Intelligent real-time pressure tracking system using a

Article

Intelligent real-time pressure tracking system using a novel hybrid control scheme

Transactions of the Institute of Measurement and Control 2018, Vol. 40(13) 3744–3759 Ó The Author(s) 2018 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0142331217730886 journals.sagepub.com/home/tim

Zhonglin Lin, Tianhong Zhang and Qi Xie

Abstract In this paper, a novel hybrid control scheme is proposed to improve the control performance in a real-time pressure tracking system using fast on-off solenoid valves. In this novel hybrid control scheme, an original approach named Time Interlaced Modulation (TIM) is developed to replace the traditional Pulse Width Modulation (PWM) approach. Besides using TIM, a new switching method which is referred as seven possible control modes is designed to ensure the proper switching states of the valves. Moreover, a controller with field programmable gate array (FPGA) is chosen to guarantee the real-time implementation of the control algorithm. All the simulations and experimental results implemented on FPGA verify the feasibility of the hybrid control scheme.

Keywords Modeling, on-off solenoid valve, electro-pneumatic system, pressure tracking, sliding-mode control

Introduction In the aircraft development process, a pressure tracking system is needed to generate the dynamic pressure for simulating the real flight environment or aero-engine running environment. The pressure tracking system is also widely used in the hardware-in-the-loop (HIL) simulation for flight control systems or aero-engine control systems. Indeed, a pressure tracking system is one kind of electro-pneumatic system. The most important part of electro-pneumatic system is the control valve, and two types of electro-pneumatic valves are mentioned frequently in recent studies: servo valves and fast onoff solenoid valves. In contrast to servo valves, fast on-off solenoid valves present nonlinear behavior in pneumatic control system but they are much cheaper and simpler than servo valves. Several articles proposed the idea of using air pressure control loop as the inner control loop to achieve accurate position of a pneumatic system (Lee et al., 2002; Miyata et al., 1991; Noritsugu and Takaiwa, 1995; Situm, 2013). The average mass flow rate of the solenoid valve controlled by the Pulse Width Modulation (PWM) (Noritsugu, 1986, 1987) is nearly linear (Nguyen et al., 2007) and approximately the one controlled by a servo valve. This is the most distinctive advantage of the PWM approach. The dead time of the on-off valve has restricted the development of the PWM approach (Ahn and Lee, 2005; Bangaru and Devaraj, 2015; Le et al., 2010). This paper is focused on designing a new approach for a realtime pressure tracking system without using the traditional PWM approach. The new control approach is called Time Interlaced Modulation (TIM). In traditional PWM-based electro-pneumatic system, every valve is controlled separately by PWM and there is no relevant article about taking two or more valves as a whole to control. TIM is a scheme that

regards two fast on-off solenoid valves as a whole and drives each valve to act for interlaced time at the same control period. On account of the determined switching speed of the fast on-off solenoid valve, this scheme optimizes the combination of switching time of the high pressure side and the low pressure side. TIM adjusts the pressure precisely by making a precise interlaced time on the basis of the minimum opening time of the valve. An accurate mathematical model is needed for calculating the interlaced time online, so the modeling of the whole electro-pneumatic system is researched. Few studies have deeply investigated the solenoid on-off valve (Ilchmann et al., 2006; Lee et al., 2002; Szente and Vad, 2001; Tao et al., 2002). This article is focused on modeling a 3-2 on-off solenoid valve. Besides using TIM to drive the solenoid valve, a controller is also needed in the electro-pneumatic system. Owing to the linear characteristics of the PWM driven solenoid on-off valve, proportional-integral-derivative (PID) control and sliding-mode control (SMC) is widely carried out in modern control industries (Modirrousta et al., 2015; Shen et al., 2004; Xing et al., 2012). The great advantage of SMC is the antidisturbance to changes in the pneumatic system and robustness

Jiangsu Province Key Laboratory of Aerospace Power System, College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, P.R. China Corresponding author: Tianhong Zhang, Jiangsu Province Key Laboratory of Aerospace Power System, College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu Province, 210016, P.R. China. Email: [email protected]

