RCGA based PID controller with feedforward control for a heat exchanger system

Transcription

1 Journal of the Korean Society of Marine Engineering, Vol. 1, No. pp. 11~17, 17 ISSN (Print) J. Korean Soc. of Marine Engineering (JKOSME) ISSN (Online) Original Paper RCGA base PID with feeforwar control for a heat exchanger system Hyo-Sung Choi 1 Yun-Hyung Lee 2 Tea-Su Ahn 3 Chan-Ha Lee Myung-Ok So (Receive October 17, 17; Revise December 1, 17;Accepte December 27, 17) Abstract: A heat exchanger is commonly use in a chemical process an/or ships to transfer heat from a hot flui through a soli wall to a cooler flui. Various types of PID s have been aopte to control the temperature of a heat exchanger to guarantee control performance. The inherent limitation of PID s, however, is that the acts after isturbance istorts the require control objective. If isturbances occur frequently, a PID woul not be able to attain the esire steay state response. To overcome this limitation, feeforwar control must be aopte with PID control. Feeforwar control works in combination with PID control as it cannot operate alone. This paper presents a metho to control the temperature of a heat exchanger by using a PID with a feeforwar. The parameters of the PID are tune using the real-coe genetic algorithm (RCGA) by minimizing the integral absolute error. A set of simulations are carrie out to compare the set-point tracking an isturbance rejection performances of the propose with conventional PID s. Keywors: Heat exchanger, PID, Feeforwar, RCGA 1. Introuction A heat exchanger is wiely use in chemical plants an/or ships because it can sustain a wie range of temperatures an pressures. There are ifferent types of heat exchangers, but a shell an tube heat exchanger system is most wiely use [1]. The main purpose of a heat exchanger system is to transfer heat from a hot flui to a cooler flui; thus, controlling the temperature of the outlet flui is of prime importance. An accurate mathematical moel is require to esign a. However, it is ifficult to obtain a suitable mathematical moel because the ynamics of a heat exchanger epens on many factors such as temperature ifference, heat transfer area, flow rate of fluis, an flow patterns. Various stuies have propose ifferent temperature control methos for heat exchangers such as feeforwar PID control [2], optimal linear fuzzy control [3], PI type fuzzy control [], PID, an internal moel control [5][6]. PID control is a classical metho, an it has been stuie for the last several ecaes an is wiely use in the fiel. The inherent limitation of a PID, however, is that the acts after isturbance istorts the require control objective. If isturbances occur frequently, a PID woul not be able to attain the esire steay state response. To overcome this rawback, feeforwar control must be aopte with PID control. This paper presents a linear PID with feeforwar control that shows a better control performance an systematic tuning than conventional PID s. The temperature control of the heat exchanger may cause time elays an isturbances; thus a PID combine with a feeforwar is esigne to improve control performance. The parameter tuning methos of the PID inclue the close-loop an open-loop tuning methos such as the Z N (Ziegler Nichols) tuning metho, (Internal Moel Control) tuning metho, an RCGA (Real Coe Genetic Algorithm) tuning metho [7]-[9]. Among them, the RCGA tuning metho provies an optimal solution by using the evaluation function uner given conitions. This stuy, therefore, uses the RCGA technique to tune the PID. In orer to improve the tracking performance of the control system, the PID is tune while the isturbance is fixe, an the set value is change stepwise. Further, the PID tune by RCGA an a feeforwar are combine to examine isturbance rejection while the measure isturbance Corresponing Author (ORCID: Division of Marine Engineering, Korea Maritime an Ocean University, 727, Taejong-ro, Yeongo-gu, Busan , Korea, smo@kmou.ac.kr, Tel: Department of Mechatronics Engineering, Grauate School of Korea Maritime University, chs890806@naver.com, Tel: Department of Eucation, Korea Institute of Maritime an Fisheries Technology, omse5@aum.net, Tel: Korea Port Training Institute, chamsuly@aum.net, Tel: Ministry of National Defense, lch1577@mn.go.kr, Tel: This is an Open Access article istribute uner the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricte non-commercial use, istribution, an reprouction in any meium, provie the original work is properly cite. Copyright c The Korean Society of Marine Engineering

