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Process control is a subject that applies principles of mathematics and engineering sciences. In this subject, students can study of automatic control principles applied to chemical/food processes. In our learning, process control is very important in most company in food processing industry which is we must know the best conditions for the raw food become food product. For example, we study the control terminology, mathematical and empirical modeling, block diagram and many more.
Food processing includes all activities that are control the nature of food between marine product and agricultural and its final eating by the humans (consumers). This processing includes everything from controlled conditions in the transport and storage of whole fresh raw fish, meat, vegetables and fruits to the complex processing producing food ingredients followed by manufacturing to produced final product. Before being eaten, biological materials from agriculture are transformed through processing into the finished food. Food processing makes the food more attractive, safer and easier to eat. It's also preventing the food from deterioration. Food products are the outcomes of food processing, and it is important to identify the desirable product qualities and the undesirable and even unsafe product qualities. The products are the aim of food processing, and processing needs to be designed and controlled to give the product qualities identified and wanted by the consumers. Food processing is diverse, complex, and often carried out on a large industrial scale.
PROCESS OF APPLE JUICE
Apple juice production was begun with fruit harvesting, transport and washing facilities. The product quality and stability of apple juice will be influenced by the cleanliness. After that, the apple will be wash and gridding and pressing but before pressing whole apples is ground into a mush for the extraction. This mashing process is accomplished with either a disintegrator, hammer, or gating mill. These mills crush or cut the apple to proper consistency, depending on the maturity of fruit. When milling firm fruit for juice, small particles are desired. As the season progress and apples become softer
Equipment used to pressing or extract juice from apple are of several types and many variations. The pressing process can be batch or continuous depending on the type of press used. But for this process, we batch reactor. Actually undue aeration must be avoided during the extraction of juices from fruit that has not been heated to destroy enzymes, since destruction of vitamin C and oxidative changes in flavor are very rapid.
The apple mash has many natural enzymes but at rather low concentrations. The enzymes are substrate specific, which means a given enzyme can catalyze only one particular reaction. Two methods of enzyme treatment are commonly used hot treatment where the enzymes are added to 54 °C juice, mixed and held for 1 to 2 hours or cold treatment where the enzymes are added to cold, room temperature, 20 °C juice and held for 6 to 8 hours
After the enzyme treatment, fining and settling process, the apple juice is pumped from the settled material (lees) and further clarified by filtration. After that preservation of apple juice can be by refrigeration and pasteurization. We would focus on heat pasteurization, which based on temperature and time of exposure. The juice is heated to over 70°C, held for 30 min, filled hot into container, and hermetically sealed. The apple juice is held 1 min. and then cooled to less than 37°C. When containers are closed hot and then cooled, a vacuum develops, reducing the available oxygen that also aids in the prevention of microbial growth.
After the heat treatment, the juice product may also be stored in bulk containers, but aseptic conditions must be maintained to prevent microbial spoilage. Aseptic packaging is another common process where, after pasteurization, the juice is cooled and packaged in a closed, commercially sterile system under aseptic conditions. Figure below show that overall process making apple.
Figure 1: Pasteurization of Apple juice
PASTEURIZATION OF APPLE JUICE
The process of "pasteurization" envisioned was aimed at the destruction of all bacteria, molds or spores. The pasteurization process can destruction of bacteria by exposing them to a certain minimum temperature for a certain minimum time or the higher the temperature, the shorter the time required. In our study of pasteurization of apple juice, the plant will be in operation for 20 hours in a day. As we all already know the microorganism inactivation depends on the combination of temperature and holding time. The juice is heated to a specific temperature for a specified period of time to inactivate bacteria that may be harmful to health and cause spoilage. The apple juice will heated at 70° C for not less than 30 min. Pasteurization will ensure apple juice quality and a longer shelf life.
There are several methods used to pasteurize milk. The most common is called the high-temperature, short-time (HTST) process in which the juice is heated as it flows through the pasteurizer continuously. This method provides the convenience of continuous processing, yet still does not adversely affect the taste of the product by "cooking" it. The other one is UHT or ultra high temperature pasteurization, the product is brought to over the boiling point (under pressure) for only a fraction of a second. This results in a sterile product that requires no refrigeration later. This type of pasteurization are commonly apply with are coffee creamer and juice boxes. However, after being brought to this temperature, a slight "cooked" taste is sometimes said to be detectable.
The other method of pasteurization is batch pasteurization, which is simple vat pasteurization. Thorough this method, it will heat apple juice to about 70 for about 30 minutes and could consider the product to be safe. This method destroys most common pathogenic bacteria.