Lin et al. to the uncertainty of the pneumatic models. Another important technique used in the systems of pneumatic actuators and manipulators is hybrid control (Christofides et al., 2005). This technique is recently implemented in physico-chemical and fluid control processes (Pourkargar and Armaou, 2013, 2015) for nonlinear distributed parameter systems and achieves great performances. The method of hybrid position/force control (Raibert et al., 1981) can also be carried out in the pressure control systems. It is also vital to choose an appropriate hardware platform when designing a real-time pressure tracking system. Traditional electro-pneumatic systems barely use field programmable gate array (FPGA) as the hardware platform. Only two articles are found using FPGA as the hardware platform in the field of electro-pneumatic control systems (dos Santos and Ferreira, 2014; Ramos-Arreguin et al., 2010). This article is focused on building a real-time pressure tracking system using FPGA platform. After the introduction section, section 2 introduces modeling of a 3-2 on-off solenoid valve including electromagnetic subsystem (solenoid), mechanical subsystem (spool) and the fluid subsystem (orifice), modeling of the power electronic converter and modeling of the air chamber. Section 3 introduces the new TIM approach, SMC and complete hybrid control scheme. Section 4 is the experimental setup which includes the FPGA setup and the experimental setup of the electro-pneumatic system. The experimental results and discussions are in Section 5. The conclusion of this research is in the last section.

Mathematical modeling of the electropneumatic system A typical 3-2 fast on-off solenoid valve is studied in this paper. The cutaway view of this valve is shown in Figure 1. This valve consists of manual operator, fixed core, epoxy encapsulated solenoid, armature, push pin, spool, orifice and return spring. As shown in Figure 1, the fixed core and the epoxy encapsulated solenoid are connected to the armature by the return spring. The spool is linked to the armature by the push pin and connected to the shell of the valve by a return spring. Figure 1(a) and 1(b) show the direction of gas flow of a 3-way normally closed connecting configuration and the valve is in the closed state (a) and open state (b), respectively. In this configuration, passage 1 is connected to the air supply, passage 2 is connected to the actuator and passage 3 is connected to the atmosphere. When the operator is de-energized, the armature keeps still and the spool is in its position of the closed state. So, the air cannot pass from the air supply to the actuator. Once the solenoid is energized by voltage and current, the magnetic field generated by the fixed core and the solenoid drives the armature to move toward the fixed core. Thus, the push pin pushes the spool to other position. In this position, the air passage between the air supply and the actuator is open through an orifice. Figure 2 shows the decomposed mathematical model of the electro-pneumatic system. The input voltage in this paper is generated by an industrial digital output module and the power output of this module cannot meet the power demand of the valve. So, a power electronic converter is designed to

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Figure 1. Cutaway view of a typical 3-2 fast on-off solenoid valve. (a) Closed, (b) Open.

meet the demand. The valve is divided into four subsystems according to previous research (Topc xu et al., 2006). The electrical subsystem and the magnetic subsystem are usually called the electromagnetic subsystem. These subsystems are based on Kirchhoff’s voltage law (KVL) and the electromagnetic field theory. The mechanical-fluid subsystem consists of the mechanical subsystem and the fluid subsystem which is based on Newton’s mechanics and the fluid mechanics. Every subsystem is closely related and makes up the valve system together. In the last part of this section, the model of the air chamber will be discussed.

Modeling of the power electronic converter In this study, the input voltage is generated by a bidirectional digital output module and the voltage type is 5 V/TTL. The circuit of the power electronic converter is shown in Figure 3. The main component of this circuit is the power N-MOSFET. The selected IRF640N is a HEXFET Power MOSFET which is designed for fast switching and ruggedized applications. When the input voltage is low, the VGS is 0 and lower than VDS , the MOSFET is turned off and ID is 0. Once the input voltage turns to 5 V, VDS is higher than the threshold voltage (VT ) of the MOSFET and the MOSFET is turned on. The dynamic switching model of this power electronic converter is based on the following equation (Sakurai and Newton, 1990)   1 2 ID = b ðVGS  VT ÞVDS  VDS 2

ð1Þ

where b is the drivability factor of the MOSFET.

