• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.269-269
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• 2000

This paper presents a predictive control with H$_{\infty}$ suboptimal performance which is robust to disturbances and has a guaranteed stability. In order to derive the control law conveniently, state-space based approach, where the state variable is involved explicitly in the controller design and implementation is allowed. So an input-output model is converted to an equivalent observable canonical state-space form. The suggested control guarantees the norm bounded system output values from disturbances. A systematic way using the LMI method is presented to obtain appropriate parameters for Quadratic stability condition and optimization problem.

• Journal of Korean Society for Quality Management
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• v.38 no.3
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• pp.413-424
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• 2010

Mixture experiments involve combining ingredients or components of a mixture and the response is a function of the proportions of ingredients which is independent of the total amount of a mixture. The purpose of the mixture experiments is to find the optimum blending at which responses such as the flavor and acceptability are maximized. We assume the quadratic or special cubic canonical polynomial model over the experimental region for a mixture since the current mixture is assumed to be located in the neighborhood of the optimal mixture. The cost of the mixture is proportional to the cost of the ingredients of the mixture and is the linear function of the proportions of the ingredients. In this paper, we propose mixture response surface methods to develop a mixture such that the cost is down more than ten percent as well as mean responses are as good as those from the current mixture. The proposed methods are illustrated with the well known the flare experimental data described by McLean and Anderson(1966).

• Korean journal of food and cookery science
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• v.25 no.2
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• pp.234-242
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• 2009

This study was performed to find the optimum ratio of ingredients for the manufacture of kiwifruit jam. The experiment was designed according to the D-optimal design of RSM (response surface methodology), which included 18 experimental points with 4 replicates for three independent variables (sugar $35{\sim}60%$, pectin $0.1{\sim}1.0.%$, kiwifruit paste $0.37{\sim}0.90%$). The compositional and functional properties of the prepared products were measured, and these values were applied to mathematical models. A canonical form and trace plot showed the influence of each variable on the quality attributes of the final product mixture. By use of the F-test, viscosity, color values (L, a, b), and sensory characteristics (color) were expressed by a linear model, while the L color value and select sensory characteristics (smell, taste, overall acceptance) were also expressed by a quadratic model. The optimum formulations by the numerical and graphical methods, were similar, and with the numerical method it presented as: sugar, pectin, and barley sproutling powder at 49.7%, 0.5%, and 0.6%, respectively. The above results demonstrate the feasibility of preparing kiwifruit jam added with barley sproutling powder, and therefore, the commercialization of a kiwifruit jam marketed as a functional food is deemed possible.

• Journal of Korean Society for Quality Management
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• v.39 no.3
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• pp.400-411
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• 2011

Process variables are factors in an experiment that are not mixture components but could affect the blending properties of the mixture ingredients. For example, the effectiveness of an etching solution which is measured as an etch rate is not only a function of the proportions of the three acids that are combined to form the mixture, but also depends on the temperature of the solution and the agitation rate. Efficient designs for the mixture components-process variables experiments depend on the mixture components-process variables model which is called a combined model. We often use the product model between the canonical polynomial model for the mixture and process variables model as a combined model. In this paper we propose three starting models for the mixture components-process variables experiments. One of the starting model we are considering is the model which includes product terms up to cubic order interactions between mixture effects and the linear & pure quadratic effect of the process variables from the product model. In this paper, we propose a method for finding robust designs and practical designs with respect to D-, G-, and I-optimality for the various starting combined models and then, we find practically efficient and robust designs for estimating the regression coefficients for those models. We find the prediction capability of those recommended designs in the case of three components and three process variables to be good by checking FDS(Fraction of Design Space) plots.

• The Korean Journal of Food And Nutrition
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• v.26 no.1
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• pp.22-28
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• 2013

The objectives of this study were to develop porridge with medicinal herbs and chicken breast meat and to find out the optimum mixing ratio. Several herb extracts such as Acanthopanacis senticosus, Rehmannia glutinosa, Disocorea japonica, and Poria cocos Wolf were used in the ratio of 2, 1, 1, and 1, respectively. The optimum processing condition for herbal chicken porridge was determined by a design expert program. Seventeen experimental points were selected, and herb extracts (82~101 g), chicken breast meat (30~50 g), and glutinous rice (40~60 g) were chosen as the independent variables. The measured responses were preference of taste, DPPH radical scavenging, SOD-like activity, and cost. The optimum formulation of herbal chicken porridge using the numerical analysis was set at herbal extracts (101 g), chicken breast meat (38.66 g), and glutinous rice (41.34 g) with a 0.714 desirability value. DPPH radical scavenging effect, preference of taste and the cost showed a linear model, whereas SOD-like activity showed a quadratic model indicating a higher interaction among the mixture. As a result of proximate composition of optimized herbal chicken porridge, the contents of moisture, carbohydrate, crude protein, crude lipid, and ash contents were 76.4, 9.0, 1.4, 0.5, and 1.6%, the calories of the porridge was 46.1 kcal/100 g.

