**1. Introduction**

88 Frontiers of Model Predictive Control

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Concentrated clear grape juices are extensively used in the enological industry. Their use as constituents of juices, jellies, marmalades, jams, colas, beverages, etc., generates a consumer market with an increasing demand because they are natural products with an industrial versatility that allows them to compete with other fruit juices.

Argentina is one of the principal producers and exporters of concentrated clear grape juices in the world. They are produced mainly in the provinces of Mendoza and San Juan (Argentine Republic) from the virgin grape juice and in the most part from sulfited grape juices. The province of Mendoza's legislation establishes that a portion of the grapes must be used for making concentrated clear grape juices. This product has reached a high level of penetration in the export market and constitutes an important and growing productive alternative.

An adequate manufacturing process, a correct design of the concentrate plants and an appropriate evaluation of their performance will facilitate optimization of the concentrated juices quality parameters (Pilati, 1998; Rubio, 1998). The plant efficiency is obtained from knowledge of the physics properties of the raw material and products (Moressi, 1984; Piva, 2008). These properties are fundamental parameters that are used in the designing and calculations on all the equipment used and also in the control process.

The juices (concentrate and intermediate products) physical properties, such as density, viscosity, boiling point elevation, specific heat and coefficient of thermal expansion, are affected by their solid content and their temperature (Schwartz, 1986). For this reason, it is necessary to know the physical properties values, as a function of the temperature and the solids content, during the manufacture process, not just to obtain an excellent quality, but also to develop a data base, that is essential for optimizing the installation design and the transformation process itself. The principal solids constituents of clear grape juices are sugars (mostly glucose and fructose) and its concentration affects directly the density, viscosity and refraction index.

Predictive Control for the Grape Juice Concentration Process 91

The GPC technique is based on the use of models derived from transfer functions (transfer matrices in the multivariate case). The use of a formulation of this kind against an internal description has certain advantages in the field of development of interactive tools. The transfer function formulation is more intuitive, being based only on information input and output measurable and arrange its elements (poles and zeros) of a clear physical meaning

This is critical in the design of interactive tools, which simultaneously shows different representations of the system that allow to analyze how the change affects any parameter of the plant-controller-model global behavior of the controlled system without ever losing its

The basic idea was proposed of GPC is to calculate a sequence of future control signals in such a way that it minimizes a multistage cost function defined over a prediction horizon. The index to be optimized is the expectation of a quadratic function measuring the distance between the predicted systems output and some predicted reference sequence over the horizon plus a quadratic function measuring the control effort. This approach was used in Lelic & Wellstead (1987) and Lelic & Zarrop (1987), to obtain a generalized pole placement controller which is an extension of the well-known pole placement controllers Allidina &

Generalized Predictive Control has many ideas in common with the predictive controllers previously mentioned since it is based upon the same concepts but it has some differences. As will be seen, it provides an analytical solution (in the absence of constraints)nit can deal with unstable and nonminimum phase plants and it incorporates the concept of control horizon as well as the consideration of weighting control increments in the cost function. The general set of choices available for GPC leads to a greater variety of control objectives compared to other approaches, some of which can be considered as subsets or limiting cases of GPC. In particular, the strategy GPC uses the model CARIMA (Controlled Auto

Figure 2 show the input and output streams in a vertical generic effect evaporator with long tubes. The solution to be concentrated circulates inside the tubes, while the steam, used to

physical sense, allowing to develop their intuition and skills.

Hughes (1980) and belongs to the class of extended horizon controllers.

Regressive Integrated Moving Average) to predict the process output.

heat the solution, circulates inside the shell around the tubes.

Fig. 1. MBPC action.

and interpretation.

**2. Process description** 

The type and magnitude of degradation products will depend on the starting reagent condition (Gogus, et al., 1998). Acetic, formic, and D/L-lactic acids were identified at the end of thermal degradation of sugar solutions (Asghari and Yoshida, 2006), and a reaction scheme was proposed by Ginz et al. (2000). Sugar degradation may result in browning of solutions with polymeric compounds as the ultimate product of degradation, generally known as "melanoidins", involving the formation of 5-(hydroxymethyl)-2 furancarboxaldehyde (5-HMF) as intermediate.

