Modelling,analysis and control of an eddy current braking system using intelligent controllers

Abstract

Combination of conventional brakes with Eddy Current Brake is the current trend in many applications where superior braking performance at high speed is desired. Eddy Current Brakes being frictionless and contactless offer numerous advantages over conventional brakes. This paper gives detailed insight into the hardware model development, analysis and control of a multi disc Eddy Current Braking System using different intelligent controllers. Firstly, Fuzzy Logic Controller has been developed which can give the feasible value of the electromagnet current required which leads to improved braking performance. Further, Artificial Neural Network Controller has been designed for existing hardware system which gives better, reliable, efficient results in comparison to the Fuzzy Logic Controller and hardware reference model for the sample period of time.

Keywords

Artificial neural network braking torque eddy current brake fuzzy controller modelling response time

1. Introduction

Eddy current brakes (ECB) offer many advantages over normally used conventional brakes such as mechanical brakes, pneumatic brakes. They are superior in terms of speed of response i.e. response time, no wear and tear as these are frictionless and contactless, no need of replacement of brake shoes, maintenance free, no use of brake fluid so no problem of spilling and replacing of brake fluid brake fluid, environment friendly as no release of dust, ease of integration with antilock system.

Working of ECB is independent of the coefficient of friction therefore it results in better performance. Even in the event of rain, snow-fall or dust on the tracks the performance of ECB remains unaffected [13].

An Eddy Current Braking System (ECBS) is a maintenance free braking system. An ECBS can be classified in two categories (1) Electromagnet (EM) type (2) Permanent Magnet (PM) type. An EM type ECBS uses ac or dc power supply for producing the main magnetic field and a PM type ECBS uses permanent magnet to produce the main magnetic field. A PM type ECBS does not use any electrical circuit as electrical control unit and power source are not required [10]. Eddy Current Brakes are also used in high speed railway trains. The traditional braking system depends on the co-efficient of friction between the rail and wheel. Friction results in noise and mechanical wear of rail and wheel [14]. ECB may be used in combination with conventional brakes to provide effective braking as in the case of commercial trucks using hilly terrain. An ECB can provide effective braking in addition to the existing braking system because traditional or existing conventional brakes may fail on long downhill path because of overheating. An ECBS may be controlled electronically (brake-by-wire) where a lesser response time can be achieved as compared to the existing hydraulic brakes with friction. The response time is 41–50 milliseconds for ECBS as compared to 300–400 millisecond for frictional mechanical brakes [8].

Figure 1 gives the basic concept of an ECBS. Authors in [2] have shown that when the coil of U-shape EM was given supply, it produced magnetic field. When a rotating disc made of conducting material cuts the magnetic flux lines produced by EM it results in induced eddy currents in the disc due to relative motion between magnetic field and disc. According to Lenz’s law induced currents oppose the cause of their origin that is relative motion between disc and magnetic field. Induced eddy currents act such that to reduce disc’s rotation which results in production of braking force on the disc. The braking force is directly proportional to conductor’s speed as well as other design parameters. Response time is very important to measure the performance of any type of braking system. Response time means the time which has elapsed since the instant when the brakes were applied till the instant the vehicle starts slowing down. Braking Time is the time from the instant brake is applied till the instant the vehicle completely stops. Improved response time is observed with the use of ECB. In braking our aim is to reduce the stopping distance. Stopping distance is the distance travelled after application of brakes and before stopping. Stopping time is the time taken to cover this distance. They are also known as braking distance and braking time respectively. Authors in [3] have designed Fuzzy controller for control of a hybrid braking system using ECB. Authors in [5] have given the in -depth analysis of ECBS when applied in high speed trains.

Fig.1

Eddy current brake concept.

Authors in [15] shows the use of eddy current brakes when used to reduce vibrations in the power steering system by changing the amount of voltage induced in aluminium disc used in steering. Design as well as performance analysis of hybrid electromagnetic brakes which use both PM and excitation winding are discussed in [11]. Application of ECBS in aircraft arrester barrier system and its model development have been shown comprehensively in [7]. Authors in [6] have discussed the performance improvement by using a new axial flux PM ECB. Single disc type ECB has been developed in [9].

In this paper hardware model of a multi disc ECBS has been developed and experimental investigations carried out to study the behavior of system under various operating conditions of material of disc. A fuzzy based controller has been proposed which can automatically adjust the amount of current supplied to electromagnet and hence the amount of braking produced as per the requirement. Design of artificial neural network controller to improve braking performance has also been discussed.