The process control is necessary for few reasons. These include safety, equipment protection, and product quality. The process of pasteurization envisioned by Louis Pasteur was aimed at the destruction of all bacteria, molds, spores, etc. Pasteur discovered that the destruction of bacteria can be performed by exposing them to a certain minimum temperature for a certain minimum time. The higher the temperature, the shorter the time required. This process killed all harmful bacteria. The plants are designed to operate safely at expected pressures and temperatures. Overpressure is the only common safety issue affecting shell and tube heat exchangers. Therefore, pressure relief must be provided for both the shell and tube sides. If the source of overpressure is from upstream, the relief valve for that stream is best placed on the inlet. If careful analysis shows that there are no process, fire, or failure conditions that could possibly require relief valves, it is still strongly advised to install thermal reliefs on both sides of any exchanger that is capable of being blocked in.
For equipment protection, severe corrosion is sometimes a problem. If so, corrosion detection devices may be installed. These consist of a thin wire or film of the same material as the exchanger. The wire is held in a holder that is inserted through a nozzle into the exchanger. Two electrical contacts are accessible from the outside. When the resistance is measured, the extent of corrosion can be determined directly. These devices are not normally connected into a data logging network. The usual practice is to make the measurements with a portable monitor on a regular basis. Intrinsically safe monitors are available for hazardous locations. As a conclusion to avoid corrosion from occurs, we can use double boiler whether stainless or aluminum, an accurate metal stem probe thermometer (cooking thermometer), and storage containers (liter size mason jars are suitable).
For product quality, we need to concern about the heat that apply and insert into the pasteurization process where the inlet temperature of the heating medium. The heating medium should be flowed into the tank at the controlled and desired temperature since excessive heating may lead to product quality deterioration and browning whereas not enough of heat transfer in the milk heating may lead to microbial growth. Insufficient heating may lead to health problem to the consumers such as diarrhea, stomachache, and so on.
In apple juice pasteurization process, we used the stirred tank heating system. There are several variable that has to be determined which are control, manipulated and disturbance variables. The selection of these variables will make our control system design easier. In general, controlled variables are the variables which quantify the performance or quality of the final product which is also called output variable. Manipulated variables are the input variables which are adjusted dynamically to keep the controlled variables at their set point while disturbances variable are also called "load" variable and represent input variables that can caused the controlled variables to deviate from their respective set point. The disturbance variables cannot be manipulated but it can affect the controlled variables.
For the first step in pasteurization of apple juice, we would like to control the temperature of the juice. We choose to control the temperature because pasteurization process only occurs in certain temperature. Only the temperature of one fluid or the other will be measured and controlled as we cannot control both temperatures. So, we need to consider the specific place where the temperature of the juice will be kept constant. Therefore, we put the thermocouple somewhere at the bottom of the outlet of the fluids. The large deviation of temperature from the set point may produce low quality of apple juice and will give big loss to the company.
The second step is to verify the manipulated variables. In this process, we choose the inlet flow rate of the steam as the manipulated variables. The temperature of the apple juice in the tank can be influenced by the inlet flow rate. The heat transfer from the steam (heating medium) to the apple juice would be increased if the steam inlet flow rate decreased. Thus, the increment of the temperature of the apple juice would be higher in the pasteurization process.
Finally, the disturbance variable is verified. The performance of the tank might decreased because of the corrosion occurs in the internal surface of the tank. Besides that, the temperature of the inlet temperature of the steam might not be constant because we did not measure the temperature at the inlet steam valve. So, we might not know the actual temperature and we do not know whether the temperature is constant or not.
For mathematical modeling, we assume that our tank containing 50kg of apple juice with specific heat capacity, Cp (apple) 3.64 kJ/kg K and the flow rate of steam, Fs is 5 kg/s. The inlet temperature, Ti of the steam is 450 K (177°C), the outlet temperature, To is 350 K (°C) and the pasteurization temperature of the apple juice, which we controlled, Ta is 343 K (70°C). The specific heat of steam, Cps is 1.909 kJ/kg K and the temperature of the steam, Ts is 455 K (182°C). We circulate the steam to supply heat to the apple juice in the tank so that the temperature of the apple juice inside the tank can be maintained.