2 Hyo-Sung Choi Yun-Hyung Lee Tea-Su Ahn Chan-Ha Lee Myung-Ok So is applie to the heat exchanger system. A set of simulations are carrie out to compare set-point tracking an isturbance rejection performances with conventional PID s an show the feasibility of the propose metho. 2. Moeling of heat exchanger Figure 1 shows the temperature control system of the shell an tube heat exchanger use in inustrial fiels. The experimental ata available for the heat exchanger system is summarize in other stuies [][11]. A linearize mathematical moel of heat exchanger is evelope from the experimental ata. 2.1 Saturator There is a physical limit to the operation of an actual actuator. Therefore, to approach a more realistic problem, a saturator is consiere an expresse as Equation (1). (1) an inicate the minimum an maximum values of the saturator, respectively. Figure 1: Temperature control system of shell an tube heat exchanger This system consists of a heat exchanger, a, an I/P converter, a control valve, an a temperature transmitter (TT). Overheate steam at a temperature of 180 [ ] supplie from the boiler flows into the tubes after the control valve ajusts the amount of steam. On the other han, flui at a temperature of 30 [ ], pumpe by a centrifugal pump, flows through the shell. These conitions are assume to be equilibrium states for simulations. Different assumptions have been consiere in this stuy. The first assumption is that the inflow an outflow rates of flui are same, so that the level of flui is constant in the heat exchanger. The secon assumption is that the heat storage capacity of the insulating wall is negligible. The inlet an outlet temperatures measure by a thermocouple are converte to current signals from [ma] to [ma] an are implemente in the feeback path of the control system. The implements the control algorithm, compares the col flui output with the esire value, an then provies the necessary comman to the final control element (valve) via the actuator unit. The actuator unit is a current-to-air pressure converter, an the final control unit is an air-to-open (fail-close) valve. The actuator unit converts the output within a range of - [ma] into a stanarize air pressure signal within a range of [bar]. The valve is actuate accoring to the ecisions. 2.2 Actuator An actuator is a evice that uses electricity, hyraulic pressure, air pressure etc. to perform proper operation for input signal. The actuator consists of an I/P converter that converts an electrical signal into a pneumatic signal an a control valve. The transfer function can be expresse as a first orer system as follows. (2) an are the outputs of the saturator an actuator, respectively. is the I/P converter gain an is the control valve gain. is the actuator gain an is the time constant of the actuator. 2.3 Heat exchanger The transfer function of the heat exchanger can be expresse as a first orer system with time elay by using Equation (3). (3) an are the gain an time constants of the heat exchanger, respectively, an L represents the time elay. 2. Sensor The transfer function of the sensor can be expresse as a first orer system as follows. () Journal of the Korean Society of Marine Engineering, Vol. 1, No.,

3 RCGA base PID with feeforwar control for a heat exchanger system an are the gain an time constants of the sensor, respectively. 2.5 Disturbance Assuming that the transfer function oes not have a time elay, can be expresse as a first orer system as follows. (5) an are the gain an time constants of isturbance, respectively. Further, it is assume that is equal to the time constant of the heat exchanger. Figure 2 shows the control system consisting of a saturator, actuator, an heat exchanger an the isturbance. u k a 1as u a Ls kxe 1 s Figure 2: Block iagram of controlle system This can be expresse by the following equation. x + y k 1xs (6) is the outlet temperature of the flui, an is the inlet temperature of the flui uner isturbance. Table 1 summarizes the various parameters use in this stuy. The minimum an maximum values of the actuator are [ma] an [ma], respectively. Table 1: Parameters of the heat exchanger system Descriptions Values Unit Gain of actuator Gain of valve 2 - Gain of I/P converter Gain of heat exchanger - Gain of isturbance 1 - Gain of sensor Time constant of actuator 3 [s] Time constant of heat exchanger 30 [s] Time constant of sensor [s] Time elay of heat exchanger 1 [s] + y 3. PID combine with feeforwar 3.1 PID A conventional linear is use as a PID, an its transfer function is expresse as follows. (7), an are the proportional gain, integral time, an erivative time, respectively. There are ifferent tuning methos of a PID. Some methos are empirical methos, some methos are base on frequency response analysis, an other methos are base on the minimization of performance measures. Despite avances, most PID s are tune using the trial an error metho. 3.2 Feeforwar The inherent limitation of a feeback is that the acts after isturbance istort the require control objective. If isturbances occur frequently, the PID woul not be able to attain the esire steay state response. To overcome this limitation, feeforwar control must be aopte with PID control. Feeforwar control limits the eviation cause by the isturbance while it works uner the conition that the isturbance woul be measure or estimate. Feeforwar control works in combination with feeback control, as it cannot operate alone. Figure 3 shows a control system incorporating the feeforwar. In this system, the close-loop transfer function of the output temperature uner isturbance is as follows. is the transfer function of the feeforwar. is the transfer function of the actuator an heat exchanger. In case the numerator of Equation (8) becomes 0, the isturbance can be remove. (9) Rewriting the above equation, the transfer function of the feeforwar is as follows. (8) () Journal of the Korean Society of Marine Engineering, Vol. 1, No.,

