- Email: [email protected]
Flow control system design without flow meter sensor
Sensors and Actuators A 185 (2012) 127–131
Contents lists available at SciVerse ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Flow control system design without flow meter sensor Jeongju Choi Technical Center for High-Performance Valves, Dong-A University, Republic of Korea
a r t i c l e
i n f o
Article history: Received 27 April 2012 Received in revised form 11 July 2012 Accepted 16 July 2012 Available online 7 August 2012 Keywords: Pressure sensor Flow control Artificial intelligent Valve Friction
a b s t r a c t This paper proposes a flow control system using only pressure meters and the flow coefficients of the valves. To obtain the flow coefficient of a control valve, flow rates for various opening and closing valve angles were first measured and an equation to approximate these values was derived. A valve disk control system was designed to improve the control function by analyzing the characteristics of mechanical friction caused by the movements of the disk. The functionality of the proposed control system was verified by comparing the measured flow rates with predicted flow rates of the proposed method. © 2012 Elsevier B.V. All rights reserved.
1. Introduction A variety of apparatus and materials are used by plumbing systems in plant engineering. Within those systems, valves are critical components controlling the flows of working fluids. Valves are classified as globe valves, butterfly valves, gate valves, etc., by disk type and driving method, and into control valves and manual valves, by operation method [1,2]. Control valves are further subdivided into pneumatic valves, hydraulic valves and motor valves, depending on their actuator type. However, regardless of the type of actuators, the flow rates and fluid pressures can be controlled by the opening and closing the disk of valve angles [3,4]. To control fluids in this way, the dynamic equation between flow rate and the valve opening degree should be estimated, which will be the basis of the design of the control system regulating the working fluids flowing through pipelines. However, the flow capacity of the valves can vary by the manufacturer of the valves even when they have the same shape. Hence, a variable determining valve capacity should be chosen for use in designing a plumbing system [5,6]. Flow coefficients are widely used as parameter among the various capacity variables [6,7]. To control flow rate in a plumbing system, the feedback control system of the control valve should be designed. The various flow control systems in process control loop have been studied in [8–10]. These approaches designed the flow control system with flow signal. However, contact type flow meters create pressure drops, which require more energy for pumping [11,12]. To address this,
E-mail address: [email protected] 0924-4247/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sna.2012.07.010
non-contact flow meters have been developed. However, the costs of non-contact type flow meters are comparatively more expensive than conventional flow meters [13]. In response to this, flow sensorless control system was proposed by [11,14], these approaches were based on the neural network algorithm. In general, the neural network algorithm is difficult to apply to the industrial field. Therefore, the novel flow rate control method is proposed in this paper. The proposed control system is used as the flow coefficient instead of the flow meter. In the control system, the main controller for the degree of valve disk is used by the sliding mode controller, and LuGre friction model was applied to improve the control performance of the valve system [9,15,16]. The performance of the proposed control method was verified by comparing the measured flow rates with the predicted flow rates of the proposed method. This paper is divided into 5 sections. Section 2 explains how the flow coefficient of a valve is experimentally estimated. Section 3 shows the analysis of the mechanical friction characteristics. Section 4 explains how a position control system for the valve disk is designed and a flow control experiment is conducted for analysis, based on the mechanical friction and flow characteristics of the valve analyzed experimentally. Lastly, Section 5 presents the conclusions.
2. Estimation of the valve flow coefficient When a valve opens, volume of fluid that passes into the valve is called capacity of valve. It is fixed and it depends on the type of valve and port size. Even if the same size and same kind of valve is used, the capacity is different according to vendors. And it is changed by various factors such as the kind of fluid, differential
128
J. Choi / Sensors and Actuators A 185 (2012) 127–131
Fig. 1. Schematic diagram for experiment of flow coefficient.