There are some assumptions for the heat transfer calculation:
No heat loss to the surroundings
Constant properties of apple juice
Steady state condition
For the calculation, we used the formula of heat evolution as shown below;
Heat evolution = overall heat transfer in stirred tank + heat obtained by apple juice by time
Q = UA(Tm - Ta) + mCm
Where Q= heat evolution in process of stirred tank heating system
U = overall heat transfer coefficient
A = heat transfer of surface area
Ta = temperature of apple juice inside the tank (controlled temperature)
Tav = average temperature of steam
m= mass of apple juice inside stirred tank
Cpm = heat capacity of apple juice at 343 K
dT/dt = change of apple juice temperature by time
We need to rearrange the unsteady state heat equation to first order model to get the Ï„p
Ï„p = =
To find UA, we use the equation;
Q = UA
Î¤p = = 0.93 min
Because there is no disturbance occurs in the system, Q/UA term is ignored. So, steady state gain, Kp = 1
The average temperature of the steam is not the manipulated variable, so this is not practical to the process. We can only manipulate the inlet or outlet temperature of the steam. Therefore, we need to relate the controlled temperature of apple juice to the flow rate of recirculation of steam into jacket to the heat of the stirred tank. In order to maintain the temperature of apple juice inside the tank at its set point pasteurization temperature, we have to manipulate the flow of steam, Fs at temperature, Ts into the recirculation loop.
From heat balance related to Ti,
Where Ti = inlet temperature of steam into jacket
To = outlet temperature of steam from jacket
Then, we substitute into Tav
Steady state gain,
By substituting the value Kp and Ï„p into general first order transfer function, we assume that the time delay is 2 seconds. So,
Figure 2: Block Diagram for Ziegler-Nichols method
The block diagram that shown above is the block diagram for Ziegler - Nichols method and it is the same as any other method: Cohen-Coon method and IMC method.
Figure 3: Block Diagram
In the block diagram above, two assumptions have been made.
Negligible of disturbance (Gd = 0).
The system is an ideal system (Gv = 1, Gm = 1)
From the transfer function of process,
Ï„ p = 0.93
K p = 1.5
Î¸ = 2 s
Table 1: Kc, Ï„I, and Ï„D values for different types of controller according to several types of methods
Type of controller
Results of tuning method
Table 2: Table of proportional, P, integral, I and derivative D
Type of controller
P = KC
D = x
CALCULATION: IMC Method
For PID controller:
Kc = 0.31
CALCULATION: Ziegler-Nichols Method
For P controller:
Kc = 0.31
For PI controller:
K.Kc = 0.9
(1.5).Kc = 0.9
Kc = 0.279
For PID controller:
K.Kc = 1.2
(5.2).Kc = 1.2
Kc = 19.04
CALCULATION: Cohen Coon method
For P controller:
Kc = 0.533
For PI controller:
K.Kc = 0.9 + 0.083
(1.5).Kc = 0.9 + 0.083
Kc = 0.3343
For PID controller:
K.Kc = 1.35
1.5Kc = 1.35
Kc = 0.599
SIMULATION OF SYSTEM AND DISCUSSION
Figure 4: Open Loop Test
Figure 4 show the open loop test for transfer function which have time delay 2 second. From the graph that we obtain, we can see that it have time delay, this graph show that our time delay, which is 2 second. The rise time of this graph is quite slow but there are not overshoot.
IMC (Internal Model Control) Method
Figure 5: P Controller for IMC method
Figure 5 shows that the P controller for IMC method. Since there is no equation for P controller in IMC method, the value remains or equal to zero.
Figure 6: PI Controller for IMC method
Figure 6 shows that the PI controller for IMC method. Since there is no equation for PI controller in IMC method, the value remains or equal to zero.
Figure 7: PID Controller for IMC method
From figure 7 we could see that from the figure the overshoot is high which is 75%, the settling time is almost 33seconds and the rise time is long (about 8seconds). The time delay from the figure is 2sconds. This method also has fast settling time
IMC (Internal Model Control) tuning method
Figure 8: The graph of the simulink using the IMC (Internal Model Control) tuning method
Figure 8 shows that the P and PI controller remains zero because there are no equations for P and PI controller for the IMC method. So, we just get the result for PID controller which is the figure takes time about 33seconds to reach the set point.
Ziegler- Nichols Method
Figure 9: P Controller for the Ziegler - Nichols method
This graph show for Ziegler - Nichols method for P controller, through this graph we can see that there are some overshoot and the delay time 2 second .This graph also show slow rise time and the settling time are faster.
Figure 10: PI Controller for Ziegler - Nichols method
Figure 10 show the graph of Controller for Ziegler - Nichols method which show there no overshoot but this graph have very slow settling time. And the middle there disturbance, this show this controller are not suitable to use.
Figure 11: PID Controller for the Ziegler - Nichols method
From figure 11, we can see that, this graph has same time delay, like another graph of Ziegler-Nichols method, which is around 2 second. Even this graph has slow rise time but it has fast settling time. The middle of the graph has a little disturbance but the graph do not have overshoot.