Modeling of the electrical subsystem The actual electrical subsystem is an AC circuit of the solenoid. The equivalent circuit of the electrical subsystem is shown in Figure 4. This circuit consists of an inductance L and a resistance Rc . By using KVL, the equation of this system can be written as VDS (t) = Rc I(t) + Vs (t)

ð2Þ

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Figure 2. Block diagram of the valve subsystems and the interactions with the power electronic converter and the air chamber.

Vs (t) = N f_ s (t)

ð3Þ

where N is the number of solenoid turns.

Modeling of the magnetic subsystem Analyzing of the magnetic subsystem is focused on fs (t). The basic equation of the magnetic subsystem can be written by applying Ampere circuit law NI(t) = Hs (t)ls (t)

ð4Þ

where Hs (t) is the magnetic field intensity in the whole magnetic circuit, and ls (t) is the total length of magnetic circuit. Substituting these following basic equations 8 B > > f > : B= A Figure 3. Circuit of the power electronic converter.

ð5Þ

into (4), the whole magnetic flux of the magnetic circuit fs (t) can be expressed as fs (t) =

msm As NI(t) ls (t)

ð6Þ

where msm and As are the permeability of the magnetic circuit and the effective cross-sectional area of flux path, respectively. The flux path is actually divided into three parts: two in the air gap and one in the fixed core. If the fringing of the flux can be ignored, the total length of the magnetic circuit ls (t) can be given as (Taghizadeh et al., 2009) 8 < ls (t) = 2ur lag (t) + li us : ur = u0 Figure 4. Equivalent circuit of the electrical subsystem.

If the whole magnetic flux of the magnetic circuit is fs (t), the equation of Vs (t) can be written according to the relationship between flux and voltage

ð7Þ

where lag (t) and li are the length of the magnetic circuit in the air gap and in the fixed core respectively. us and u0 are the permeability of the fixed core and the air, and ur is the relative permeability of the fixed core. As shown in Figure 5, before the solenoid is energized, the distance Zk between the fixed core and the armature is the maximum distance of lag (t). Once

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Figure 5. Movement of the armature in the magnetic subsystem. Figure 6. Force analysis of the mechanical subsystem.

the solenoid is energized, the armature moves towards the fixed core and the moving distance is Z(t). So, the equation of lag (t) can be written as lag (t) = Zk  Z(t)

ð8Þ

Substituting us , (7) and (8) into (6), the equation of fs (t) can be stated as ms As NI(t) fs (t) = 2ur (Zk  Z(t)) + li

ð9Þ

Modeling of the electromagnetic subsystem Substituting the derivative form of fs (t) into (2) and (3), we can get the equation of VDS (t) as 

ms As NI(t) 2u (Z r k  Z(t)) + li VDS (t) = Rc I(t) + N f_ s (t) = Rc I(t) + N dt ! _ _ 2 ð2ur (Zk  Z(t)) + li ÞI(t) + 2ur I(t)Z(t) = Rc I(t) + ms As N ð2ur (Zk  Z(t)) + li Þ2



d

ð10Þ Also, the equation of I(t) can be stated as

FM (t) =

ms As N 2 I 2 (t) ð2ur (Zk  Z(t)) + li Þ2

ð13Þ

Modeling of the mechanical subsystem The force analysis of the push pin and the spool is shown in Figure 6. The movement of the push pin and the spool is mainly affected by the magnetic attraction force of the solenoid and the pressure forces from port 1 to port 2 and from port 3 to port 2. It is also under the effect of the damp force and the spring force. By applying Newton’s second law, the equation of mechanical subsystem is achieved as € FM (t) + Fin  Fout  Fdamp  Fspring1  Fspring2 = ms Z(t) ð14Þ in which ms is the whole mass of the push pin and the spool. The expressions of these forces can be stated as 8 _ Fdamp = BZ(t) > > > > < Fspring1 = K1 (Z(t) + b1 ) Fspring2 = K2 (Z(t) + b2 ) > > > > Fin = (A1  A2 )Pin : Fout = (A4  A3 )Pout