pressure, temperature, viscosity, specific gravity, pressure, port design and dimensions. Furthermore, even the same size valves have both big pressure loss and small pressure loss which also depends on the kind of valve. These fluid conditions are called coefficient capacity, it can be selected kind of valve and size easily. There is a Cv factor for coefficient capacity. Cv is used generally and it is a represented factor for fluid at 5–40 ◦ C that flows into valve by 1 gal/min (3.785 l/min). In a situation of special travel and differential pressure 1 lbf/in.2 (0.07 kg/cm2 ), the formula equation for Cv is represented by
Cv = Q
G p
(1)
where Q is flow rate, G is specific gravity and p is differential pressure. The flow coefficient measuring methods indicated in international standards IEC 534-1 and IEC 534-2-3 were used to determine the flow coefficient, Cv . To analyze the relationship between the opening and closing angles of a valve and its flow coefficient, the valve was opened in 10% increments and the flow coefficient was calculated for each increment. The estimation equation was derived from the flow coefficients calculated experimentally and a nonlinear curve fitting algorithm. Fig. 1 shows the schematic diagram of the flow coefficient experiment. A 100 mm diameter butterfly valve was used for the experiment. The pressure meter used was a PSHF 0500RCBJ model from Sensys and the flow meter used was an MC 308C from Euromag. To estimate the flow coefficient according to the opened valve angle, flow coefficients at different percentages of valve openings were obtained through experiments as shown in Fig. 2. Based on the experiment results, the estimated flow coefficient is fitted by nonlinear curve fitting method. Fig. 3 shows the fitted and
Fig. 3. Estimated flow coefficient.
experiment results. The fitted result is evaluated by R2 which is calculated based on Eq. (3). The result of R2 is 0.99953. Cˆ v = 767.25 −
2.67
(2)
where Cˆ v is approximated flow coefficient and x is percentage of opened valve.
R2 ≡ 1 −
(Cv − Cˆ v )
2
(Cv − C¯ v )
2
(3)
where C¯ v = (1/n) Cv , n is number of experiment data. Using Eqs. (1) and (2), the estimated flow rate can be induced as follows:
Qˆ = Cˆ v
p G
(4)
3. Analysis of valve friction characteristics To design a control system for the angle of valve disk, not only did the characteristics of the valve disk movement have to be analyzed, but the friction caused by mechanical contact should also be properly compensated. Accordingly, this paper analyzes the friction characteristics of the butterfly valve and suggests a friction compensation control system based on it. First, to analyze the friction characteristics of the butterfly valve, an experimental apparatus for torque measurement was set up, as in Fig. 4. The torque sensor used in the experiment was an SBS-100K from Sensortech. The signals recorded by the torque sensor were measured by an NI USB-6221 DAQ (Data Acquisition) board from NI (National Instruments). In general, there are two types of friction – static friction (such as viscous friction and Coulomb friction) and dynamic friction (such as the Streibeck effect, stick-slip and hysteresis) [15]. In order to represent these friction phenomena, LuGre model which is widely used to mathematically describe the characteristics of static and dynamic frictions is applied. LuGre model is represented in Eqs. (5)–(7). fLuGre = 0 z + 1 z˙ + 2 v
(5)
˙ || z˙ = ˙ − z ˙ g()
(6)
˙ = g()
Fig. 2. Flow coefficient in accordance with percentage of opened valve.
766.38 1 + (x/68.75)
2 1 ˙ [Fc + (Fs − Fc )e−(/vs ) ]. 0
(7)
where 0 , 1 and 2 are positive constant, Fc and Fs are Coulomb and static friction, vs is Streibeck velocity.
J. Choi / Sensors and Actuators A 185 (2012) 127–131
129
Fig. 6. Measured torques and fitted result according to velocity. Fig. 4. Experimental apparatus for friction measuring.
To identify the LuGre model’s parameters, the torque values were recorded as the valve opens at constant velocity. The friction values measured during the experiment are in Fig. 5. The torque values measured are averaged with consideration for noises and the torque value per velocity and they are used to identify the coefficient of LuGre model. Since the characteristic of friction depends
on the mechanical contact dynamics, we used the G.A. algorithm to find the coefficient of LuGre model for the butterfly valve. The estimated results based on LuGre model and measured frictions for butterfly valve are represented in Fig. 6. The specific values of LuGre model are in Table 1. The simple procedure of G.A. logic is represented as follows:
Fig. 5. Measured frictions in accordance with velocity.
