Mpc o4916

2016 International Conference on Instrumentation, Control and Automation (ICA) Institut Teknologi Bandung (ITB), Bandung, Indonesia, August 29-31, 2016

Model Predictive Control Design and Performance Analysis of a Pasteurization Process Plant Anang1, Sutanto Hadisupo2, Edi Leksono3 Department of Engineering Physiscs Faculty of Industrial Technology Bandung Institute of Technology, Bandung, Indonesia 1 [email protected]

contaminate the food products). On the other hand, if the temperature exceeds this range then the nutritional contents of the product can be damaged. The requirement of maintaining a fairly narrow range of temperature in the pasteurization process suggests the need for appropriate controller to maintain the system to achieve specified operational criteria. The study reported in this paper is aimed at developing a model-based predictive control (MPC) technique that can provide appropriate control signals for maintaining the pasteurization process to operate within a specified range of temperature. The developed control method is developed under MATLAB software and implemented in real time on a laboratory scale pasteurization process mini plant Armfield PCT23MKII which is equipped with programmable logic controller Allen Bradley SLC 5/02 and OPC KepServer5 for real time interfacing and data communication. Performance comparison between the developed MPC method and conventional PID and PID cascade controllers is also reported.

Abstract— Pasteurization is a process of heating food products at a specified temperature to eliminate micro bacteria contaminants that may endanger consumer health. In dairy food industries, the pasteurization process often set to achieve products’ temperature between 70°C to 75°C during 15 seconds. This paper reports the development of control system for a lab scale pasteurization process plant Armfield PCT23MKII which is equipped with programmable logic controller (PLC) Allen Bradley SLC 5/02 and OPC KepServer5 real time interface. A MATLAB based model predictive control (MPC) algorithm is developed for the mini plant and its performance is compared to standard PID and PID cascade controllers. Based on the experimental results, it was found that the developed MPC was capable of eliminating over shoot, achieve a fast settling time with an integral absolute error (IAE) of 3884 and energy consumption 613.2 kJ. In comparison with both the PID and PID cascade controllers, it is also shown that the proposed MPC algorithm has better performance in of adapting to load change and mitigating disturbances. Keywords— Pasteurization; Heat exchangers; Model predictive control; PID control; Programmable logic controller

Based on the experimental results, it was found that the developed MPC was capable of eliminating overshoots, achieve a fast settling time with an integral absolute error (IAE) of 3884 and energy consumption 613.2 kJ. In comparison with both the PID and PID cascade controllers, it is also shown that the proposed MPC algorithm has better performance in of adapting to load change and mitigating disturbances

I. INTRODUCTION Pasteurization, named after its inventor Louis Pasteur, is a process of applying heat into food product in order to keep their temperature at specific range and maintain the quality of the food during storage. The pasteurization process is intended to destroy pathogenic bacteria which contaminate the food without having to damage the nutritional content of the food ingredients [1]. The Indonesian national standard document (SNI 19-15021982) specifies that the pasteurization process usually requires the maintenance of a temperature range between 63°C - 66°C for a minimum of 30 minutes or to maintain a temperature of 72°C for at least 15 seconds. In either case, the process is followed by immediate cooling the product to achieve a 10°C temperature, then treated aseptically and stored at a maximum temperature of 4.4°C. As can be seen in TABLE I, the High Temperature Short Time (HTST) pasteurization process required by milk and dessert products require the temperature to be maintained within the range of 70°C - 75°C in about 15 seconds. On the one hand, if the temperature is lower than this range, the pathogen micro bacterial will not die and thereby may

TABLE I.

METHOD OF PASTEURIZATION, TEMPERATURE AND DURATION OF HEATING

Method Batch or Vat (holder) Pasteurization Milk Cream Frozen Dessert Mix High Temperature Shor Time (HTST) Milk Cream Frozen Dessert Mix Condensed Milk Ultra High Temperature (UHT) All Product

978-1-5090-1335-7/16/$31.00 ©2016 IEEE 81

Time

Temperature

30 min 30 min 30 min

62.8°C 65.6°C 68.3°C

15 s 15 s 25 s 15 s

71.7°C 74.4°C 79.4°C 74.4°C

1s 0.5 s 0.1 s 0.05 s 0.01 s

88.3°C 90.0°C 93.0°C 95.6°C 100°C

II. PROCESS DESCRIPTION

Fig. 2 shows the control architecture that is used in the system. It can be seen that dedicated application software that can be used for deg controller for the system is integrated on the workstation. The control command from the software is then implemented in real time to the plant using OPC server.