ð15Þ

I(t) =

 ð _ 2ur (Zk  Z(t)) + li 2ur I(t)Z(t) ð V (t)  R I(t) Þ  DS c ms As N 2 ð2ur (Zk  Z(t)) + li Þ ms As N 2

ð11Þ By applying the following fundamental formula FM (t) =

f2 As ms

ð12Þ

the magnetic attraction force of the solenoid can be given as

in which B is the damping coefficient, K1 and K2 are the spring coefficients of spring 1 and 2, b1 and b2 are the pre-tensions of spring 1 and 2, A1 , A2 , A3 and A4 are cross sections that are affected by the pressure from three ports and Pin and Pout are the pressures at port 1 and 2. So, the equation of the magnetic attraction force of the solenoid can also be given as FM (t) = (A2  A1 )Pin + (A4  A3 )Pout + b1 + b2 _ + ms Z(t) € + (K1 + K2 )Z(t) + BZ(t)

ð16Þ

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Modeling of the fluid subsystem The electrical subsystem, magnetic subsystem and mechanical subsystem are all focused on describing the movement of the spool controlled by the fluid flow through the valve orifice which is shown in Figure 1. The fundamental equation (Andersen and Binder, 1967; McCloy and Martin, 1980) for the mass flow rate through a valve orifice is stated as 8 0:0405C pffiffiffid Pin S > ; > Tsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <  2  gþ1  _ in ; Pout Þ ¼ C P S mðP g 2g Pout g d in >  PPout ; > Pin Rðg1Þ : pffiffiTffi in

Pout Pin

 Pcr

Pout Pin

> Pcr ð17Þ

where Cd is the discharge coefficient of the valve, T is stagnation temperature at the air supply, S is the effective crosssectional area of the orifice and R is ideal gas constant. This equation consists of two nonlinear equations for subsonic and sonic (choked) flow regimes. A critical value Pcr for the pressure ratio is used to divide these two regimes.

Modeling of the air chamber The thermodynamic analysis based on energy conservation and continuity equations is the foundation of the modeling of the pressure dynamics of the air chamber. In this research, the air chamber is an air chamber (container) with fixed volume V. The sketch map of the air chamber is shown in Figure 2. By applying the ideal gas law, the pressure P inside the chamber can be described as PV = mRT

ð18Þ

where P, V, m and T are the pressure, volume, mass and temperature of the air inside the chamber. As the volume of the air chamber V is fixed, the derivative form of P can be achieved by differentiating equation (18) and using the energy equation and the heat transfer terms

Figure 7. The simulating frame of the integrated model.

gRT _ in , Pout ) P_ = m(P V

ð19Þ

Verification of the mathematical modeling All the mathematical models are numerically simulated in the MATLAB/Simulink 2016a environment. The simulating frame of the integrated model of the electro-pneumatic system is shown in Figure 7. The integrated simulation in MATLAB/ Simulink is divided into several subsystems: input signal, model of power electronic converter, model of valve, model of air chamber and output signal. In Figure 7, each block represents an m-file in MATLAB and all the equations used in each block (m-file in MATLAB) are marked out. The equations used in the blocks are written in the form of S-function and saved as m-file. The system parameters are also written into the m-file. After building each block, all blocks are connected in the Simulink. Using the S-function module in the Simulink and setting up the inputs and outputs of each block, all the blocks can be linked in the order of Figure 7. Then, the solver of the configuration parameters in Simulink is set to ode45 (Dormand-Prince) and variable-step (max step size 0.0002 and min step size 0.0001), other options are in default state. Simultaneously, the actual current, pressure and mass flow rate are also measured from the real system for verification of the mathematical model. From the model of valve, we can get the switching time characteristics of the on-off valve that are shown in Figure 8. In the opening period Ton of the valve, the current in the solenoid increases rapidly with the growth of the magnetic attraction force of the solenoid until the end of Ton1 . In Ton2 the magnetic attraction force of the solenoid starts to be larger than the spring force and the pressure force, so the spool starts to move. In the actual test, we can find that the spring force helps the spool move. The current in this period decreases to a certain level because the inductance of the solenoid is increased with the movement of the armature. In the