4 Hyo-Sung Choi Yun-Hyung Lee Tea-Su Ahn Chan-Ha Lee Myung-Ok So Controller f Process Figure 5 shows the step response for the SOPTD(Secon Orer Plus Time Delay) system an FOPTD system as the approximate moel. Comparing the two responses shows that the step responses showe goo agreement. y r k s c u usat p y 6 5 s Figure 3: PID control system combine with feeforwar Because there is a time elay in, the orer of the numerator is larger than that of the enominator in. In orer to replace the time elay, is ae in the enominator of, an then, Equation () is expresse as follows. (11) is the filter time constant, an its value varies between 0 an 1. In this paper, was set to 0.9 an to 1 through trial an error.. Tuning of the PID.1 Z N tuning technique The Z N technique presente in this paper repeats trial an error by using the MATLAB software. The limit gain was 16., an the limit cycle was 3.6 [s] at this time..2 tuning technique In orer to use the technique, the transfer function of the plant have to be given by the FOPTD (First Orer Plus Time Delay) system. Figure shows the process of searching,, an the values of FOPTD obtaine using RCGA, an we can obtain =.976, = , = Outputs SOPTD FOPTD Figure 5: Step responses of SOPTD an FOPTD system.3 RCGA-base tuning technique First, in orer to improve the tracking performance, the parameters of the PID are tune while the isturbance is fixe an the set value is change stepwise. This paper proposes RCGA as a tuning metho an the IAE(Integral Absolute Error) is use as an evaluation function. (13) is [,, ] an e(t) is the error between the set value an the output, an the integration time is a sufficiently large value enough to ignore integral values thereafter. Because optimization techniques operate on a probabilistic basis in general, the solutions obtaine vary slightly epening on the configuration of the initial group. Therefore, in orer to ensure that the solution searche with RCGA is optimal, simulations are performe five time by using ranom see values, an the average value of the results is etermine as final solutions. Figure 6 shows the concept of searching each parameter of the PID by RCGA. Objective function J k L Parameters y r k s RCGA e(t) t 0 PID u 0 f p y Generation Figure : Search for,, an using RCGA s Figure 6: Parameter optimization of PID using RCGA Journal of the Korean Society of Marine Engineering, Vol. 1, No.,