The object of study discussed in this paper is the High Temperature Short Time (HTST) process in a miniature of a pasteurization plant Armfield PCT23MKII that uses water and heat exchanger for heating process. The process flow diagram of the pasteurization plant used in this study is shown in Fig. 1. It can be seen that the plant consists of the following three important parts [2]:

A. System Identification A system identification process was conducted to model the process’ dynamics. In the experiment, an input power of 21.6% which is equal to 0.35kW is used to satisfy the limitations of the heating temperature T2 to only up to 80°C. By maintaining the flow of the cold water at pump N1 (feed pump) at 150ml/min and at pump N2 at 60%, we found that the system may achieve a steady state response. In particular, the following first order plus time delay transfer function is chosen for the system

 Heated Vessel (tank heater): this heating unit is the part where the water is heated and then circulated using a pump (N2) through a heat exchanger and then transferred back into the heater tank. The temperature of the content of the tank is measured by the temperature sensor T2.  Heat Exchanger: this part is a heat exchanger media where the hot water coming from the tank heater is circulated and the cold water from the cold water tank is also ed through to allow for the heat exchange process occurs.  Feed Tank: This part is a cold water storage tank that provides input water to the heat exchanger. The cold water will be circulated through the heat exchanger by the pump N1 and the flow rate is measured by the flow meter F1. The output from the heat exchanger is the final product that will be measured by the T1 as the system product.

(1) The model parameters were identified by applying a load of 150ml/min at N1 and use a set point temperature T1 at 54°C under a PID controller operation. The selection of the temperature set point T1 should satisfy the temperature limitations of T2: greater temperature T1 may result in an overshoot of T2 which, if exceed 85°C, eventually can activate the alarm and turn off the overall process (trip). Some control strategies will be compared in this study including using various PID tuning algorithms and MPC method. The system response is illustrated in Fig. 3. From which the following transfer function can be obtained: .

(2)

.

i.e. Kp = 0.98691, Ts = 1011.3 secon, and Td = 91 secon.

Fig.1. Process Flow Diagram of Armfield PCT23MKII pasteurization plant.

Work Station, OPC Client/Server

DF1 communication link

PLC SLC 5/02

Fig. 3. System response against Heater Power

I/O hardwired

B. Heater and Heat Exchanger Modelling Based on Fig. 3 we also identified the model of the heater by considering the response temperature T2 as follows. .

Plant PCT23MKII Miniatur

i.e. Kp = 1, Ts = 1543.6 secon and Td = 25 secon.

Fig. 2 Control System Architecture

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(3)

TABLE II.

System identification is also done to the heat exchanger with heater temperature T2 as an input and temperature T1 as an output. T2 was set at 70°C and the initial temperature T1 was set at 36°C. The water was then circulated to a heat exchanger with a fixed flow rate of 150ml/min whereas the hot water circulation N2 is kept constant at 60%. The system response to input step temperature T2 at 70°C is shown in Fig. 4. From which the following transfer function of the heat exchanger was obtained. .

(4)

.

COHEN COON TUNING METHOD

Controller

Kc

P

1

PI

9 10

12

PD

5 4

6

PID

4 3

4

Ti

Td

-

-

3 30 3 9 20

/ /

6 2 / 22 3 /

32 13

6 8

/ /

4 2

11

/

i.e. Kp = 0.6351, Ts = 30.143 secon and Td = 30 secon. TABLE III.

CONTROLLER DESIGN

A. Control Strategy The system block diagram of closed loop PID control as follows: Set Point

+-

PID

Set point +_

Kc

Ti

Td

PI

0.9/a

3Td

-

PID

1.2/a

2Td

Td/2

Output PIDp

+_

PIDs

Gp(s)

Gs(s)

Output Plant (G(s))

Fig. 6. Block diagram of the PID Cascade control system.