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J. Choi / Sensors and Actuators A 185 (2012) 127–131
Table 1 Estimated parameters of LuGre model for the butterfly valve. Parameter
Estimated value
0
1
2
Fc
Fs
vs
1.02 × 105
0.145
11.251
5.214
14.325
0.014
Procedure GA( ) initialize (population); evaluate (population); while not (terminal condition satisfied) do m Pool = reproduce(population); mutationPool = crossover(m Pool); population = mutation(mutationPool); evaluate(population); end while end procedure
4. Flow control system design and experiments To control flow in a plumbing system, the fluid flow rate through a pipeline should be measured. However, flow meters are expensive and have spatial limitations. For this reason, the novel flow control method is proposed in this paper. The main idea of proposed control method is that the pressure meters attached at both ends of the valve are used instead of a flow meter. The pressure deviation at both ends of the valve can predict the flow coefficient and the flow rate can be predicted from this flow coefficient. Using the relationship among flow coefficient, flow rate and the percentage of valve opening, the flow rate control system can be designed without flow meter. In order to apply to the proposed method, the robust position control of valve disk should be designed. To design a robust position control of valve disk, a sliding mode controller, widely used in nonlinear robust control systems, was used in this paper. The considered valve was the butterfly valve. Since a sliding mode controller generates chatter through a switching term, which negatively impacts the hardware, a structure including a continuous term based on the reaching law was used to reduce this effect [17,18]. The value of the switching term within the sliding mode controller affected by uncertainties was also minimized in advance by compensating for the frictions included in the valve’s dynamic behavior. The dynamic equation for the valve’s disk rotation is in Eq. (8). J ¨ = u − Ffriction
(8)
where J is inertia of valve disk. The sliding surface for the sliding mode controller was chosen, as in Eq. (9). s = e˙ + e
Fig. 7. Experimental apparatus for the flow control.
To determine the reference angle for the robust position control of valve disk, d in accordance with the desired flow rate, Qd , the relationship among flow rate, flow coefficient and valve opening induced in previous section was used. As shown in Eqs. (13) and (14), the designed valve angle, d , can be decided by pressure difference at both ends of the valve, p and the flow rate control law can operate only using the pressure difference.
d = 61.88
Cv,d = Qd
1/2.67
766.38 −1 767.25 − Cv,d
(13)
G p
(14)
To evaluate the performance of the proposed control system, the experiment equipment was set up as shown in Fig. 7. For the experiment, a desired flow rate of 120 m3 /h was used. The resulting experimental flow rate is indicated in Fig. 8. In the figure, the solid line shows the result of flow rate control based on the proposed control system and the dotted line shows the flow rate from flow meter. The average of deviation between the proposed method and the desired flow rate is 98.5%. The measured pressure difference at both ends of the valve is indicated in Fig. 9. At this time, the estimated friction torque is represented in Fig. 10. From the experimental results, it is found that the proposed control system
(9)
where e = d − , d is reference angle and is positive definite design parameter. The equivalent control law based on the reaching law for the sliding mode control system was designed, as in Eq. (10). ˙ ueq = Ffriction + J(¨ d + e)
(10)
The robust term with a continuous term is in Eq. (11). ur = −Ds − Ksgn(s)
(11)
where D and K are positive definite design parameters. In order to reduce the modeling uncertainty, friction term, Ffriction , in Eq. (10) was used by LuGre friction model identified in previous section. Finally, the robust position controller for the valve disk is designed as follows: ˙ − Ds − Ksgn(s) u = Ffriction + J(¨ d + e)
(12)
Fig. 8. Estimated and measured flow rate.
J. Choi / Sensors and Actuators A 185 (2012) 127–131
131
The functionality of the proposed flow control system was validated by comparing the flow rates measured by a conventional flow meter with the predicted flow rates of the proposed control method. Acknowledgment This study was supported by the Valve Center from the Regional Innovation Center (RIC) Program of Ministry of Knowledge Economy (MKE). References
Fig. 9. Pressure deviation between inlet and outlet.
Fig. 10. Estimated friction torque during flow rate control.
can perform sufficiently the control of fluid flow without a flow meter. 5. Conclusions A variety of valves are installed within a plumbing system to control the flow and pressure of working fluids. However, expensive flow meters are required to implement a flow control system. This paper proposes a method of controlling the flow rate by only installing pressure meters at both ends of the valve instead of installing flow meters. The proposed control system utilizes the flow coefficient and the pressure difference between the front and back ends of the valve. The valve disk position controller is designed with consideration of the characteristics of mechanical frictions.
