Gap Width Control in Electrical Discharge Machining, Using Type-2Fuzzy Controllers

Kotler Ter Pey Tee, Reza Hoseinnezhad∗, Milan Brandt and John Mo

Abstract— This paper presents a new method for controllingthe gap distance between the electrode and the workpiece in anelectrical discharge machining (EDM) system. Due to the highlynonlinear and time-varying nature of the EDM process, con-ventional gap width control methods do not perform efficiently,and their parameters need frequent tuning to achieve stable andefficient machining. The proposed gap control method uses anintelligent type-2 fuzzy logic inference system to control the gapdistance between the electrode and the workpiece. The mainadvantage of this proposed method is its robustness to variationsin machining conditions. In addition to removing the need forconstant parameter tuning, the proposed control system resultsin enhanced accuracy and stability in the control performance.

I. INTRODUCTION

Electrical discharge machining (EDM) is a process involv-ing the removal of conductive and semi-conductive materialby a series of rapidly recurring current discharges betweenan electrode and a workpiece in presence of a dielectric.In this process, the electrical discharge sparks occur withina physical gap between the workpiece and the electrode(henceforward, called the gap). The gap width is usuallybetween 0.01 and 0.05mm. The EDM process is knownto involve complex and time-varying phenomena that areyet well understood. Experts in the field of EDM havedemonstrated that effective control of the gap distance cansignificantly improve the efficiency of sparking process interms of material removal rate [1]. Thus, maintaining the gapwidth at a desired level is an important task to be consideredwithin any EDM system design.

In the past two decades, researchers have developed sev-eral advanced monitoring and control strategies to improveEDM process. Usually the gap width is assumed to bedirectly related to the voltage measured across the gap(henceforward called the gap voltage). Thus, As it is shownin Fig. 1, existing controller designs receive an error inputwhich is the difference between actual and desired valuesof the gap voltage and generate the output, a feed-ratecommand, to be send to an actuator (usually a servo system)that would move the workpiece accordingly.

The gap control mechanism is in charge of the most chal-lenging yet crucial task for a stable and efficient machining,that is, to maintain an optimum gap distance between the

This work was supported by Advanced Manufacturing Corporate Re-search Centre under the Australian Governments Cooperative ResearchCentres Program as Project No. 2.2.1

All authors are with School of Aerospace, Mechanical and ManufacturingEngineering, RMIT University, Victoria, Australia.

* corresponding author email: rezah@rmit.edu.au

Fig. 1. Typical components of an EDM system

electrode and workpiece during the erosion process. Electri-cal discharge in EDM occurs over a very short period of timein a very narrow gap, filled with dielectric. The electricaldischarge process starts with a high voltage, henceforwardcalled the gap voltage, applied across the gap. Robustness ingap control is essential to overcome and quickly recover fromdisturbances and unstable machining conditions. Examplesof such conditions include short circuit or arcing which canhappen due to several reasons. Examples of such reasons are:

1) the electrode is feeding faster than the rate of gapenlargement, or

2) accumulation of melted particles (debris) which bridgethe inter-electrode gap distance, or

3) a sudden increase in the eroding area during a singlecycle.

Short circuits and arcing pulses can damage the surfacequality of the workpiece and reduce the efficiency of theEDM process. A common strategy to avoid such unstablemachining conditions, is based on the following gap controlpolicy.

Generally, upon detecting such harmful pulses (e.g. shortcircuit or arcing), the gap controller would pull the electrodeaway from the workpiece as fast as possible but not too far,in such a way that subsequent pulses are most likely to benormal discharges not open circuits.

EDM process operates in highly dynamic, uncertain envi-ronments and experiences fast changes in the gap condition.This leads to high uncertainties in the input(s) of the gapcontroller. Commonly, the gap distance is indirectly mea-sured by looking at the average gap voltage which can beaffected by high levels of noise, and its characteristics canalso change due to changes in machining conditions. Hence,to achieve accurate and robust control performance, it is vitalto design and implement a sophisticated control system thatcan handle the encountered uncertainties.

Due to its simplicity and suitability for implementingusing embedded processors, commonly a perfectly tuned

Td

Fig. 2. Typical gap voltage measured from an oscilloscope.

PI controller is used in the industry for controlling thegap distance. However, with highly nonlinear and time-varying processes such as EDM, traditional PI controllersneed constant tuning. An adaptive intelligent solution wouldrid the practitioners from the tedious tuning job and wouldprovide the industry with better accuracy and confidence inthe control performance in presence of nonlinearity, time-variations and disturbances.

Recently, researchers have suggested to replace the tradi-tional PI controller with conventional fuzzy logic controllers(also called type-1 fuzzy logic controllers) [2]. This hasachieved significant improvements in material removal rate(MRR). However, quite often it happens that the knowledgeused to construct the fuzzy rule-base in such methods isuncertain. These uncertainties are usually caused by theexcessive level of noise in the input data, or the fact thatthe words used in antecedents and consequents of the fuzzyrules can mean differently in different machining conditions.