In Fig. 6, PIDp denotes the primary PID controller, PIDs is the PID secondary controller, Gp is the transfer function of the primary system and Gs is the transfer function of the secondary system. The tuning of the parameters of the cascade controller is summarized in TABLE IV. [6].

Fig. 5 system block diagram.

There are several methods of tuning or configuring the PID controller showed in Fig. 5. In this paper, the Cohen Coon and Ziegler Nichols tuning methods as well as the cascade PID control configuration are applied to the system and their performances are then compared to the MPF control method.

TABLE IV.

B. PID Controller Tuning Considering that the process can be modeled as first order system plus time delay, the PID controllers utilized in the systems are tuned using the Cohen Coon [4] and the Ziegler Nichols [5] methods. The tuning parameters of the PID controller for both cases are shown in TABLE II and TABLE III, respectively. In these tables, the parameters Kp is the gain of the system, Td is the delay time, T is the time constant of the system, and a = Kp x (Td/T).

CASCADE TUNING

-

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Controller

C. Cascade Control In addition to standard tuning methods of the PID controller mentioned above, this paper also reports the cascaded configuration of the PID controller. Cascade control has an advantage of reducing the effects of interference on the system. In this study, the secondary controller is set to be the water heating system and the primary controller is set to be the heat exchanger. Fig. 6 shows the diagram block of the cascade controller implemented in this study.

Fig. 4. Response of Heat Exchanger against Hot Water T2

III.

ZIEGLER-NICHOLS TUNING

where 0.5

0.5

and K1 is the gain of the primary system, τ1 is the time constant of the primary system, θ1 is the delay time, K2 is the gain of the secondary system, τ2 is the time constant of the secondary system, and θ2 is time delay of secondary system. D. Model Predictive Control (MPC) In this paper, the MPC method is also applied to the system. In short, the MPC method can be explained as follows [7] : 1. The output on the next time horizon N, called the prediction horizon, is predicted at time t by using the process model. The predicted output is denoted as y(t + k | t) for k = 1 .... N, and depends on the input - output of the system at time t and the control signal u (t + k | t) with k = 0 .... (N-1) is then calculated and sent to the system. 2. The control signal will be calculated by optimizing the cost function to keep the process remains in the reference trajectory. The objective function often chosen to be a quadratic function of the error. 3. The obtained control signal u(t | t) is then sent to the process, and control signal prediction at time t + 1 discarded because the output sampling value y( t + 1 ) is already known. This algorithm then repeated from step 1.

Fig. 7. Process response using cascade controller

At set point 54°C, the simulation dead time is 57 seconds and the experiment dead time is 61 seconds. The simulation steady state error (ESS) is 0.00067 and the experimental ESS is ± 0.14. The experimental maximum overshoot is 53%, whereas the simulation maximum overshoot is 10%. The experimental settling time with 2% tolerance is at t = 955 seconds and the simulation settling time is at t = 869 seconds. Finally, the simulation IAE was obtained to be 2537 while the experimental IAE is 5067.18. At steady state, shown on Fig. 7, disturbance is observed and was arising from the decrease of the flow of cold water F1 from 150ml/min to 50ml/min which isapplied at t=2000 seconds for 500 seconds. The flow was then returned again to its original state that is 150ml / min at t = 2500 seconds. In this case, overshoot arising at a value of 2.3°C or 12.7% at t = 2254 seconds. Once the load is normalized, the temperature increases immediately. The temperature finally undershoot by 2.88°C of the set point or 16% at t = 2593 seconds. The settling time finally return back to normal with a tolerance of 2% at t = 513 seconds.