[1] P. Thomas, Simulation of Industrial Processes for Control Engineers, Elsevier, 1999, pp. 60–67. [2] K. Ogawa, T. Kimura, Hydrodynamic characteristics of a butterfly valve – prediction of torque characteristics, ISA Transactions 34 (4) (1995) 327–333. [3] P. Naseradinmousavi, C. Nataraj, Nonlinear mathematical modeling of butterfly valves driven by solenoid actuators, Applied Mathematical Modelling 35 (5) (2011) 2324–2335. [4] M.J. Chern, C.C. Wang, C.H. Ma, Performance test and flow visualization of ball valve, Experimental Thermal and Fluid Science 31 (6) (2007) 505–512. [5] H.E. Merritt, Hydraulic Control System, John Wiley & Sons, 1967. [6] P. Macini, E. Mesini, R. Viola, Laboratory measurements of non-Darcy flow coefficients in natural and artificial unconsolidated porous media, Journal of Petroleum Science and Engineering 77 (3–4) (2011) 365–374. [7] M. Shanwei, Z. Chuan, C. Jiangping, C. Zhiujiu, Experimental research on refrigerant mass flow coefficient of electronic expansion valve, Applied Thermal Engineering 25 (14–15) (2005) 2351–2366. [8] R. Srinivasan, R. Rengaswamy, Approaches for efficient stiction compensation in process control valves, Computers and Chemical Engineering 32 (1–2) (2008) 218–229. [9] A. Kayihan, F.J. Doyle, Friction compensation for a process control valve, Control Engineering Practice 8 (7) (2000) 799–812. [10] A. Stenman, F. Gustafsson, K. Forsman, A segmentation-based approach for detection of stiction in control valves, International Journal of Adaptive Control and Signal Processing 17 (2003) 625–634. [11] T. Leephakpreeda, Flow-sensorless control valve: neural computing approach, Flow Measurement and Instrumentation 14 (6) (2003) 261–266. [12] M.A. Atmanand, M.S. Konnur, A novel method of using a control valve for measurement and control of flow, IEEE Transactions on Instrumentation and Measurement 48 (6) (1999) 1224–1226. [13] Q. Yang, Z. Zhang, M. Liu, J. Hu, Numerical simulation of fluid flow inside the valve, Procedia Engineering 23 (2011) 543–550. [14] E. Pathmanathan, R. Ibrahim, Development and implementation of fuzzy logic controller for flow control application, in: International Conference on Intelligent and Advanced Systems (ICIAS), 2010, pp. 1–6. [15] A.H. Brian, P. Dupont, D.W.C. Canudas, A survey of models, analysis tools and compensation methods for the control of machines with friction, Automatica 30 (7) (1994) 1083–1138. [16] G. Claudio, Comparison of friction models applied to a control valve, Applied Mathematical Modelling 189 (9) (2008) 97–112. [17] J.J. Slotine, W. Li, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ, 1991. [18] D.Q. Zhang, S.K. Panda, Chattering-free and fast-response sliding mode controller, Proceedings of IEE Control Theory and Application 146 (2) (1999) 171–177.
Biography Jeongju Choi received the B.S. in mechanical engineering from Dong-A University in 1997. He received the M.S. and Ph.D. in mechanical and intelligent systems engineering from Pusan National University in 2001 and 2006, respectively. He studied as a postdoctoral fellow in the Department of Industrial and Manufacturing Systems Engineering at the University of Michigan-Dearborn in 2008. He is a research professor in Dong-A University. His research interests include dynamics and control of mechanical systems.
Contents lists available at SciVerse ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Flow control system design without flow meter sensor Jeongju Choi Technical Center for High-Performance Valves, Dong-A University, Republic of Korea
a r t i c l e
i n f o
Article history: Received 27 April 2012 Received in revised form 11 July 2012 Accepted 16 July 2012 Available online 7 August 2012 Keywords: Pressure sensor Flow control Artificial intelligent Valve Friction
a b s t r a c t This paper proposes a flow control system using only pressure meters and the flow coefficients of the valves. To obtain the flow coefficient of a control valve, flow rates for various opening and closing valve angles were first measured and an equation to approximate these values was derived. A valve disk control system was designed to improve the control function by analyzing the characteristics of mechanical friction caused by the movements of the disk. The functionality of the proposed control system was verified by comparing the measured flow rates with predicted flow rates of the proposed method. © 2012 Elsevier B.V. All rights reserved.