5 RCGA base PID with feeforwar control for a heat exchanger system In orer to obtain ing the optimal parameter using RCGA, the number of generations, population, crossover, mutation were set to, 30, 0.9 an 0.05, respectively. Figure 7 shows the process of searching,, of the PID using RCGA. Objective function J K p Generation Figure 7: RCGA-base tuning process for PID Table 2 summarizes the parameters obtaine from the propose technique an the other techniques. Table 2: Parameters of the PID s Metho RCGA () Simulation an review In orer to valiate the propose, simulations were performe with the sampling time of 0.01[s], an the propose was compare with the Z N an technique. 5.1 Tracking performance of PID Figure 8 shows the outputs an control inputs when the set value is change from [ C] to 60 [ C], uner the assumption that isturbance oes not exist. y(t)[ ] [ma] K i K Figure 8: Tracking responses when is step-wisely increase from [ C] to 60 [ C] Parameters Table 3 summarizes the rising time, overshoot, setting time an absolute error integration. Table 3: Tracking performance Z N RCGA () rising time [s] Overshoot [ ] Settling time [s] IAE From Figure 8 an Table 3, it can be seen that rising time of the Z N technique is the shortest, while the overshoot value an settling time are very large. The overshoot value of the technique is slightly smaller than those of other methos, but the rising an settling times are very large. The overshoot value of the propose RCGA technique is very similar to that of other techniques, while the rising an settling times are very small, corresponing to excellent results. 5.2 Disturbance rejection performance of PID without feeforwar In the above iscussion, it was foun that the RCGA-base PID has a relatively goo performance in the tracking problem compare with other methos. Next, simulation is performe to examine the isturbance rejection performance when a measure isturbance is applie to the heat exchanger system. The temperature of col flui is assume to ecrease stepwise from 30 [ C] to [ C] after [s]. Figure 9 shows the control results, an Table summarizes MV (maximum variation) an MV time, recovery time, an absolute error integration. y(t)[ ] [ma] Figure 9: Disturbance rejection responses without feeforwar when ecreases stepwise from 30 [ C] to [ C] Journal of the Korean Society of Marine Engineering, Vol. 1, No.,

6 Hyo-Sung Choi Yun-Hyung Lee Tea-Su Ahn Chan-Ha Lee Myung-Ok So Table : Disturbance rejection performance without feeforwar Z N RCGA () MV time [s] MV [ ] Recovery time [s] IAE Disturbance rejection performance of PID combine with feeforwar Because the feeforwar oes not affect the tracking performance, the isturbance rejection performance with feeforwar is shown intensively in Figure. Table 5 summarizes the MV an MV time, recovery time, an absolute error integration. y(t)[ ] [ma] Figure : Disturbance rejection responses with feeforwar when is step-wisely ecrease from 30 [ C] to [ C] Table 5: Disturbance rejection performance with feeforwar Z N RCGA () MV time [s] MV [ ] Recovery time [s] IAE Accoring to Figure 9 an Figure, the PID combine with the feeforwar shows better isturbance rejection performance. Especially, the RCGA-base PID shows excellent isturbance rejection performance when the feeforwar is combine. From these simulations, it is clear that a PID combine with a feeforwar is a much better option for isturbance rejection control problem rather than conventional PID control. 6. Conclusion This paper implemente a conventional PID an a PID with a feeforwar to control the outlet temperature of a shell an tube heat exchanger system. A mathematical moel of the heat exchanger was evelope using experimental ata of previous stuies. The parameters of the PID were tune using the RCGA technique. The performance of the s was evaluate using transient characteristics an error inices. From the simulation results, it was foun that the performance of the RCGA-base PID combine with the feeforwar control was superior uner isturbance. The classical PID showe a higher MV an MV time whereas the RCGA-base PID with feeforwar reuce the MV, MV time an also obtaine a goo recovery time. Reference [1] T. N. L. Vu, J. T. Lee, an M. Y. Lee, Design of multi-loop PID s base on the generalize -PID metho with Mp criterion, International Journal of Control, Automation, an Systems, vol. 5, no. 2, pp , 07. [2] N. K. Navi, A. Sakhvati an S. H. Hosseini, Design of a PID fee-forwar for controlling output flui temperature in shell an tube heat exchanger, Journal of Electrical an Electronic Engineering, vol. 3, no. 2-1, pp. 30-3, 15. [3] A. Maii, M. Diaf, an J. P. Corriou, Optimal linear PI fuzzy esign of a heat exchanger, Chemical Engineering an Processing: Process Intensification, vol. 7, no. 5, pp , 08, [] M. Paney, K. Ramkumar, an V. Alagesan, Design of fuzzy logic for a cross flow shell an tube heat- exchanger, IEEE-International Conference On Avances In Engineering, Science An Management, pp. 1-15, 12. [5] S. Pahee, Controller esign for temperature control of heat exchanger system: Simulation stuies, WSEAS Transactions on Systems an Control, vol 9, pp , 1. [6] G. M. Sarabeevi an B. M. Laila, Temperature control of shell an tube heat exchanger system using internal moel s. 16 International Conference on Next Generation Intelligent Systems, pp. 1-6, 16. Journal of the Korean Society of Marine Engineering, Vol. 1, No.,

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