Ziegler - Nichols tuning method
Figure 12: The graph of the simulink using the Ziegler - Nichols tuning method
From this graph show that the comparison of all controllers for the Ziegler - Nichols method, we can see that almost graph have time delay around 2 second, and there are not overshoot except for P controller.
Figure 13: P Controller for Cohen - Coon method
Figure 13 show the graph of P controller for Cohen - Coon method, from this graph we can see that there has time delay around 2 second. Also the graph show that a lot of overshoot and slow settling time.
Figure 14: PI Controller for the Cohen-Coon method
From this graph, it show that it have time delay, which is around 2 second. And very slow settling time and rise time, even there are no overshoot but at the middle there have a little disturbance.
Figure 15: PID Controller for the Cohen-Coon method
Figure 15 shows that the Cohen-Coon Relation PID controller. From the figure, we could see that overshoot is too high which is about 88.9% and the rise time is fast. By using this method, it takes very long time to reach steady state. The time delay for this graph must equal to 2 seconds. Maybe there are too many disturbances while running this process.
Cohen-Coon tuning method
Figure 16: The graph of the simulink using the Cohen-Coon tuning method
Figure 16 shows that the combination of Cohen -Coon tuning method in one graph which is includes Ideal, Open Loop, P controller, PI controller and PID controller. Here, the set point is equal to 1 and from figure we see that only PID controller is reach the set points while the others away from the set point. Actually from our calculation, the time delay is equal to 2seconds. Overall from this method, the PID is the best one with lower rise time and reaches set point.
From all graph for all controller and method, we simplify that the most suitable controller tuning method are PID, Controller for IMC method could be applied to control the change in temperature of apple juice which is undergoing pasteurization process with a some overshoot and settling time around 28 second. Actually this method is also known as the closed-loop or on-line tuning method. The Closed Loop method determines the gain at which a loop with proportional only control will oscillate, and then derives the controller gain, reset, and derivative values from the gain at which the oscillations are sustained and the period of oscillation at that gain.
For graph of the simulink using the Cohen-Coon tuning method, there have high overshoot. Besides that, it takes very long time to reach steady state. Maybe there are too many disturbances while running this process so it not suitable method for control the change in temperature of apple juice which is undergoing pasteurization process
The graph of the simulink using the Ziegler - Nichols tuning method, has a slow rise time and settling time, it also have a disturbance at the middle process so that mean this controller and method not suitable at all
For IMC method, there is no equation for P and PI controller that why the value remains or equal to zero. But for PID, IMC method has a little big overshoot and disturbance, but it has fast settling time.
As a conclusion, the best performance with the a little Overshoot, fast Rise Time, fast settling point and no Steady-state error can be obtained by apply PID controller for IMC method tuning method, which is the most suitable controller and method.
From the graph, the most suitable controller that we choose is PID controller IMC method. From the tuning, we do not know whether the controller is stable or not. Therefore, we have to determine the stability of the process. An unconstrained linear system is said to be stable if the output response is bounded for all bounded inputs. Otherwise it is said to be unstable.
First, using block diagram algebra that was developed earlier, we obtain
Y= Ysp + D
Where Gm=Gv=Km=1 Gd=0
= GOL = GvGcGpGm
1 + GvGmGpGc =0
1 + GcGp = 0
Gc = Kc (1 + + Ï„Ds) Kc=0.31 Ï„Is = 0.93 Ï„Ds = 0
= 0.31(1+ 1/0.93s)
The Routh stability criterion can only be applied to systems whose characteristics equations are polynomials in s. Since our transfer function has time delay, the Routh stability is not directly applicable unless the term is replaced by a Pade approximation.
This is 1/1 Pade approximation because it is first order in both numerator and denominator.
1 + Ã- = 0
1 + ( =0
1.7949+ 0.8649 + 0.93s + 0.43245s - 0.43245 - 0.465s +0.465 =0
CE: 0.8649s3 + 1.36245s2 + 0.89745s + 0.465 = 0
b1 = = 0.60226
:. 0.60226 > 0
Thus, the closed loop system is stable.
From the calculation that we have done in this project, we could say that the stability of the system is stable which is the output response is bounded for all bounded inputs. Before we check the stability, we do the tuning and from our observation, the best tuning that we get is PID controller for IMC method. The PID controller for IMC method have successfully reduce the rise time, settling time and overshoot of the control system.
Dale E.Seborg,Thomas F.Edgar,Duncan A.Mellichamp, Process Dynamics and Control, 2nd Edition.