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System parameters

Nominal value

V Ps P0 T N Rc ur As

Volume of the air chamber Supply pressure Ambient pressure Stagnation temperature of the supply Number of solenoid turns Resistance of the solenoid Relative permeability of the fixed core Effective cross-sectional area of flux path Length of the magnetic circuit in fixed core Maximum distance between fixed core and armature Damping coefficient Spring coefficient Pre-tension of spring Discharge coefficient of the valve Effective cross-sectional area of the orifice

1:63104 m3 83105 Pa 13105 Pa 293.15 K 1 100 10 O 110 0.85 cm2

li Zk

Figure 8. The switching time characteristics of the on-off valve.

end of Ton2 , the armature reaches its final position and the current stops decreasing. Ton1 , which is influenced by the magnetic attraction force, the spring force and the pressure force is the first period of Ton and Ton2 , which is governed by the movement of the armature is the second period of Ton . In this research, the total opening time Ton is approximately 6 ms, Ton1 is nearly 3.62 ms, which is of 60.33% of the total opening time and Ton2 is nearly 2.38 ms. The closing time Toff is similar to the opening time and consists of Toff 1 and Toff 2 . The total closing time Toff is approximately 2 ms, Toff 1 , which is governed by the magnetic force, the spring force and the pressure force, is nearly 1.41 ms, which is 70.5% of the total opening time and Toff 2 , which is influenced by the movement of the armature, is nearly 0.59 ms. Figure 8 also shows the measured current of the solenoid and the curves of the simulated current and the measured current show great agreement. To verify the fluid model of the valve and the model of air chamber, the filling and exhausting of the air chamber is simulated and measured. As shown in Figure 9, the two curves are well matched. All the system parameters used in modeling and control designs are listed in Table 1.

Figure 9. The filling and exhausting curves of the air chamber.

B K b Cd S

11 cm 0.33 mm 0.21 Ns/m 13104 N/m 1 mm 0:173103 m/v 113106 m2

Controller design for the electropneumatic system Traditional PWM method is widely used in the pneumatic systems for position control applications because of its linear characteristics between the input signal and average output voltage. While only using PWM method cannot achieve good performances in pressure control as nonlinearity of the fluid equation (17). A new control approach called Time Interlaced Modulation (TIM) is proposed to overcome this problem.

TIM TIM is based on PWM and combines two PWM waveforms into one TIM. In TIM, the net air flow inside the air chamber is adjusted by the differential air flow created by the inlet onoff valve and the outlet on-off valve under the premise that

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Figure 10. Principle of TIM. (a) Fill, (b) Exhaust.

the maximum and minimum switching condition of the onoff valve is satisfied. Figure 10 shows the basic filling and exhausting condition with TIM. TIM1 is the driving pulse for the inlet valve and the pulse time of TIM1 is Tc + Ton . TIM2 is the driving pulse for the outlet valve and the pulse time of TIM2 is Ton . The periods of the TIM1 and TIM2 are both Tt . Obviously, both TIM1 and TIM2 satisfy the minimum switching condition of the on-off valve. To meet the maximum switching condition, the following condition must be satisfied Tc  Tt  Toff  Ton