The prediction output of the MPC follows the following formula

|

∑



|

(5)

where gi is the output when the control signal is u(t-1). The cost function in general can be expressed as ,

B. PID controller tuning using Ziegler-Nichols method The PID controller parameters based on the ZieglerNichols method was found to be Kp = 13 513, Ti = 182 and Td = 45.5. The simulation and experimental results was done for a set point of 54°C. It was obtained that the dead time simulation was 91 seconds and the experiment was 69 seconds. In addition, the simulation settling time with 2% tolerance is 1116 seconds while on the experiment the system could not reached the steady state with 2% tolerance and instead continue to oscillate (cf. Fig. 8).

|

, ∑

∆

1

(6)

where N1 And N2 are the minimum and maximum prediction horizon, respectively, Nu is the control horizon, δ(j) is the error weighting and λ(j) is the control signal weighting. Nu should be chosen smaller than N2 to achieve a fast response whereas N2 must be set bigger than the system time delay. IV.

RESULT AND ANALYSIS

A. PID Tuning on Cascade Control Using TABLE IV, the value of the cascade controller are as follows: secondary controller Kp = 41.385, Ti = 1551.93 and Td = 8.2886. Primary controller with Kp = 1.164, Ti = 60.976 and Td = 19.00042. The response of the system using the cascade controller at set point 54ºC is shown in Fig. 7.

Fig. 8. System response using Ziegler-Nochols tuning method

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The experimental maximum overshoot is found to be 10.40% whereas in the simulation the value is at 17.75%. Moreover, the settling time with ± 5% tolerance are achieved at t = 788 and t = 716 seconds for the experiment and simulation, respectively. Fig. 11 shows the system responses when changes of load of cold water is performed at t = 2000 seconds for 500 seconds. It can be seen that overshoot occurs at 3°C or 17.38% at t = 2331 seconds. After the normalized case, undershoot occurs at 2.14°C of set point or by 15.58% at t = 2644 seconds. C. PID controller tuning using Cohen-Coon method The PID controller parameters are calculated as Kp = 15.267, Ti = 215.83, Td = 32.56. For a set point of 54 C, the dead time of 91 and 70 seconds were observed for simulation and experiment cases. Additionally, maximum overshoot of 12% and 19% were observed in experiment and simulation, respectively. The response in experiment can not reach steady state with ± 2% or ± 5% tolerances, whereas the settling time in simulation with tolerance of ± 2% was achieved at t = 1495 with an IAE of 4631 (cf. Fig. 9).

Fig. 10. System response using MPC.

Fig. 11 Comparison of controller performance under disturbance.

Fig. 11 shows the comparison of different control methods mentioned previously. Since the Cohen-Coon and ZieglerNichols methods result in oscillation that is more than ± 2% (cf. TABLE V), they can not be applied to the system. TABLE V.

Parameters Ts Mp ESS Td SSE MSE Disturbance Mp Ts Undershoot Impulse IAE

Fig. 9. System response using Cohen-Coon tuning method.

Fig. 11 shows the system responses when changes of load of cold water is performed at t = 2000 seconds for 500 seconds. It can be seen that overshoot occurs at 3°C or 41% at t = 2373 seconds. After the normalized case, undershoot occurs at 2.2°C of set point or by 12.7% at t = 2733 seconds. D. MPC Controller The system response using MPC controller is shown in Fig. 10. For a set point of 54°C, the simulation and experimental dead times are 91 and 70 seconds, respectively. The error steady state of the system response is ± 0.18 and without overshoot for both the simulation and experiment case. The settling times in the experiment and simulation with a tolerance of ± 2% are t = 712 seconds and t = 521 seconds, respectively. Fig. 11 shows the system responses when changes of load of cold water is performed at t = 2000 seconds for 500 seconds. It can be seen that overshoot occurs at 3°C or 22% at t = 2437 seconds. Once the load is normalized, the temperature rises by 4.67°C above the set point at t = 2530 sec, then the temperature drops below the set point at t = 2685 seconds.

