algorithm (GA) operation is then carried out to produce a NARX (Nonlinear Auto-Regressive with exogenous input) model to fit the plant data. The components of the NARX model are comprised of a time series expansion of the optimum selection of term pool elements. (More details on the algorithm may be found in [8]). The following models for pressure at time t were developed independently for each material and tested on the unseen validation data. The models and the root mean squared (rms) error are shown in equations (4) and (5): PE1: P = Pt x10 Et 3 N t 1 η + 3.9x10 3 t 4 t 1 t E N η (4) t t 3 Error = 0.67% PE2: P = P t x10 Et 4 Nt 1 η + 2.4x10 2 t 5 t 2 t E N η (5) t t 5 Error = 0.45% Apart from the constant term, the models are extremely similar in structure and parameters for the two materials tested. To illustrate the similarity of the identified relationships for the different materials, the performance of the PE1 model on PE2 data is shown in Figure 3. It can be seen that there is an offset error which is attributed to the problem of transducer calibration; removal of the offset value reduces the model error to 0.56%. Figure 3. Percent error of PE1 Feedback model on unseen PE2 data. The time series expansion of the model and the inclusion of the motor power term in the equation enable extremely accurate pressure predictions. The fact that almost identical low-order models were identified for two different grades of material, suggests that the model is likely to be to a large extent a signature of the machine and apply fairly generally to many polymer materials in normal operation. Development of Prediction Model As stated above, the Prediction model is required to estimate the melt viscosity based on the inputs to the process and is a function of the material properties and the physical processes occurring in the extruder. This may be based on a rheological model of the material but for control purposes a dynamic-input model relating the extruder inputs to the viscosity is more relevant. Dynamic modelling of extrusion is complex; computational models based on mass flow and heat transfer have been developed, however these models require time-intensive solution and involve material parameters which may not be well defined; they are therefore unable to capture inherent differences in material properties between different grades of a particular polymer. Furthermore, empirical modelling techniques are insufficient to capture the non-linearity of the process [9-12] or tend to be highly complex and specific to the training data in the case of non-linear identification techniques such as NARX, Artificial Neural Networks etc. In order to address these issues the semi-physical, grey-box system identification technique outlined above was also applied to generate the Prediction model. Basic model terms were proposed based on the power law relationship between viscosity and shear rate and also on the temperature dependence of viscosity where heat is generated both from the barrel heaters and the mechanical working of the polymer by the screw. The technique is detailed in previous work [8] where the optimal models for PE1 and PE2 are given by (6) and (7); the model performance on unseen validation data is shown in Figure 4 (a) and (b) where the r.m.s. errors are 0.95% and 0.79% respectively. PE1: η = 2.7x η 1.3x (6) ( 9) N( t 1) 3.9x 10 T ( t 2) 4.8x 10 t + + T ( t 40 ( t) )

5 PE2: x η = 7.7x η 7.5x10 ( 2) N( t 1) 2.2x10 T1( t 15) 4.5x10 t + + T3 (7) ( t 45 ( t) ) (a) Figure 4. Performance of (a) PE1 and (b) PE2 Prediction models on unseen data In this case it is clear that the Prediction models for each material are quite different and will not apply more generally to different materials. In order to determine if the feedback structure can indeed compensate for errors in the prediction model for changing materials, on-line testing of the system was carried out. Plant Testing The Soft Sensor algorithm was implemented in real-time on the aforementioned plant using LabVIEW software. In keeping with the preprocessing applied for model development, all inputs were sampled at 10Hz and smoothed over every ten points for execution of the algorithm at a rate of 1Hz. The in-line rheometer was also fitted during these tests for comparison with the Soft Sensor measurements. The Prediction and Feedback models developed for the PE2 material were used in the implementation. Initially the constant coefficient of the Feedback model was adjusted to eliminate offset between the measured and predicted pressure values during steady-state operation. The Feedback model was thus: P (8) t = + Pt 1 + x Et 4 N t 1 η + x 2 t 5 t 2 t E N ηt 5 No other adjustments were made. Initially the extruder was run with PE2 at 80rpm and a number of screw speed step changes were made to the system as shown in Figure 5 (a). The Soft Sensor takes about 30s to come to steady-state from initialization but subsequently responds extremely quickly and accurately to the screw speed changes. The system was then run steadily at a screw speed of 80rpm when a different LDPE which has not been modelled of lower viscosity was added to the feed hopper. This was allowed to purge out the previous material before reintroducing PE2 to the hopper. The responses of both the in-line rheometer and the Soft Sensor to these changes in feed material are shown in Figure 5 (b). (b) Low viscosity LDPE added PE2 reintroduced Time (s) (a) (b) Figure 5. In-line rheometer and Soft Sensor viscosity measurements in response to (a) screw speed changes (b) changes in feed material.

