DOI 10.1007/s10692-016-9745-y
Fibre Chemistry, Vol. 48, No. 1, May, 2016 (Russian Original No. 1, January-February, 2015)
CELLULOSE DIGESTION FOR CHEMICAL PROCESSING UNDER NOISY CONDITIONS: ROBUST CONTROL EXPERIENCE R. Z. Pen* and A. A. Polyutov**
UDC 519.6:676.16
An example of the potential for robust control of soluble cellulose production was proposed and illustrated.
Stable properties for both feedstocks and finished products represent a critical problem for the chemical fiber industry. Current mathematical modelling and optimization methods make effective control of industrial processes possible and reduce to a minimum deviations of properties from the required values under external destabilizing effects (noise). Robust control is one such method. The goal of the study was to demonstrate the robust control technique using digestion of soluble cellulose as an example. The developed algorithm was suitable for use at any subsequent stage of cellulose processing in the manufacturing of viscose chemical materials, e.g., threads and yarns. The situation where only a part of the independent variables (factors) affecting the process are controlling (X1, …, Xm) and another part is not controlling (Z1, …, Zn) is characteristic of industrial processes although both can be measured or identified. The first group of variables often characterizes the process regime parameters whereas the second group characterizes the properties of the processed feedstock. If the feedstock properties vary randomly for relatively short time periods (e.g., plant feedstock for cellulose production is supplied by different suppliers and is immediately sent to production), the technologist must choose a processing regime with some uncertainty and the choice is random in nature. The problem of process optimization in such instances can be meaningfully formulated and solved by robust control methods. The term “robustness” is used in control theory to designate the system stability to external effects. With respect to industrial processes, robust control addresses the retention of the product properties within given acceptable limits in the face of noise such as uncertainties and interference. The Taguchi method, named for its inventor and main ideologue, the Japanese professor Genichi Taguchi, is one direction of robust control that has earned global recognition because it is highly effective in various industrial sectors. The Taguchi method has now transformed into a broad section of applied statistics that borders quality-control methods and includes, in turn, dispersion and regression analytical methods, mathematical experiment theory, optimization, etc. [1]. A key point in the Taguchi method is the use of the signal-to-noise ratio (S/N) to characterize the process. Here, the change of a property of the manufactured product Y through the action of controlled factors X is called the signal; deviations of Y (characterized by the dispersion s2) because of the effects of uncontrolled factors Z, the noise. The S/N is maximized in order to satisfy the process robustness requirement. In practice, various functions of the S/N W that were introduced by Taguchi and successors and not the S/N are used as the optimization parameter. Input parameters Y and W as functions of variables X and Z are usually obtained as regression equations using mathematical experiment designing methods [2, 3]. Let us note two specifics of experiment designs. First, two designs must be selected. One varies variables X (design X matrix); the other, Z (Z matrix). The rows of these matrices are factorial coordinates of points in the corresponding design, i.e., Xiu and Zju values in each u-th *Siberian State Technological University; **Siberian Federal University, Krasnoyarsk; E-mail:
[email protected]. Translated from Khimicheskie Volokna, No. 1, pp. 80-82, January—February, 2016.
0015-0541/16/4801-0083© 2016 Springer Science+Business Media New York
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Table 1. Experimental Design and Results from Using It Blocks
X1 , °C
X2, min
X3, ° C
X4 , min
X5 , g/dm3
Z1 , %
Z 2, %
Y, DP
1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8
160 160 160 160 160 160 160 160 160 160 160 160 160 160 160 160 170 170 170 170 170 170 170 170 170 170 170 170 170 170 170 170
120 120 120 120 120 120 120 120 180 180 180 180 180 180 180 180 120 120 120 120 120 120 120 120 180 180 180 180 180 180 180 180
165 165 165 165 175 175 175 175 165 165 165 165 175 175 175 175 165 165 165 165 175 175 175 175 165 165 165 165 175 175 175 175
180 180 180 180 240 240 240 240 240 240 240 240 180 180 180 180 240 240 240 240 180 180 180 180 180 180 180 180 240 240 240 240
50 50 50 50 60 60 60 60 60 60 60 60 50 50 50 50 50 50 50 50 60 60 60 60 60 60 60 60 50 50 50 50
5 5 10 10 5 5 10 10 5 5 10 10 5 5 10 10 5 5 10 10 5 5 10 10 5 5 10 10 5 5 10 10
4 8 4 8 4 8 4 8 4 8 4 8 4 8 4 8 4 8 4 8 4 8 4 8 4 8 4 8 4 8 4 8