Type-1 fuzzy logic controllers most commonly employ asingleton fuzzifier which is precise and can be inadequatefor dealing with the high level of uncertainties involvedin the fast changing EDM process [3]. To handle suchuncertainties in EDM process, this paper proposes a noveltype-2 fuzzy logic control technique, in which the antecedentand consequent membership functions are type-2 fuzzy sets.

II. GAP CONTROL IN EDM

As it was mentioned earlier, to achieve a stable andefficient EDM process, an optimal gap distance needs to bemaintained throughout the complete erosion cycle. Before wecan control the gap distance, we need to somehow measureit. Direct measurement of the actual gap distance betweenthe workpiece and the electrode is practically infeasible, andit is usually measured indirectly using feedback signal of thegap voltage.

Figure 2 shows typical gap voltage waveforms that aremeasured from an oscilloscope during discharging process.As it is highlighted in Fig. 2, an important characteristic ofeach pulse is its ignition delay time (Td), the time requiredfor the formation of the plasma channel before allowing theelectrons and ions to flow through the gap. The length of theignition delay time is generally assumed proportional to thegap distance. The rationale behind the assumption is that ingeneral, at a larger gap distance, the plasma channel requires

a longer time to achieve its dielectric breakdown state. Inother words, each gap voltage pulse will has a long ignitiondelay time when the gap distance is large and short or 0ignition delay time when the gap distance is small, or whenlarge amount of debris is trapped in the gap.

During the ignition delay time, the gap voltage rises upto the maximum (open circuit) voltage. Once the plasmachannel is formed, the gap voltage drops to a burning voltagelevel. Let us denote the pulse period by T which is comprisedof the delay time Td , the burning time Tb and the off-timeToff,

T = Td +Tb +Toff. (1)

In practice, all these time periods are usually betweenmicroseconds to tens of microseconds. The statistical averageof gap voltage samples during a period is given by

Vg =Td

TVoc +

Tb

TVb (2)

where Voc and Vb denote the open-circuit and burning volt-ages, respectively.

Typically, the burning voltage is around 20V-30V andusually very small compared to the open-circuit voltage.Thus, the first term in the above equation is dominant, andthe average gap voltage can be approximately assumed to beproportional to the delay time, hence to the physical gapdistance. In other words, to monitor and control the gapdistance, one can directly measure and control the averagegap voltage.

A commonly used non-linear PI gap control system isshown in Fig. 3. In this figure, a gap voltage sensor isused to measure the gap voltage during eroding processand a low pass filter is used to calculate the average ofthese gap voltage pulses. This average gap voltage feedbacksignal (Vfb) is then compared with a reference gap voltage(Vref) to calculate the error signal for the PI controller. ThePI controller will increase the feeding rate of the electrodetowards the workpiece when the error is positive and reducesor retracts from the workpiece when the error is negative.

III. INTERVAL TYPE-2 FUZZY LOGIC GAP CONTROL

Fuzzy logic-based methods have shown great success invarious linear and non-linear control problems [4]. Type-2fuzzy sets were first introduced by Zadeh [5]. They representan extension of the ordinary type-1 fuzzy sets to increase thefuzziness of a relation. Many researchers demonstrated thatan intelligent type-2 FLC (IT2FLC), that uses interval type-2 fuzzy sets, outperforms the type-1 fuzzy logic controllers(T1FLC) in terms of handling the uncertainties encapsulatedin a system [4].

Similar to a T1FLC, the IT2FLC includes a fuzzifier,a fuzzy rule-base, a fuzzy inference engine and an outputprocessor. However, in an IT2FLC, the output processorincludes a type reducer block that generates type-1 fuzzysets output from type-2 fuzzy sets output and a defuzzi-fication block that generates a crisp output. This IT2FLCis also characterized by IF-THEN fuzzy rules-base, but itsantecedents and consequents are now type-2 fuzzy sets.

Fig. 3. Typical PI gap control system used in the industry

Figure 4 shows a typical triangular shape type-2 member-ship function which is also used in experiments presented inthis paper. The uncertainties in the primary grades of a type-2 membership function are modeled by the bounded regionwhich is shaded in grey in Fig. 4. This region is bounded byan upper bound membership function (UBMF) and a lowerbound membership function (LBMF). The UBMF is themaximum membership grade of uncertainties and the LBMFrepresents the minimum membership grade of uncertainties.