Organization of Paper is in given sequence. Part 2 deals with the mathematical model of ECBS. Part 3 shows the hardware implementation work in detail. Part 4 discusses the design of Fuzzy Logic Controller. Part 5 shows the design of Artificial Neural Network Controller. Part 6 gives the results and discussion. Part 7 deal with conclusion.

2. Mathematical model of ECBS

A mathematical model of an ECBS derives an expression of the braking torque in terms of different design parameters like disc thickness, excitation current, air gap length, magnetic field strength. Gosline and Hayward [4] proposed a mathematical model of an ECBS. In Fig. 1, if J represents the current density of current induced in the conductor, its unit being ampere per square meter, depends on the angular velocity $\dot{θ}$ (measured in radian per second). Current density also depends on the conductivity of the material σ (measured in mho per meter), the radius R (meter) and the magnetic field B (Tesla). Therefore, expression of current density J is given by $| J | = σ R \dot{θ} | B |$ (1)

If we assume that magnetic flux is uniform throughout the air gap, the power dissipated by eddy currents can be calculated by taking the integral of currents over the volume of disc covered by the magnetic pole: - $P_{diss} = \frac{1}{σ} | J |^{2} dV = \frac{π σ}{4} D^{2} {dB}^{2} R^{2} {\dot{θ}}^{2}$ (2)

Where D (in meter) is magnet core diameter. The braking torque, T_b (measured in Nm) given by: - $T_{b} = \frac{P_{d}}{\dot{θ}} = \frac{π σ}{4} D^{2} {dB}^{2} R^{2} \dot{θ}$ (3)

From Equation (3) we can conclude that braking torque is directly proportional to angular velocity and electrical conductivity of disc. While formulating Equations (1–3) it has been assumed that applied magnetic field, B, is much larger than eddy current induced magnetic field. The above model relies on the model proposed by authors in [1].

Lee and Park [12] also discussed about the braking torque of eddy current brake. Let us assume that σ denotes electrical conductivity of disc, S the area of pole, r distance between center of disc and pole center, d disc thickness, μ₀ permeability of air, N number of turns of coil, l_g distance of air-gap, i applied current to EM coil, $\dot{θ}$ angular velocity of disc. The braking torque T_b has been found to be given by: - $T_{b} = σ r^{2} Sd {(\frac{μ_{0} N}{l_{g}})}^{2} i^{2} \dot{θ}$ (4)

Where i denotes the applied current to electromagnet coil and $\dot{θ}$ the angular velocity of the disc. From Equation (4) it can be concluded that braking torque is directly proportional to electrical conductivity of disc, square of EM current and disc speed.

3. Hardware model implementation of ECBS

Hardware model of a multidisc ECBS has been developed. Performance of system under different operating conditions has been observed to see the effect of variation of different model parameters like material of disc, thickness of disc, distance of disc from (EM), type of supply to EM. Table 1 gives the values of various parameters of EM coil used. Table 2 gives the parameters of electric motor used.

Table 1
Parameters of electromagnet coil

Sr. No. Parameter Value

1. Number of turns 6000

2. Material of wire used Copper

3. Wire gauge number 26

Sr. No.	Parameter	Value
1.	Number of turns	6000
2.	Material of wire used	Copper
3.	Wire gauge number	26

Table 2

Parameters of electric motor

Sr. No.	Parameter	Value	Unit
1.	Rating	1	Hp
2.	No load current	0.75	A
3.	Full load current	4	A
4.	Rated speed	1500	RPM
5.	Rated voltage	220	V

In the developed hardware model four discs of EN31 alloy (cast iron) mild steel (high carbon steel), and four of LM6 Aluminium alloy (high aluminium content) were placed on shaft taking one type of disc at a time. With the help of supporters placed on extended motor shaft four equally spaced discs are placed on extended motor shaft. At the outer periphery of each disc two U-shaped EMs are placed at diametrically opposite positions such that disc passes through EM. When motor was given supply, it rotates and along with it discs also rotate, when supply is given to EM it produces magnetic flux, when rotating disc cuts this magnetic flux Eddy-currents are induced in disc, which by Lenz’s Law oppose the cause of origin of eddy currents and produce braking torque in the disc. This braking torque causes braking in the discs to slow down, disc speed decreases and ultimately stops. As discs are mounted on the motor shaft, braking also leads to decrease in motor speed and stopping of motor. RPM indicator shows the motor speed sensed by RPM sensor placed near motor shaft. Table 3 shows the values of different parameters of developed hardware model of ECBS.

