A HYBRID CONTROLLER DESIGN FOR KEEPING CONSTANT VOLTAGE AND CURRENT OF A GAS METAL ARC WELDING SYSTEM

Pandu Sandi Pratama, Tan-Tung Phan*, Hak Kyeong Kim, and Sang Bong Kim

Department of Mechanical and Automotive Engineering, Pukyong National University, Busan 608-739, Korea

*Faculty of Mechanical Engineering, Hochiminh City University of Technology, Hochiminh, Vietnam

ABSTRACT

This paper aims to design a hybrid controller for keeping constant voltage and current of a Gas Metal Arc Welding (GMAW). The proposed controller makes output welding current and voltage of digital GMAW system track their setting values easily and quickly. Modellings of GMAW power supply and wire feeding unit are presented. Based on the modelings, two controllers are designed. First, P controller is proposed in order to keep the output welding voltage of GMAW power supply to the setting value based on modeling of GMAW power supply (PS-GMAW). Second, a fuzzy-sliding mode controller (FSMC) is proposed to change the electrode feed rate in order to achieve the output welding current to the setting value based on dynamics modeling of wire feeding unit (WFU). The feedback control gain from the fuzzy inference rule base can be obtained by fuzzifying the sliding surface. To verify the effectiveness of the proposed controller, the proposed controller is compared with the conventional PID controller using simulation. The output current of GMAW system using Fuzzy-Sliding Mode Control (FSMC) is better than using conventional PID with regard to not only rising time but also settling time and steady state error.

1. INTRODUCTION

Gas Metal Arc Welding (GMAW) is the most popular welding machine used in various industries. GMAW is a welding process which joins metals by heating the metals to their melting point with an electric arc. The arc is shielded from contaminants in the atmosphere by a shielding gas. In the welding process, the output welding current and voltage are the decisive factors on the quality of welding product. In order to get the best quality of welding results, the output welding current and voltage must be constantly controlled during the welding process. Several controllers have been applied to the welding systems. PID is very simple, but it is not suitable for nonlinear systems [1]. In sliding mode control, chattering phenomenon in digital application will excite high frequency unmodelled dynamics which are undesired in the control system [2]. To solve

the problem, a new control method is needed. This paper proposes a controller for keeping

constant voltage and constant current of GMAW. The proposed digital GMAW system makes output welding current and voltage track their setting values easily and quickly. Based on modeling of GMAW power supply (PS-GMAW), P controller is proposed to keep the output welding voltage of GMAW power supply to the setting value. Based on dynamics modeling of wire feeding unit (WFU), fuzzy-sliding mode controller (FSMC) is proposed to change the electrode feed rate in order to achieve the output welding current to the setting value. To verify the effectiveness of the proposed controller, the proposed controller is compared with the conventional PID controller using simulation results. The output current of GMAW system using Fuzzy-Sliding Mode Control (FSMC) is better than using conventional PID with regard to not only rising

time but also settling time and steady state error.2. DYNAMIC SYSTEM MODELING

The basic of GMAW equipment is shown in Fig. 1. The GMAW system uses CO2 as shielding gas. The wire feed speed of Wire Feeding Unit (WFU) has range from about 1.9 to 30m/min. It consists of 24V DC motor, gearbox, guide tube clamp and feed rolls. For welding electrode, 1.2 mm aluminum electrode is used.

Fig. 1 Basic GMAW equipment. (1) Shielding gas; (2) DC motor and gear box;

(3) welding electrode roll; (4) WFU; (5) GMAW power supply; (6) control box; (7)

welding gun; (8) workpiece; (9) control cable.

The schematic circuit of GMAW power supply is shown in Fig. 2. Power supply with 220V AC and 60 Hz is rectified using 1 phase bridge diode, and then using DC link capacitor smooths the rectified DC voltage. Two pairs of IGBT with full bridge configuration inverts the smoothed DC voltage into 20 kHz AC voltage. The output voltage can be controlled by changing the duty cycle of PWM for IGBT’s gate trigger. High frequency step down transformer with ferrite core reduces the output voltage to 16 VAC - 36 VAC, and then this output voltage is rectified by one pair of high frequency diode.

Fig. 2 Schematic circuit of GMAW.

The GMAW power supply is designed with two feedback, voltage and current. Based on the setting values and the feedback values, the error of voltage and current are determined. Using error of voltage, the proportional controller is designed and applied to control the duty of PWM of an IGBT’s gate to track the voltage setting value during welding process. Using error of current, the Fuzzy-Sliding Mode Controller (FSMC) is designed and applied to control the speed of wire feeding motor to track the current setting value during the welding process. The change of electrode feed rate makes the output welding current change.