6 It can be seen that the Soft Sensor viscosity predictions correspond extremely well with the measurements taken by the in-line rheometer. The Soft Sensor eliminates much of the noise present in the pressure transducers, giving rise to a smoother signal. The values do lag the rheometer measurements slightly; this is in the order of a few seconds which is insignificant in terms of the overall dynamics of a change in feed material. Diagnostics and on-line updating of models As well as tracking of melt viscosity, it is desirable to be able to detect a disturbance such as a change in the feed material and to use the Feedback model to update model parameters accordingly. In order to demonstrate how this might be achieved, a rheological model was used to provide the viscosity predictions, such that the updating of the parameters can be used to infer the differences in the rheology of the new feed material. An often used rheological model, appropriate for polyethylene, is of the form: b( T T0 ) n 1 η = m0e & γ (9) where m 0 = consistency index at some reference temperature T 0 ; γ& =shear rate; n = shear-thinning index of the material and b is a constant. The parameters m 0, b and n will vary from material to material. In order to facilitate on-line updating of these parameters, equation (5) is converted to a linear-in-the-parameters model by taking natural logarithms: lnη = ln m 0 b( T T0 ) + ( n 1) ln & γ (10) this model is in the form: y = a + a x + a (11) x 2 where, y = lnη; a 0 = lnm 0 ; a 1 = -b; x 1 = (T-T 0 ); a 2 = n-1; x 2 = lnγ&, and as such, parameter fitting can be achieved by linear regression techniques. This can be implemented on-line using a Recursive Least Squares (RLS) algorithm, where at each time step the corrected viscosity prediction (achieved from the feedback error) is used to update the model parameters. The on-line updating sequence in the Soft Sensor is represented by Figure 6. initial values Predict viscosity using parameter values Input to Feedback model to predict pressure Determine pressure error and multiply by K Add to viscosity prediction to give corrected viscosity Take log of new viscosity and execute RLS to update parameters Figure 6. On-line updating strategy Initial parameter values could be obtained from off-line testing in a laboratory capillary rheometer, however due to the calibration errors of the pressure transducers in this case, these values did not reflect the actual data recorded by the inline rheometer. For this reason, initial parameters were identified using the in-line rheometer itself, where the above rheological model was fitted to plant data. The temperature in the final barrel zone was used to indicate the temperature at the barrel exit and a median value of C was taken as T 0. Approximate values of m 0 = 3860, b =0.0340, and n = 0.57 were obtained for PE1. The on-line updating sequence above was then applied to the unseen data generated during the above experimental trials. The pressure error signal and the Soft Sensor viscosity estimates obtained over the data set are shown in Figure 7 (a) and (b) where the error signal gain, K, was set at 5. (a) (b) Figure 7 (a) Pressure Error and (b) Viscosity results for on-line updating of Soft Sensor on unseen PE1 data

7 Figure 7 (b) shows that this model does not fit the plant data quite as well as the identified model in equation (6). This is expected as errors are introduced in the rheological model by using the temperature of the barrel at the extruder exit which does not give a true indication of melt temperature. It is interesting to examine how the values of parameters a 0, a 1 and a 3 vary over the data sequence: (a) (b) (c) Figure 8. Variation in values of (a) a 0 (b) a 1 (c) a 2 during on-line updating of PE1 rheological predictive model The parameter values stabilize over about 15 minutes to give final values of m 0 = 3900; b= and n = The ability to adapt to a change in feed material was investigated by running the same algorithm on the plant data for PE2 where the initial parameter values are unchanged from the final values obtained for PE1. This simulates an abrupt change in feed material. The pressure error value immediately jumped to 1.15MPa, this is 10 times the magnitude of the error when running with the same material and is a clear indicator that a material feed change occurred. In order to adapt the viscosity estimates to the new material quickly, the pressure error gain K is increased to 75 and a forgetting factor is introduced to the RLS algorithm to weight recent data more heavily. The resulting pressure error signal and a comparison of the Soft Sensor viscosity values and the measured values are shown in Figure 9. (a) (b) Figure 9 (a) Pressure Error and (b) Viscosity results for on-line updating of Soft Sensor on new material It can be seen that the Soft Sensor estimates converge towards the actual plant values after about ten minutes. Examining the parameter values (Figure 10) we see that with the exception of b, they do not manage to converge over the 35 minute data set. The relatively high gain, although necessary to adapt the Soft Sensor estimates, induces instability in the on-line updating procedure. It can be seen that over the first ten to twelve minutes, the parameters vary widely and are often physically unfeasible, for example a 1 should be in the region C -1 [13], and a 2 should be in the region 0 1 for a shear thinning polymer such as LDPE. We can see that towards the end of the data set m 0 is converging to 1100, b and n is in the range If the in-line rheometer measurements are used for on-line updating rather than the Soft Sensor feedback, convergence to m 0 = 2580, b 0 = and n = 0.59 is achieved within 10 minutes. Therefore further work is required to improve the on-line updating algorithm to achieve comparable performance using the Soft Sensor feedback. This will require filtering of the pressure signal to prevent instability due to amplification of spurious noise in the error signal; consideration of using a dynamic gain K, such that it is large when