Barbieri and Rossi (1980) worked with white concentrated clear grape juice in a falling film multiple effect evaporators. They obtained 18.2, 27.3, 38.6, 48.6 and 64.6 °Brix samples. They measured density, viscosity and boiling point elevation as a function of soluble solids concentration and temperature. They presented the results in plots with predictive equations for the properties studied.

Di Leo (1988) published density, refraction index and viscosity data for a rectified concentrated grape juice and an aqueous solution of a 1:1 glucose/levulose mixture, for a soluble solids concentrate range from 60 to 71% (in increments of 0.1%) and 20 °C. The author determinated the density in undiluted and 2.5-fold diluted samples (100 g of clear grape juice in 250 ml of solution at 20 °C), finding different results between both determinations. He recommended measuring density without dilution.

Pandolfi et al., (1991) studied physical and chemical characteristics of grape juices produced in Mendoza and San Juan provinces, Argentina. They determined density at 20°C in sulfited grape juices of 20–22°Bx and concentrated grape juices of 68–72°Bx. They obtained no information on intermediate concentrations or other temperatures. In general, the clarified juice concentrates have a Newtonian behavior (Ibarz & Ortiz, 1993; Rao, Cooley & Vitali, 1984; Sáenz & Costell, 1986; Saravacos, 1970).

Numerous industrial processes are multivariable systems which require a large number of variables to be controlled simultaneously (Kam, 1999; Kam, 2000). The controller design is for this type of system has a great interest in control theory (Doyle, 1979; Freudenberg, 1988; Friedland, 1989; Middleton, 1990; Zang, 1990; Aros, 2008; Suarez, 2010). This work presents an interactive tool to facilitate understanding of the control of multivariable systems (MIMO) using the technique of Generalized Predictive Control (GPC). The tool can handle the main concepts of predictive control with constraints and work both as monovariable and multivariable systems.

The GPC for systems multivariable, MBPC or Model Based Predictive Control includes a set of techniques to cover wide range of problems from those with relatively simple dynamics to other more complexes (unstable, large delays, nonminimum phase systems, etc.). Among its many advantages (Camacho & Bordons, 1999) is its easy adaptation to multivariable systems. One of the most important techniques in academia for predictive control is the Generalized Predictive Control (Clarke et al., 1987). The characteristic of this strategy, as shown in figure 1, is that at each sampling time and using a process model, predicting the future outputs for a given horizon. With these predicted outputs, using an objective function and taking into account the constraints that affect the process (eg on the inputs and outputs) are calculated future control increments. Finally, we apply the first control signal is calculated, the rest is discarded and the horizon moves forward, repeating the calculations in the next sampling period (receding horizon strategy).

Fig. 1. MBPC action.

90 Frontiers of Model Predictive Control

The type and magnitude of degradation products will depend on the starting reagent condition (Gogus, et al., 1998). Acetic, formic, and D/L-lactic acids were identified at the end of thermal degradation of sugar solutions (Asghari and Yoshida, 2006), and a reaction scheme was proposed by Ginz et al. (2000). Sugar degradation may result in browning of solutions with polymeric compounds as the ultimate product of degradation, generally known as "melanoidins", involving the formation of 5-(hydroxymethyl)-2-

Barbieri and Rossi (1980) worked with white concentrated clear grape juice in a falling film multiple effect evaporators. They obtained 18.2, 27.3, 38.6, 48.6 and 64.6 °Brix samples. They measured density, viscosity and boiling point elevation as a function of soluble solids concentration and temperature. They presented the results in plots with predictive