Cascade 955 53% 0.14 61 61.2 0.122

MPC 712 0.18 70 6.73 0.013

CC 8.80% 70 734.7 1.47

ZN 10.4% 69 76.76 0.15

12.70% 513 16%

22% 463 14%

38.80% 11.80%

17.38% 15.58%

-

-

164.41

56.09

Note: CC : Cohen-Coon, ZN : Ziegler-Nichols, ESS : Error, Ts : time settling, Td : time delay

E. Set Point Tracking and Impuls Response Performance comparison of both the cascade controller and MPC to a set point change from 54°C to 55°C, 57°C, 52°C and back to 54°C are conducted to the systems. Fig. 12 shows the system response for a set point change at t = 1500 from 54°C to 55°C. There exists a delay in the simulation and experiment at 91 seconds. The set point is then raised to 57°C at t = 2000, then decreased to 52°C at t = 2500 and finally returned to 54°C. From the comparison between the simulation and experimental responses, it can be concluded that the system is capable of following the change of set points quite well.

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PERFORMANCE COMPARISON OF VARIOUS CONTROLLERS

This can be seen on total IAE during entire step change for MPC is 1669.78 and 2065.37 for Cascade. For a change in form of impulse disturbance, the effect on observed using cascade controller is a temperature change of 1.7°C while the MPC temperature change only of 0.5°C (cf. Fig. 14). F. Comparison on Power Consumption The comparison of power consumption between MPC and Cascade control is summarized in TABLE VI. TABLE VI. Description

Fig. 12 MPC response to set point changes.

Fig. 13 shows that the cascade controller respondS fast enough to track the new set point but with oscillation. In particular, the greater the set point is increased, the greater the oscillation that occurs and even lead to overshoot. The total IAE due to input changes is 2065.37. Both cascade or MPC have a good response but Cascade Control provides temperature decrease (undershoot) that is higher than the MPC when the change of set point is set from 57ºC to 51ºC.

MPC Power Total (kW) (kJ)

Cascade Power Total (kW) (kJ)

Settling time

0.85

548.85

0.76

650.76

Steady state

0.38

171.82

0.33

162.50

Flow Disturbance

0.26

259.79

0.25

268.41

Step input

0.38

731.40

0.32

653.04

Impulse

0.52

11.51

1.62

30.78

At settling time, the MPC consume smaller energy than the cascade controller. This IS because the cascade controller experiences overshoot before the steady state. At steady state, the MPC energy consumption is greater than the cascade controller. This is because the MPC provides a certain amount of power to maintain the temperature according to the set point. On the other hand, the cascade controller works based on the error between the output and set point, causing output ripple phenomenon occurs. With the provision of load changes, namely by reducing the flow rate of cold water (feed water) from 150ml/min to 50ml/min, the MPC consumes less energy than the cascade controller (cf. Fig. 15). This occurs because the MPC achieves settling condition more quickly than the cascade controller, i.e. 955 seconds for MPC and 1008 seconds for cascade controller. For the set point tracking, the total energy consumed by the MPC is larger than the cascade control (cf. Fig. 16). However, the cascade controller produces greater error as indicated by IAE of 2065.37 as compared to IAE of 1669.78 in MPC.

Fig. 13 Comparison to set point changes.

The lowest temperature that may occur is 49ºC and the MPC is able to follow the set point temperature setting. It can also be observed that the IAE of the cascade controller is higher at 1350.49, and MPC IAE is 901.46. The overall response for a step input using MPC is better than the cascade controller.

Fig. 15 Comparison of power consumption under load disturbance.

Fig. 14. Comparison of system response against impuls set point.

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COMPARISON OF POWER CONSUMPTION

energy consumption of 268.41 kJ of energy consumption and settling time of 1008 seconds. The best performance of MPC is observed if the process variables change drastically due to the presence of input disturbances. This is indicated by the MPC controller which produces an IAE of 19.1%, which is lower when compared to the cascade. REFERENCES [1]

[2]

Fig. 16 Comparison of power consumption for step input

[3]

V. CONCLUSION In this paper, the development of control systems for a pasteurization process plant based on cascade controller and MPC method is presented. The simulation and experimental result shows that the MPC performance is better than the cascade controller as shown with by the absence of overshoot, a settling time of 712 seconds, an integral absolute error (IAE) of 3884, an energy consumption of 613.2 kJ and the ability to resist a step input interference while maintaining an IAE of 1669.78. Under disruption due to load changes, it was found that the cascade controller performs better with an IAE of 1197.84, an

[4] [5]

[6]

[7]

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