2.1. GMAW power supply

The equivalent circuit of the GMAW system can be expressed as Fig. 3. U a, Ra, Rp, Rn, I w and L represent the average output voltage of GMAW power supply, resistance of PS, parasitic resistance in the circuit, resistance between contact tip and wire, welding current and inductance of the GMAW power supply, respectively. The voltage for welding circuit can be expressed as follows [5] :

U a=Ld I w

dt+( Ra+R p+Rn )× I w+(U w+U s h eat h)× Ψ

(1)

where U s heat h is given as a constant value of 14.5 V, and Ψ is a switch parameter and defined as follows :

Ψ ={ 1if arc is on0 if short circuit

(2)Equation (1~2) show that the value of

welding voltage Uw is dependent on GMAW

power supply voltage U a. For this system, welding current is considered as disturbance.

Weldingelectrode

WFU

nR

PR

L

aU

aRArc Work pice

Contact tip

Fig. 3 Circuit layout of the GMAW system2.2. Dynamic model of wire feeding unit

(WFU).

From [5], the relationship between melting rate and welding current is describe by :

W m=K i I w−K uU w (3)

where K i and Ku are the coefficient ratios of the melting-rate to the welding current and welding voltage, respectively. The electrode feed-rate W f must be equal to the electrode melting-rate W m to maintain a stable arc length [5].

W f=W m (4)W f=K i I w−Ku Uw (5)

Therefore, the welding current can be expressed as follows:

I w=W f (s )

K i

+ ∆ GK i

(6)

Where ∆ G=KuU w In this system, a DC servomotor is utilized

to control the DC motor of WFU which controls the electrode feed-rate to keep the welding arc. The dynamic relationship between the electrode feed-rate and the voltage of a DC servomotor can be expressed as follows:

Gm(s)=W f (s)V m(s )

=b0

s2+a1 s+a0

(7)

If ∆ G is considered as disturbance of the system, the transfer function G(s) of the WFU

between V m(s) and I w can be expressed as follows:

G (s )=I w(s )V m(s)

= 1K i

[Gm (s )+∆ Gd ] (8)

G (s )=I w(s )V m(s)

= 1K i [ b0

s2+a1 s+a0

+∆ Gd](9)

where ∆ Gd=∆G /V m

Fig. 4. Block diagram of open loop of WFU

3. CONTROL METHOD.3.1. Voltage controller design for GMAW

power supply.

When the arc is ON, the average voltage output of GMAW power supply in Eq. (1) can be rewritten as follows:

U a=( Rs+R p+Rn ) I w+(Uw+U s h eat h) (10)

The average output voltage of GMAW power supply can be expressed as follows:

U a=2× D× U s (11)

where D is duty of PMW that ranges from 0 to 48%, U s is output voltage of transformer. In this GMAW system, output voltage of transformer is 86V. Using Eqs. (10) and (11), the duty D can be expressed as:

D= 1172 [ ( R s+Rp+Rn) I w+¿(U w+U s h eat h)]

(12)

The relationship between the controller U u and D can be written as:

U u=16 ×100

3D=

U a

H(13)

H= 129/400. From Eqs. (10~13), the average voltage of GMAW can be written as follows:

U u=400129

[(R s+Rp+Rn)I w+(Uw+U s h eat h)](14)

Uw=U a−U s heat h−∆ D ¿ H ×U u−U s h eat h−∆ D (15)

∆ D=(R s+Rp+Rn)× I w is considered as

disturbance. The error voltage eu is defined as:

eu (t )=(U s−Uw)K w (16)

The proposed controller can be stated as:

U u (i )=U u (i−1)+K p× eu (i−1 ) (17)

Fig. 5 Proportional controller for PS-GMAW

3.2. Current controller design for WFU.

In order to control the welding current, Fuzzy-Sliding Mode Control (FSMC) will be applied in WFU system [1]. Recalling Eqs. (6) and (7), the state-equation with zero initial values of system can be expressed as follows :

{x1=W f

x2=W f

x1=x2

x2=−a1 x2−a0 x1+b0 u1

y=I w=c [ x1+∆ G ]

(18)

where x∈ R2=[W f W f ]T is the state vector,

y=I w is the scalar output, and ui=V m is the

scalar controller for WFU, and c=1 /K i. The current error e i is defined as follows :

e i=I s−I w

c(19)

where I s is the constant setting current value. From Eq. (18), derivative of the error in Eq.

(19) can be expressed as,

e i=− x1−∆G=− I w

c(20)

In order to obtain the controller of sliding mode, the sliding surface is defined as [2] :

S= ei ( t )+ λ e i( t) (21)

where λ is a positive constant value. The error e i in the Eq. (21) converges to

zero along the trajectory of S=0. From Eq. (21), if S=0, e i is negative when e i is positive, and vice versa. That is, e i ei ≤ 0. Thus, the equilibrium point of e i converges to zero as t→∞. Derivative of sliding surface can be calculated as follows :

S=[ ( λ−a1 ) e i+a0

c( I s−cei )−b0ui]+d (22)

where d=−a0 ∆ G−a1 ∆ G− ΔG is bounded value.