Di Leo (1988) published density, refraction index and viscosity data for a rectified concentrated grape juice and an aqueous solution of a 1:1 glucose/levulose mixture, for a soluble solids concentrate range from 60 to 71% (in increments of 0.1%) and 20 °C. The author determinated the density in undiluted and 2.5-fold diluted samples (100 g of clear grape juice in 250 ml of solution at 20 °C), finding different results between both

Pandolfi et al., (1991) studied physical and chemical characteristics of grape juices produced in Mendoza and San Juan provinces, Argentina. They determined density at 20°C in sulfited grape juices of 20–22°Bx and concentrated grape juices of 68–72°Bx. They obtained no information on intermediate concentrations or other temperatures. In general, the clarified juice concentrates have a Newtonian behavior (Ibarz & Ortiz, 1993; Rao, Cooley & Vitali,

Numerous industrial processes are multivariable systems which require a large number of variables to be controlled simultaneously (Kam, 1999; Kam, 2000). The controller design is for this type of system has a great interest in control theory (Doyle, 1979; Freudenberg, 1988; Friedland, 1989; Middleton, 1990; Zang, 1990; Aros, 2008; Suarez, 2010). This work presents an interactive tool to facilitate understanding of the control of multivariable systems (MIMO) using the technique of Generalized Predictive Control (GPC). The tool can handle the main concepts of predictive control with constraints and work both as monovariable and

The GPC for systems multivariable, MBPC or Model Based Predictive Control includes a set of techniques to cover wide range of problems from those with relatively simple dynamics to other more complexes (unstable, large delays, nonminimum phase systems, etc.). Among its many advantages (Camacho & Bordons, 1999) is its easy adaptation to multivariable systems. One of the most important techniques in academia for predictive control is the Generalized Predictive Control (Clarke et al., 1987). The characteristic of this strategy, as shown in figure 1, is that at each sampling time and using a process model, predicting the future outputs for a given horizon. With these predicted outputs, using an objective function and taking into account the constraints that affect the process (eg on the inputs and outputs) are calculated future control increments. Finally, we apply the first control signal is calculated, the rest is discarded and the horizon moves forward, repeating the calculations

determinations. He recommended measuring density without dilution.

furancarboxaldehyde (5-HMF) as intermediate.

1984; Sáenz & Costell, 1986; Saravacos, 1970).

in the next sampling period (receding horizon strategy).

multivariable systems.

equations for the properties studied.

The GPC technique is based on the use of models derived from transfer functions (transfer matrices in the multivariate case). The use of a formulation of this kind against an internal description has certain advantages in the field of development of interactive tools. The transfer function formulation is more intuitive, being based only on information input and output measurable and arrange its elements (poles and zeros) of a clear physical meaning and interpretation.

This is critical in the design of interactive tools, which simultaneously shows different representations of the system that allow to analyze how the change affects any parameter of the plant-controller-model global behavior of the controlled system without ever losing its physical sense, allowing to develop their intuition and skills.

The basic idea was proposed of GPC is to calculate a sequence of future control signals in such a way that it minimizes a multistage cost function defined over a prediction horizon. The index to be optimized is the expectation of a quadratic function measuring the distance between the predicted systems output and some predicted reference sequence over the horizon plus a quadratic function measuring the control effort. This approach was used in Lelic & Wellstead (1987) and Lelic & Zarrop (1987), to obtain a generalized pole placement controller which is an extension of the well-known pole placement controllers Allidina & Hughes (1980) and belongs to the class of extended horizon controllers.

Generalized Predictive Control has many ideas in common with the predictive controllers previously mentioned since it is based upon the same concepts but it has some differences. As will be seen, it provides an analytical solution (in the absence of constraints)nit can deal with unstable and nonminimum phase plants and it incorporates the concept of control horizon as well as the consideration of weighting control increments in the cost function. The general set of choices available for GPC leads to a greater variety of control objectives compared to other approaches, some of which can be considered as subsets or limiting cases of GPC. In particular, the strategy GPC uses the model CARIMA (Controlled Auto Regressive Integrated Moving Average) to predict the process output.