Table 3

Parameters of developed hardware model

Sr. No.	Parameter	Value	Unit
1.	Air gap	5	mm
2.	Radius of disc	127	mm
3.	Thickness of disc	5	mm
4.	Width of cross-section of iron core	20	mm
5.	Height of cross-section of iron core	40	mm
6.	Distance between centre of disc and centre of pole	95	mm
7.	Electrical conductivity LM6 alloy disc	37×10⁷	S/m
8.	Electrical Conductivity of EN31 alloy disc	46×10⁵	S/m

Figure 2 shows the developed hardware model of ECBS. DC shunt type vertical flange Motor has been used. It was placed in vertical position and its shaft has been extended. On the extended shaft four discs were mounted at equal distance from each other. Rheostats were used to vary the field current of motor. Variac 1 was used to vary the supply voltage of motor. Variac 2 was used to vary the supply voltage to EM. Control panel contains Digit Panel Meters (DPMs) for displaying the measured value of motor voltage, motor current, EM ac voltage, EM ac current, EM dc voltage, EM dc current, RPM of motor. Two diode bridge rectifiers were used one to supply dc voltage to EM and second to give supply to field winding of dc motor. For DC analysis dc supply has been given to EMs to observe the brake performance. Variac 1 was used to vary the supply voltage to motor.

Fig.2

Developed hardware model of eddy current braking system.

4. Fuzzy logic controller (FLC) design

A fuzzy controller having two input parameters and one output parameter can be applied to improve the performance of our ECBS. One input parameter can be taken as error in the drop-in speed E (ΔN) which is defined as $E (Δ N) = Δ N_{f} - Δ N_{a}$ (5)

Where ΔN_f denotes the desired drop in speed of disc and ΔN_a denotes the actual drop in speed of disc after applying brakes.

Second input parameter can be taken as the rate of change of drop in speed (NC), defined as

$\frac{d (Δ N)}{dt} = (Δ \dot{N}) = \frac{d (Δ N (t) - Δ N (t - T))}{dt}$ (6)

Where ΔN (t) is the drop in speed at time t and ΔN (t - T) is the drop in speed at the previous time (t - T). The output of FLC is the change in EM current DO. Speed drop difference value Universe E = [740, 0], the change rate universe NC = [490, 72], the current change universe DO = [10, 6].

The logic based on which the rule base is derived is as follows:

If E (ΔN) is High and $\frac{d (Δ N)}{dt}$ is High then I_EM is Medium.

If E (ΔN) is High and $\frac{d (Δ N)}{dt}$ is Low then I_EM is High.

If E (ΔN) is Low and $\frac{d (Δ N)}{dt}$ is High then I_EM is Low.

If E (ΔN) is Low and $\frac{d (Δ N)}{dt}$ is Low then I_EM is High.

If E (ΔN) is Low and $\frac{d (Δ N)}{dt}$ is Medium then I_EM is Medium.

If E (ΔN) is Medium and $\frac{d (Δ N)}{dt}$ is Low then I_EM is High.

If E (ΔN) is High and $\frac{d (Δ N)}{dt}$ is Medium then I_EM is Low.

If E (ΔN) is Medium and $\frac{d (Δ N)}{dt}$ is Medium then I_EM is Medium.

If E (ΔN) is Medium and (d(ΔN))/dt is High then I_EM is Low.

Figure 3 shows the fuzzy rule base matrix based on the logic defined previously. PL, PM, PH denote positive low, positive medium and positive high respectively. Advantages of this FLC lies in its adaptive nature as it can change the EM current automatically depending on the amount of braking required, reduced losses, precise control, more saving, faster and accurate response.

Fig.3

Fuzzy rule base matrix.

Figure 4 shows the designed Fuzzy Inference System (FIS) for ECBS with two inputs and one output. Figure 5 shows the rule viewer for the FIS. It can be seen that when input 1 (E) equals 347 and input 2 (NC) equals 169, output (DO) equals 9. Similarly, by varying input values different output values can be obtained. With further tuning and modification, it can be integrated with hardware model to improve its overall braking performance. Mamdani type FIS has been taken, with triangular membership function for inputs and output. Centroid method has been used for defuzzification.

Fig.4

Designed fuzzy inference system for ECBS.

Fig.5

Rule viewer for the designed fuzzy inference system.

5. Artificial neural network (ANN) controller

ANN was used to train the system by taking input as change in speed and the output as electromagnet current (EM current). In order to have desired output, system was trained by using 10 weights between input and output. The input was trained from 440 to 0 with step size of 10 whereas output was trained from 6 to 6.9 with step size of 0.02.

The input to the ANN controller was taken as change in speed and the output as EM current and it has been represented as shown in the Fig. 6.

Fig.6

ECBS block diagram ANN controlled.

The structure of ECBS ANN controlled system consists of 10 neurons and 1 hidden layer as shown in the Fig. 7. Feed-forward neural network has been used. From Fig. 6 we can depict output as EM current (I) and the input as change in speed (Δw) according to Equation (7).