The Fuzzy-sliding mode controller (FSMC) can be drawn from the Lyapunov’s condition,

V=S S ≤ 0 (23)The fuzzy control rules are as follows:

NB : Negative Big NM : Negative Medium NS : Negative Small ZE/Z: ZeroPS : Positive Small PM : Positive Medium PB : Positive Big and their universe of discourse are all assigned to be {-6, 6}.

The membership functions for these fuzzy sets corresponding to S, S or ui are defined in Fig. 6.

Fig. 6 Membership functions of S, S and ui

In the following, we show that the rule base of the FSMC can be constructed base of Lyapunov’s condition in Eq. (23).

S S=S [( λ−a1 ) ei+a0

c( I s−cei )−b0 ui]+S d

(24)

From Eq. (24), it is seen that if S < 0, then decreasing ui will result in decreasing of S S and that if S > 0, and vice versa. Hence, the control variable ui can designed in an attempt to satisfy the hitting condition S S < 0.

The fuzzy control rule base is shown in Table 1. Then apply the Mamdani's mini- operation fuzzy implication and adopt the center of area as defuzzification method to construct the rule set shown as surface in Fig. 7.

Table 1 Rule Base of FSMC

uiS

P Z N

SP PB PM PSZ PS ZE NSN NS NM NB

Fig. 7 Rule surface of SMFC

4. SIMULATION RESULT.4.1. Identification of parameters for the

transfer function

The transfer function in Eq. (7) can be written as follows :

Gm=W f

V m

=ωmotor × b '

V m

(25)

Gm=b ' kT

( Lam+Ram) (J m s+bm+ke k t)(26)

Gm=b ' kT

Lam J m s2 ( Lam bm+Ram Jm ) s+(Ram bm+ke k t)(27)

Gm=b0

s2+a1 s+a0

(28)

Table 2 Numerical values of DC motor WFUParameters values Units

k e 57.3x10-3 [V sec/ rad ]k T 48x10-2 [ N×m / A ]Ram 1.1 [Ω]Lam 0.9x10-3 [ H ]Jm 0.157x10-4 [ kgm2 ]

τ m=Ram J m/k e k t 6.28x10-3 [ s ]τ e=Lam/Ram 0.82x10-3 [ s ]

In this system the rate of gear box

K gear=1/34, the diameter of feed roll = 40 x 10-3 m. the ratio between the electrode feed-rate and the angular velocity of DC motor is given as:

Fig. 8 GMAW system simulation using MATLAB SIMULINK

b '=W f

ωmotor

=Droll

2× K gear ×60

¿0.0353 (29)

The parameters of transfer function Gm, can be calculate as follows :

b0=b ' k T

Lam Jm

=141542 (30)

a1=Lam bm+Lam Jm

Lam J m

=7077 (31)

a0=Ram bm+k e k t

Lam Jm

=7979476 (32)

The nominal mathematical model of the transfer function Gm(s) is as follows :

Gm(s)=W f (s)V m(s )

= 1415442s2+7077 s+7979476

(33)

The K i depends on a diameter of welding electrode. Based on experimental results, the gain K ican be approximated ranging from 0.041~0.046 for 1.2 mm aluminum electrode [5]. In this paper, K i=0.043 is chosen.

4.2. Simulation Result

Numerical value and initial value used in simulation and experiment are shown in Tables 3 and 4.

Table 3 Numerical value and initial valueParameters Values Unit

Setting current 110 [ A ]Setting voltage 22 [V ]

Diameter Electrode

1.2 [ mm ]

Ra 0.019 [Ω]Rp 0.096 [Ω]Rn 0.017 [Ω]

Table 4 Numerical values and initialGains value Gains Value

K i 0 .043 GS 1/5Kw 0.14 G S 1/10K P 0.51 G U 200λ 350

To verify the effectiveness of proposed controller, the controller is compared with PID controller. Parameters of PID controller are derived using ziegler-nichols method. From this method, PID parameters, K p= 0.3, K i=0.25 , andKd=0.165, are chosen for simulation.

Fig. 9 shows that the performance of rising time, settling time and steady state error of the output current of GMAW is better using the proposed fuzzy-sliding mode controller than using conventional PID controller.

Fig. 9 Output current I w.

Figs. 9 show that the FSMC makes the system reach the steady state condition after 0.8 seconds. PID controller needs 4.5 seconds to reach steady state condition. The sliding surface of FSCM in Fig. 10 shows that reachability condition to the sliding surface S S<0 is proved.

Fig. 10 Sliding surface

Fig. 11 Output voltage.

Fig. 11 shows that the simulation result of output welding current and voltage are 110A and 22V, respectively. Fig. 11 shows that the welding supply voltage U a changes depend on the welding current I w to maintain the welding

voltage Uw.

5. CONCLUSION.

Based on the dynamics models of GMAW, the hybrid controller was proposed by combining proportional controller and fuzzy sliding mode controller. The proposed hybrid controller tracks its setting value and keeps constant voltage and current of a Gas Metal Arc Welding (GMAW). Simulation result shows that the performance of rising time, settling time and steady state error of the output current of GMAW is better using proposed controller than using conventional PID controller.

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