1. Introduction A variety of apparatus and materials are used by plumbing systems in plant engineering. Within those systems, valves are critical components controlling the flows of working fluids. Valves are classified as globe valves, butterfly valves, gate valves, etc., by disk type and driving method, and into control valves and manual valves, by operation method [1,2]. Control valves are further subdivided into pneumatic valves, hydraulic valves and motor valves, depending on their actuator type. However, regardless of the type of actuators, the flow rates and fluid pressures can be controlled by the opening and closing the disk of valve angles [3,4]. To control fluids in this way, the dynamic equation between flow rate and the valve opening degree should be estimated, which will be the basis of the design of the control system regulating the working fluids flowing through pipelines. However, the flow capacity of the valves can vary by the manufacturer of the valves even when they have the same shape. Hence, a variable determining valve capacity should be chosen for use in designing a plumbing system [5,6]. Flow coefficients are widely used as parameter among the various capacity variables [6,7]. To control flow rate in a plumbing system, the feedback control system of the control valve should be designed. The various flow control systems in process control loop have been studied in [8–10]. These approaches designed the flow control system with flow signal. However, contact type flow meters create pressure drops, which require more energy for pumping [11,12]. To address this,
E-mail address: [email protected] 0924-4247/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sna.2012.07.010
non-contact flow meters have been developed. However, the costs of non-contact type flow meters are comparatively more expensive than conventional flow meters [13]. In response to this, flow sensorless control system was proposed by [11,14], these approaches were based on the neural network algorithm. In general, the neural network algorithm is difficult to apply to the industrial field. Therefore, the novel flow rate control method is proposed in this paper. The proposed control system is used as the flow coefficient instead of the flow meter. In the control system, the main controller for the degree of valve disk is used by the sliding mode controller, and LuGre friction model was applied to improve the control performance of the valve system [9,15,16]. The performance of the proposed control method was verified by comparing the measured flow rates with the predicted flow rates of the proposed method. This paper is divided into 5 sections. Section 2 explains how the flow coefficient of a valve is experimentally estimated. Section 3 shows the analysis of the mechanical friction characteristics. Section 4 explains how a position control system for the valve disk is designed and a flow control experiment is conducted for analysis, based on the mechanical friction and flow characteristics of the valve analyzed experimentally. Lastly, Section 5 presents the conclusions.
2. Estimation of the valve flow coefficient When a valve opens, volume of fluid that passes into the valve is called capacity of valve. It is fixed and it depends on the type of valve and port size. Even if the same size and same kind of valve is used, the capacity is different according to vendors. And it is changed by various factors such as the kind of fluid, differential
128
J. Choi / Sensors and Actuators A 185 (2012) 127–131
Fig. 1. Schematic diagram for experiment of flow coefficient.
pressure, temperature, viscosity, specific gravity, pressure, port design and dimensions. Furthermore, even the same size valves have both big pressure loss and small pressure loss which also depends on the kind of valve. These fluid conditions are called coefficient capacity, it can be selected kind of valve and size easily. There is a Cv factor for coefficient capacity. Cv is used generally and it is a represented factor for fluid at 5–40 ◦ C that flows into valve by 1 gal/min (3.785 l/min). In a situation of special travel and differential pressure 1 lbf/in.2 (0.07 kg/cm2 ), the formula equation for Cv is represented by
Cv = Q
G p
(1)
where Q is flow rate, G is specific gravity and p is differential pressure. The flow coefficient measuring methods indicated in international standards IEC 534-1 and IEC 534-2-3 were used to determine the flow coefficient, Cv . To analyze the relationship between the opening and closing angles of a valve and its flow coefficient, the valve was opened in 10% increments and the flow coefficient was calculated for each increment. The estimation equation was derived from the flow coefficients calculated experimentally and a nonlinear curve fitting algorithm. Fig. 1 shows the schematic diagram of the flow coefficient experiment. A 100 mm diameter butterfly valve was used for the experiment. The pressure meter used was a PSHF 0500RCBJ model from Sensys and the flow meter used was an MC 308C from Euromag. To estimate the flow coefficient according to the opened valve angle, flow coefficients at different percentages of valve openings were obtained through experiments as shown in Fig. 2. Based on the experiment results, the estimated flow coefficient is fitted by nonlinear curve fitting method. Fig. 3 shows the fitted and
Fig. 3. Estimated flow coefficient.