1020 1270 710 1040 560 810 260 540 680 960 440 710 950 890 1250 620 940 1210 660 970 1030 1290 690 970 1140 1400 850 1140 910 1200 610 900
WT
12.8
7.6
10.3
11.1
12.5
12.1
14.0
11.5
experiment (observation). The X matrix is called internal; Z matrix, external. The total experiment design is produced by the direct product X × Z. It includes all combinations of rows in these matrices. Second, two-level orthogonal first-order designs with a small number of experiments that is the minimum required to obtain unique evaluations of the principal effects are chosen most often in order to economize resources. This is especially critical in the first stages of a study with a large number of examined factors. The following problem is examined. A cellulose plant manufactures conifer prehydrolysis sulfate pulp intended for subsequent preparation of synthetic fibers. One of the important requirements for production of such a product is the maintenance of the degree of cellulose polymerization at a given level with minimal deviations from this level. The goal of the experiment was to find the cellulose digestion conditions that satisfy this requirement most fully. The controlled variables were five factors (their variation ranges in parentheses) X1, prehydrolysis temperature (160-170°C); X2, prehydrolysis duration (60-180 min); X3, sulfate pulping temperature (165-175°C); X4, digestion time (180-240 min); and X5, concentration of active base in the digestion solution (50-60 g Na2O/dm3). A small amount of deciduous wood in the conifer feedstock is allowed under the supply terms. Combined digestion produces from it cellulose with a lower degree of polymerization (DP). Furthermore, shredded feedstock contains fractions of non-uniform thickness, which also results in polydisperse cellulose because of non-uniform digestion. These are uncontrolled factors, the harmful effects of which must be eliminated if possible. Both factors are included in the experiment design. The quantity Z1 is the mass fraction of deciduous wood in the feedstock (5-10%); Z2, the mass fraction of unconditioned (thick) shredded feedstock (4-8%). Output parameter Y is the cellulose DP. The regulated value of this parameter is Yreg = 1200. The experiment was carried out under laboratory conditions. Statgraphics Centurion XVI, Design of Experiments (DOE) module, and Signal-to-Noise Ratio (Target Value) procedure were used for experiment designing and mathematical 84
processing of the results [4]. Matrix X is a fractional factorial experiment (FFE) of the 25–2 type; matrix Z, a total factorial experiment (TFE) of the 22 type. Table 1 presents the overall design X × Z with column Y filled with experimental results. All experiments were divided into eight blocks according to the number of rows in internal matrix X. Matrix Z, which is an external experiment design of two columns and four rows, is included in each block. The program computes separately for each block the averages of output parameter Y , their dispersions s2, the S/N Y 2 s 2 , and Taguchi functions
WT = – 10 lg ( Y 2 /s2). The WT values are given in the last column of Table 1. The function WT of variables X was approximated by the linear regression equation WT = 19.95 + 0.205 X1 + 0.00785 X2 – 0.18 3– X3 – 0.0342 X4 – 0.094 X5, which can be viewed as a mathematical model of the studied process. Multi-dimensional dispersion analysis confirmed that this model was adequate for the actual process with a confidence probability of >95%. The high correlation coefficient R2 = 98.8% also indicated that the mathematical model had good predictive properties. The optimization problem was formulated in terms of linear programming. The Taguchi parameter acted as the target function WT → max for the condition Y = Yreg = 1200 in factorial space limited by the ranges over which the independent experimental variables varied. This problem was solved using Microsoft Excel capabilities [5] and the aforementioned mathematical model with X1 = 170°C, X2 = 180 min, X3 = 165 min, X4 = 180 min, and X5 = 50 g/dm3. The predicted value of target function WT in this mode was 15.16, i.e., greater than any value in Table 1. This corresponded to the maximum S/N, i.e., the process robustness criterion in the Taguchi formulation. REFERENCES 1. 2. 3. 4. 5.
K. Dehnad, Quality Control. Robust Design. and the Taguchi Method, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, Calif., 1989 [Russian translation, Seifi, Moscow, 2002, 384 pp]. S. M. Ermakov and A. A. Zhiglyavskii, Mathematical Theory of the Optimum Experiment [in Russian], Nauka, Moscow, 1987, 320 pp. Yu. P. Adler, E. V. Markova, and Yu. V. Granovskii, The Design of Experiments to Find Optimal Conditions [in Russian], Nauka, Moscow, 1976, 284 pp. R. Z. Pen, The Design of Experiments in Statgraphics Centurion [in Russian], SibGTU, Krasnoyarsk, 2014, 293 pp. B. Ya. Kuritskii, Finding Optimal Solutions Using Excel 7.0 [in Russian], BHV – St. Petersburg, St. Petersburg, 1997, 384 pp.
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