Based on the membership function shown in Fig. 4, theUBMF is given by:

µN jA(XA) =

0 if XA < l1N jA

XA−l1N j

AK1

N jA−l1

N jA

if l1N jA≤ XA < K1N j

A

1 if K1N jA≤ XA < K2N j

AR2

N jA−XA

R2N j

A−K2

N jA

if K2N jA≤ XA < R2N j

A

0 if XA ≥ R2N jA

(3)

Fig. 4. The triangular shape interval Type-2 membership functions.

and the corresponding LBMF is

µN j

A(XA)=

0 if XA < l2N jA

XA−l2N j

AK1

N jA+K2

N jA

2 −l2N j

A

if l2N jA≤ XA <

K1N j

A+K2

N jA

2

R1N j

A−XA

R1N j

A−

K1N j

A+K2

N jA

2

ifK1

N jA+K2

N jA

2 ≤ XA < R1N jA

0 if XA ≥ R1N jA

(4)where XA = {eA, eA}, eA represents the error signal of theaverage gap voltage signal input into the control system,eA represents the derivative of the input error, and N j

A ischaracterized by a type-2 membership function for j-th fuzzyset associated with the A-th input.

The fuzzy rules for IT2FLC remain the same as T1FLC,but their antecedents and the consequents are representedby interval type-2 fuzzy sets (consisting of LBMF andUBMF). There are five labels of fuzzy sets used in theproposed control system: negative large (NL), negative (N),zero (Z), positive (P) and positive large (PL). The generalrule structure of a IT2FLC for the l-th rule can be expressedas:

Rl : If eA is N j1 and eA is N j

2 then y1 is Y j (5)

where y1 is the control output of this system.In the control scheme proposed in this paper, the type-2

fuzzy inference engine of the IT2FLC adopts a product t-norm for input antecedent operations, which gives the resultas a firing set that can be expressed as

f l(X) = µN j

1(X1)?µ

N j2(X2) (6)

f l(X) = µN j1(X1)? µN j

2(X2) (7)

where the ? operator represents the t-norm product andµ

N j1(·) and µN j

2(·) represent the lower and upper bound

membership functions, respectively.

Fig. 5. Simulink block diagram of the proposed type-2 fuzzy logic controller for EDM process.

The output of the fuzzy inference engine for both upperbound firing levels and the lower bound firing levels willthen be combined by the type reducer. There are manytype reducer methods in the literatures [6]. We proposethe Wu-Mendel Uncertainty Bounds method [7] which iscomputationally efficient for real time implementation.

IV. SIMULATION RESULTS

To demonstrate that the proposed type-2 fuzzy logic con-troller works in principle to efficiently guide the workpiecein an EDM process, its performance was evaluated in asimulation study. To conduct the simulations, we logged along train of actual average gap voltage data during a samplerun of the EDM process using a real EDM system. Thelogged data points were then imported into a simulationmodel developed in Matlab/Simulink environment as shownin Fig. 5. The simulation model is comprised of four mainmodules:

– Fuzzifier: Two inputs are adopted in this module: theerror of the average gap voltage and the derivative ofthe error in which both of these inputs are scaled to therange of (0-1). The fuzzifier maps this real valued inputto interval type-2 fuzzy sets.

– Type-2 Fuzzy Inference Engine: This module combinesall the fired rules and gives a non-linear mapping ofthese input type-2 fuzzy sets to multiple type-2 fuzzysets output. Each of these fired rules is generated byconnecting its antecedents using the product t-normoperation and each of these rules are then combinedby using the join operation.

– Type Reducer: The type reducer represents the mappingof the type-2 fuzzy sets output from previous moduleinto type-1 fuzzy sets output. The Wu-Mendel methodis used in this simulation as it is computationallycheaper than other methods and suitable for real timeimplementation.

– Defuzzification: The output of a type-reduced set, yl andyr is generated from the output of the type reducer mod-ule. The defuzzified crisp output y1 is then calculatedby taking the average of yl and yr.

Figure 6 shows a snap-shot of the crisp outputs generatedin our simulation. The yellow signal represents the error inputinto our Simulink model and the pink signal represents the

Yellow-error, Pink-Crisp outputs [0-1]

Timme [s]

Fig. 6. A snapshot of output commands generated by the type-2 fuzzycontroller.

outputs of our simulation. As shown in Fig. 6, our simulationmodel demonstrated its capability to generate a smooth servocommand signal that helps to create a stable and efficienterosion process by comparing the input error signal with thecrisp output signal.

V. CONCLUSIONS

Due to the highly non-linear and uncertain nature of EDMprocess, its control is a challenging task.This paper presentsa new method to control the EDM process by processingthe average gap voltage measurements using a type-2 fuzzylogic controller. The controller generates feed-rate commandsfor the actuator that would lead to workpiece movementsin such a way that the gap distance between the electrodeand the workpiece is maintained at a desired value duringerosion. The main advantage of this method is that it allowsthe system to handle uncertainties that are encapsulated inthe feedback signal and output quality control signal. Oursimulation demonstrates that a smooth servo command signalis generated from a noisy average gap voltage signal andit shows that the interval type-2 fuzzy logic gap controllerperforms more robustly compared to the conventional PIcontroller.

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