experiment results. The fitted result is evaluated by R2 which is calculated based on Eq. (3). The result of R2 is 0.99953. Cˆ v = 767.25 −
2.67
(2)
where Cˆ v is approximated flow coefficient and x is percentage of opened valve.
R2 ≡ 1 −
(Cv − Cˆ v )
2
(Cv − C¯ v )
2
(3)
where C¯ v = (1/n) Cv , n is number of experiment data. Using Eqs. (1) and (2), the estimated flow rate can be induced as follows:
Qˆ = Cˆ v
p G
(4)
3. Analysis of valve friction characteristics To design a control system for the angle of valve disk, not only did the characteristics of the valve disk movement have to be analyzed, but the friction caused by mechanical contact should also be properly compensated. Accordingly, this paper analyzes the friction characteristics of the butterfly valve and suggests a friction compensation control system based on it. First, to analyze the friction characteristics of the butterfly valve, an experimental apparatus for torque measurement was set up, as in Fig. 4. The torque sensor used in the experiment was an SBS-100K from Sensortech. The signals recorded by the torque sensor were measured by an NI USB-6221 DAQ (Data Acquisition) board from NI (National Instruments). In general, there are two types of friction – static friction (such as viscous friction and Coulomb friction) and dynamic friction (such as the Streibeck effect, stick-slip and hysteresis) [15]. In order to represent these friction phenomena, LuGre model which is widely used to mathematically describe the characteristics of static and dynamic frictions is applied. LuGre model is represented in Eqs. (5)–(7). fLuGre = 0 z + 1 z˙ + 2 v
(5)
˙ || z˙ = ˙ − z ˙ g()
(6)
˙ = g()
Fig. 2. Flow coefficient in accordance with percentage of opened valve.
766.38 1 + (x/68.75)
2 1 ˙ [Fc + (Fs − Fc )e−(/vs ) ]. 0
(7)
where 0 , 1 and 2 are positive constant, Fc and Fs are Coulomb and static friction, vs is Streibeck velocity.
J. Choi / Sensors and Actuators A 185 (2012) 127–131
129
Fig. 6. Measured torques and fitted result according to velocity. Fig. 4. Experimental apparatus for friction measuring.
To identify the LuGre model’s parameters, the torque values were recorded as the valve opens at constant velocity. The friction values measured during the experiment are in Fig. 5. The torque values measured are averaged with consideration for noises and the torque value per velocity and they are used to identify the coefficient of LuGre model. Since the characteristic of friction depends
on the mechanical contact dynamics, we used the G.A. algorithm to find the coefficient of LuGre model for the butterfly valve. The estimated results based on LuGre model and measured frictions for butterfly valve are represented in Fig. 6. The specific values of LuGre model are in Table 1. The simple procedure of G.A. logic is represented as follows:
Fig. 5. Measured frictions in accordance with velocity.