8 the pressure error is high and reduces when the error decreases to improve stability. Furthermore, the RLS algorithm used here, while simple to implement has many disadvantages; improvement on the updating algorithm could be achieved by using a constrained optimization algorithm where the parameter values are limited to a physically feasible range and by only updating parameters where they lead to a reduction in the pressure error signal. (a) (b) (c) Figure 10. Variation in values of (a) a 0 (b) a 1 (c) a 2 during on-line updating of rheological predictive model for new material Such enhancements to the on-line updating procedure to track rheological parameters would be extremely useful for quality control purposes and for diagnosis of feed material properties. An alternative approach to on-line updating would be to use the predictive dynamic model and Soft Sensor feedback structure in a Model Predictive Control scheme which enables multi-objective optimization of the process. The fundamental idea in predictive control is utilising a model to predict the process response to a given sequence of inputs generated by the controller to the process. The goal is to find the input sequences which yield the optimal response with respect to one or more criteria (e.g. minimising viscosity fluctuation, minimising energy consumption). An optimiser is incorporated into the control system to search for the best actuation sequences. The Soft Sensor feedback can thus be used to adapt the model parameters on-line to changing feed material properties or process conditions. Clearly further work is required before this can be successfully achieved. Conclusions The proposed Soft Sensor structure has been shown to be simple to implement and is capable of accurate and robust tracking of polymer viscosity in extrusion. The success of the device is due to the identification of a Feedback model which captures the fundamental physical relationships between the polymer viscosity and extruder outputs of pressure and torque. A novel, semi-empirical modelling technique was applied which resulted in a highly accurate model which is independent of material properties and is effectively a signature of the machine set-up. However, in order to operate a Predictive model of polymer viscosity is also required. This model is related to the material properties and therefore differs from material to material. As clearly demonstrated in this work, this model does not have to be accurate to facilitate convergence to the correct viscosity value over time. The potential of the Soft Sensor technique for identification of feed material variations and on-line updating of model parameters has been indicated. While further work is required before this can be utilized in the implementation of advanced control schemes, there is clear potential to achieve higher quality tolerances, reduce set-up and downtime and consequently reduce energy and material wastage through adaptive optimisation of the operating conditions. The technology enables a much more holistic approach to optimisation of settings, disturbance rejection and self-tuning ability than previously attempted in extrusion control. Techniques developed in this programme are likely to be applicable not only in conventional extrusion but also in twin-screw processes, reactive extrusion and injection and blow moulding. References 1. M.McAfee, Trans. Inst. Meas. Cont. 2006, 28, C. Ross; R. Molloy; S. Chen; Proc. Annual Technical Conference - ANTEC, 1990, Society of Plastics Engineers, D.J. Fleming, PhD Thesis, University of Bradford, C. Rauwendaal; F. Fernandez, Polym. Eng. Sci., 1985, 25, 765

9 5. M. Padmanabhan; M. Bhattacharya, Rheologica Acta, 1994, 33, M. McBrearty; S. Perusich, Proc. Annual Technical Conference - ANTEC, 1998, Society of Plastics Engineers B.H. Maddock, SPE Journal, 1964, 20, M. McAfee; S. Thompson. Proc. Instn. Mech. Engrs.,, Part I: J. Systems and Control, [In Press]. 9. A.K. Kochhar; J. Parnaby, Proc. Instn. Mech. Engrs., 1978, 192, S. Dormeier, Proc. Annual Technical Conference - ANTEC 1979, Society of Plastics Engineers. 11. S. Chiu; C. Lin, J. Polymer Research, 1998, 5, F. Previdi; S.M. Savaresi; Panarotto, A. Control Engineering Practice, 2006, 14, Ferry, J.D., Viscoelastic properties of polymers. Wiley, New York