• Journal of the Korean Society of Food Science and Nutrition
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• v.44 no.9
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• pp.1364-1373
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• 2015

The purpose of this study was to determine the optimum sodium concentration (0~8%), soaking time (4~20 min) and storage time (0~60 day) for preparation of persimmon jangachi with kochujang sauce using response surface methodology. Physicochemical properties (salinity, pH, Hunter's color value, cutting force, and sensory evaluation) of persimmon kochujang jangachi were analyzed during storage at $20^{\circ}C$ for 60 days. When the proximate composition of persimmon was analyzed, moisture content, crude protein content, crude lipid content, and crude ash content were 85.41%, 0.51%, 0.22%, and 0.20%, respectively. For persimmon kochujang jangachi manufactured with different sodium concentrations, soaking times, and storage times, salinity, pH, Hunter's color value of L, a, and b, color, flavor, taste, texture, and overall preference were represented by a quadratic model. Cutting force was represented by a linear model pattern. In conclusion, the optimal formulation for persimmon kochujang jangachi, as assessed by numerical and graphical optimization methods, was a sodium concentration of 6.91%, soaking time of 11.36 minutes, and storage time of 25.18 days.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.267-280
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• 2007

Various single-valued design optimality criteria such as D-, G-, and V-optimality are used often in constructing optimal experimental designs for mixture experiments in a constrained region R where lower and upper bound constraints are imposed on the ingredients proportions. Even though they are optimal in the strict sense of particular optimality criterion used, it is known that their performance is unsatisfactory with respect to the prediction capability over a constrained region. (Vining et at., 1993; Khuri et at., 1999) We assume the quadratic polynomial model as the mixture response surface model and are interested in finding efficient designs in the constrained design space for a mixture. In this paper, we make an expanded list of candidate design points by adding interior points to the extreme vertices, edge midpoints, constrained face centroids and the overall centroid. Then, we want to propose a robust design with respect to D-optimality, G-optimality, V-optimality and distance-based U-optimality. Comparing scaled prediction variance quantile plots (SPVQP) of robust designs with that of recommended designs in Khuri et al. (1999) and Vining et al. (1993) in the well-known examples of a four-component fertilizer experiment as well as McLean and Anderson's Railroad Flare Experiment, robust designs turned out to be superior to those recommended designs.

• Korean journal of food and cookery science
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• v.22 no.6 s.96
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• pp.815-824
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• 2006

This study was performed to determine the optimum ratio of each ingredient in the steamed foam cake with barley (Hordeum vulgare L.) sproutling powder. The experiment was designed according to the D-optimal design of mixture design, which showed 14 experimental points including 4 replicates for three independent variables (sugar 112${\sim}$139%, barley sproutling powder 1${\sim}$8%, and oil 5${\sim}$25%). The compositional and functional properties of test were measured, and these values were applied to the mathematical models. A canonical form and trace plot showed the influence of each ingredient on the mixture final product. The results of F-test, volume, color values (L, a, b), textural properties (hardness, gumminess, chewiness) and sensory characteristics (softness) decided a linear model, while the sensory characteristics (color, smell, taste, overall acceptance) decided a quadratic model. The volume of steamed foam cake was increased by sugar addition, and a negative effect was exerted by barley sproutling powder and oil. L and a of color values increased but the b value decreased with increasing sugar and oil content, whereas barley sproutling powder tended to decrease all color values. The addition of barley sproutling powder also had a positive effect on the textural properties (hardness, gumminess, chewiness). Sensory characteristics (color, smell, softness, taste, overall acceptance) could suffer counter results with the excessive addition of sugar, barley sproutling powder, and oil. The optimum formulations by numerical and graphical methods were similar: sugar, barley sproutling powder, and oil were 130.4%, 4.0%, and 10.7% by numerical method, compared to 130.4%, 4.0%, and 10.7% by graphical method, respectively.

• Journal of the Korean Society of Food Science and Nutrition
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• v.35 no.5
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• pp.641-648
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• 2006

In an attempt to get basic data for the utilization of saltwort powder (Salicornia herbaceae L.) as a ingredient in the Sulgidduk. D-optimal design of mixture design showed 14 experimental points including 4 replicates for three independent variables. The three independent variables selected for the experiment were water ($13{\sim}18%$), saltwort powder ($2{\sim}6%$), and sugar ($8{\sim}13%$). The optimum responses variables such as color value. texture, and sensory characteristics were evaluated. The compositional and functional properties of test were measured, and these values were applied to the mathematical models. According to the result of measuring probability of the color value, texture and sensory characteristics were respectively and significance was acknowledged (p<0.05). According to the result of F-test, color values (L, a, b), textural properties (gumminess, chewiness) and sensory characteristics (taste, softness) decided linear model, textural property (hardness) and sensory characteristics (color, smell, moistness, overall acceptance) decided quadratic model. A canonical form and trace plot showed that the influence of each ingredient on the mixture final product. An optimum formulation by numerical and graphical methods were similar. Water, saltwort powder, and sugar were 15.2%, 3.0%, and 9.8% respectively by numerical method, and 15.2%, 3.1%, and 9.7% respectively by graphical method.

• Journal of the Korean Society of Food Science and Nutrition
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• v.37 no.4
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• pp.497-504
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• 2008

This study was conducted for the optimization of ingredients in salad dressing using Bokbunja (Rubus coreanum Miquel) juice. The experiment was designed according to the D-optimal design of mixture design, which included 14 experimental points with 4 replicates for three independent variables (Bokbunja juice $15.70\sim47.10%$, oil $23.50\sim39.20%$, vinegar $3.90\sim19.60%$). The compositional and functional properties of the prepared products were measured, and these values were applied to the mathematical models. A canonical form and trace plot showed the influence of each variable on the quality attribute of final mixture product. By the use of F-test, viscosity, color values (L, a, and b), emulsion stability and sensory characteristics (color) were expressed by a linear model, while the color values (L) and sensory characteristics (smell, taste, and overall acceptance) were by a quadratic model. The optimum formulations by numerical and graphical method were analogous: Bokbunja juice, oil and vinegar of 36.02%, 26.48%, and 12.00% by numerical method, respectively; those of 36.00%, 26.44%, and 12.06% by graphical method, respectively.