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J. Choi / Sensors and Actuators A 185 (2012) 127–131
Table 1 Estimated parameters of LuGre model for the butterfly valve. Parameter
Estimated value
0
1
2
Fc
Fs
vs
1.02 × 105
0.145
11.251
5.214
14.325
0.014
Procedure GA( ) initialize (population); evaluate (population); while not (terminal condition satisfied) do m Pool = reproduce(population); mutationPool = crossover(m Pool); population = mutation(mutationPool); evaluate(population); end while end procedure
4. Flow control system design and experiments To control flow in a plumbing system, the fluid flow rate through a pipeline should be measured. However, flow meters are expensive and have spatial limitations. For this reason, the novel flow control method is proposed in this paper. The main idea of proposed control method is that the pressure meters attached at both ends of the valve are used instead of a flow meter. The pressure deviation at both ends of the valve can predict the flow coefficient and the flow rate can be predicted from this flow coefficient. Using the relationship among flow coefficient, flow rate and the percentage of valve opening, the flow rate control system can be designed without flow meter. In order to apply to the proposed method, the robust position control of valve disk should be designed. To design a robust position control of valve disk, a sliding mode controller, widely used in nonlinear robust control systems, was used in this paper. The considered valve was the butterfly valve. Since a sliding mode controller generates chatter through a switching term, which negatively impacts the hardware, a structure including a continuous term based on the reaching law was used to reduce this effect [17,18]. The value of the switching term within the sliding mode controller affected by uncertainties was also minimized in advance by compensating for the frictions included in the valve’s dynamic behavior. The dynamic equation for the valve’s disk rotation is in Eq. (8). J ¨ = u − Ffriction
(8)
where J is inertia of valve disk. The sliding surface for the sliding mode controller was chosen, as in Eq. (9). s = e˙ + e
Fig. 7. Experimental apparatus for the flow control.
To determine the reference angle for the robust position control of valve disk, d in accordance with the desired flow rate, Qd , the relationship among flow rate, flow coefficient and valve opening induced in previous section was used. As shown in Eqs. (13) and (14), the designed valve angle, d , can be decided by pressure difference at both ends of the valve, p and the flow rate control law can operate only using the pressure difference.
d = 61.88
Cv,d = Qd
1/2.67
766.38 −1 767.25 − Cv,d
(13)
G p
(14)
To evaluate the performance of the proposed control system, the experiment equipment was set up as shown in Fig. 7. For the experiment, a desired flow rate of 120 m3 /h was used. The resulting experimental flow rate is indicated in Fig. 8. In the figure, the solid line shows the result of flow rate control based on the proposed control system and the dotted line shows the flow rate from flow meter. The average of deviation between the proposed method and the desired flow rate is 98.5%. The measured pressure difference at both ends of the valve is indicated in Fig. 9. At this time, the estimated friction torque is represented in Fig. 10. From the experimental results, it is found that the proposed control system
(9)
where e = d − , d is reference angle and is positive definite design parameter. The equivalent control law based on the reaching law for the sliding mode control system was designed, as in Eq. (10). ˙ ueq = Ffriction + J(¨ d + e)
(10)
The robust term with a continuous term is in Eq. (11). ur = −Ds − Ksgn(s)
(11)
where D and K are positive definite design parameters. In order to reduce the modeling uncertainty, friction term, Ffriction , in Eq. (10) was used by LuGre friction model identified in previous section. Finally, the robust position controller for the valve disk is designed as follows: ˙ − Ds − Ksgn(s) u = Ffriction + J(¨ d + e)
(12)
Fig. 8. Estimated and measured flow rate.
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131
The functionality of the proposed flow control system was validated by comparing the flow rates measured by a conventional flow meter with the predicted flow rates of the proposed control method. Acknowledgment This study was supported by the Valve Center from the Regional Innovation Center (RIC) Program of Ministry of Knowledge Economy (MKE). References
Fig. 9. Pressure deviation between inlet and outlet.
Fig. 10. Estimated friction torque during flow rate control.
can perform sufficiently the control of fluid flow without a flow meter. 5. Conclusions A variety of valves are installed within a plumbing system to control the flow and pressure of working fluids. However, expensive flow meters are required to implement a flow control system. This paper proposes a method of controlling the flow rate by only installing pressure meters at both ends of the valve instead of installing flow meters. The proposed control system utilizes the flow coefficient and the pressure difference between the front and back ends of the valve. The valve disk position controller is designed with consideration of the characteristics of mechanical frictions.
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Biography Jeongju Choi received the B.S. in mechanical engineering from Dong-A University in 1997. He received the M.S. and Ph.D. in mechanical and intelligent systems engineering from Pusan National University in 2001 and 2006, respectively. He studied as a postdoctoral fellow in the Department of Industrial and Manufacturing Systems Engineering at the University of Michigan-Dearborn in 2008. He is a research professor in Dong-A University. His research interests include dynamics and control of mechanical systems.