ð20Þ

In the filling condition, the open time of the inlet valve in one TIM control period is larger than the open time of the outlet valve in one TIM control period by Tc .Tc is noted as the effective control pulse. In fact, Ton also influences the air flow as the filling speed is not equal to the exhausting speed at the same time that both valves are open. The exhausting condition is similar to the filling condition, the open time of the outlet valve in one TIM control period is larger than the open time of the inlet valve in one TIM control period by Tc . TIM has two periods of time interlaced; the first one is Ton , which is the synchronized time that inlet and outlet valves are open for. In one control period, the synchronized pulse can start from 0 to Tt  Toff  Ton . Figure 11 shows three typical conditions of the synchronized pulse. From the fluid equation (17) we can see that the filling speed and exhausting speed vary in different pressure. If the synchronized pulse starts from 0 of a control period, the pressure changes can be seen in Figure 11(a). When filling speed is smaller than exhausting

speed, the pressure decreases below the primitive value and then starts to increase. From Figure 11(b) to Figure 11(c), we can find that later time the synchronized pulse is on, better the pressure change looks. In Figure 11(c), the variation trend of the pressure fits the control input in the best way. The control effect of exhausting is similar to the effect of filling. So, we put the synchronized pulse in the end of the whole control pulse in TIM. The second time interlaced time of TIM is Tc , which is the main control time of the inlet valve. We propose an experienced equation based on the mathematical model of the electro-pneumatic system

DPup = P_ up Tc + k(P_ up + P_ dowm )Toff , for filling DPdown = P_ down Tc + k(P_ up + P_ dowm )Toff , for exhausting ð21Þ

or ! 8 > DPup P_ dowm > > Toff , for filling < Tc = _  k 1 + _ Pup Pup   > P_ up DPdown > > : Tc = Toff , for exhausting  k 1+ P_ down P_ down

ð22Þ

where DPup and DPdown is the pressure change in Tc , P_ up is the time derivative of the filling speed, P_ down is the time derivative of the exhausting speed, and k is the experienced factor. In this equation, P_ up and P_ dowm are both calculated from the model and Tc can be directly calculated from the pressure change in the air chamber.

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Figure 11. The synchronized pulse starts from different time for filling. (a) The synchronized pulse starts from 0, (b) The synchronized pulse starts after a short period, (c) The synchronized pulse starts from Tc .

Sliding-mode controller

The Lyapunov-like function can be defined as

Besides using TIM as the basic driving pulse, a sliding-mode controller is designed for the nonlinear system. Considering electro-pneumatic system as a one order nonlinear system, x is the state variable, y is the system output, u is the control signal and f is the system dynamic function, then

x_ = f + u + d y=x

ð23Þ

If yo is the input signal, the error signal e and the time derivative of the error signal can be defined as

e = yo  y e_ = y_ o  y_

ð24Þ

As the system is one order nonlinear system, the sliding function s=e

ð25Þ

We select the sliding function as s_ =  esgn(s)  ks

ð26Þ

Substituting (23), (24) and (25) into (26), the control law can be achieved as u = y_ o  f  d + esgn(e) + ke

ð27Þ

1 V = s2 2

ð28Þ

V_ = s_s

ð29Þ

and

Considering the selected sliding function (26), we can get k k V_   ejsj  ks2 =  V  ejsj   V 2 2

ð30Þ

According to the lemma (Petros et al., 1996), for V : ½0, ‘) 2 R, the solution of the inequation V_   aV + f , 8t  t0  0 is V (t)  ea(tt0 ) V (t0 ) +

ðt

ea(tt) f (t)dt

ð31Þ

t0

k If the parameters are a = , f = 0, then (30) can be achieved 2 as k  (t  t0 ) V (t)  e 2 V (t0 )

ð32Þ

So V (t) converges to 0 in exponential form, the parameter k decides the rate of convergence. The sliding surface s = 0 can be reached within a finite time.

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Table 2. Seven possible control modes. Mode

Mode 1 Rapidly fill

Mode 2 Slowly fill

Mode 3 Slightly fill

Mode 4 Close

Condition Inlet Valve Outlet Valve

Sp\e Fully open Fully closed

St\e