Fig.7

Design of ANN controller hidden layer system.

I = \sum_{i = 1}^{10} W_{i} * Δ w + b

(7) W_i are the weights and their values given by

W₁= 13.92, W₂= 13.97, W₃= –14.19,

W₄= 13.98, W₅= 13.71, W₆= –13.81, W₇= –13.96, W₈= 13.78,

W₉= 13.94, W₁₀= 14.04

Bias value b has been taken as 13.81.

6. Results & discussion

The experimental investigations have been carried out on the ECBS hardware developed model. Table 4 gives the experimental investigations for dc analysis of ECBS with EN31 MS alloy disc. Table 5 gives the dc analysis readings for LM6 Aluminium alloy disc. DC analysis means that EM coils are supplied with dc supply. It has been observed from experimental wok that use of LM6 disc gives much better braking performance in comparison to EN31 disc due to better electrical conductivity property of LM6 disc. This observation matches with the behaviour of ECBS according to literature and as per the derived expression of braking torque.

Table 4
DC analysis of ECBS with EN31 MS alloy disc

Sr. No. Motor Voltage V_MR(V)initial, final Motor Current I_MR(A)initial, final EM Voltage V_EM(V) EM Current I_EM(A) Stopping Time T(s) Initial speed(rpm)-Final speed(rpm) Drop in Speed N(rpm) Braking Torque T_b(KNm)

1 55,51.2 0.41,8.9 45.3 6.96 2.70 440-00 440 0.369

2 55,45 0.42,9.14 50.5 7.65 2.50 440-00 440 0.446

3 60,46.6 0.43,9.43 50.6 7.69 1.60 488-00 488 0.488

4 60,46.8 0.43,9.32 56.7 8.02 1.55 489-00 489 0.545

5 80,61.2 0.5,9.49 46.5 7.00 3.03 658-00 658 0.559

6 80,61 0.5,9.60 56.5 8.00 2.51 660-00 660 0.732

7 100,76.0 0.52,9.70 46.3 6.91 3.34 846-00 846 0.7

8 100,78.2 0.53,9.81 55.1 7.75 2.92 849-00 849 0.884

9 122,102.6 0.57,9.82 46.8 7.2 4.7 1011-340 671 0.603

10 122,102.7 0.57,9.9 57.8 8.5 3.6 1017-288 729 0.913

Sr. No.	Motor Voltage V_MR(V)initial, final	Motor Current I_MR(A)initial, final	EM Voltage V_EM(V)	EM Current I_EM(A)	Stopping Time T(s)	Initial speed(rpm)-Final speed(rpm)	Drop in Speed N(rpm)	Braking Torque T_b(KNm)
1	55,51.2	0.41,8.9	45.3	6.96	2.70	440-00	440	0.369
2	55,45	0.42,9.14	50.5	7.65	2.50	440-00	440	0.446
3	60,46.6	0.43,9.43	50.6	7.69	1.60	488-00	488	0.488
4	60,46.8	0.43,9.32	56.7	8.02	1.55	489-00	489	0.545
5	80,61.2	0.5,9.49	46.5	7.00	3.03	658-00	658	0.559
6	80,61	0.5,9.60	56.5	8.00	2.51	660-00	660	0.732
7	100,76.0	0.52,9.70	46.3	6.91	3.34	846-00	846	0.7
8	100,78.2	0.53,9.81	55.1	7.75	2.92	849-00	849	0.884
9	122,102.6	0.57,9.82	46.8	7.2	4.7	1011-340	671	0.603
10	122,102.7	0.57,9.9	57.8	8.5	3.6	1017-288	729	0.913

Table 5

DC analysis of ECBS with LM6 aluminium alloy disc

Sr. No.	Motor Voltage V_MR(V)initial, final	Motor Current I_MR(A)initial, final	EM Voltage V_EM(V)	EM Current I_EM(A)	Stopping Time T(s)	Initial speed(rpm)-Final speed(rpm)	Drop in Speed N(rpm)	Braking TorqueT_b (KNm)
1	55,51.2	0.41,8.9	45.3	6.96	2.10	540-00	540	82.325
2	55,45	0.42,9.14	50.5	7.65	1.80	542-00	542	99.826
3	60,46.6	0.43,9.43	50.6	7.69	1.20	588-00	588	111.178
4	60,46.8	0.43,9.32	56.7	8.02	1.00	589-00	589	119.23
5	80,61.2	0.5,9.49	46.5	7.00	2.5	740-00	740	114.116
6	80,61	0.5,9.60	56.5	8.00	1.98	740-00	740	149.049
7	100,76.0	0.52,9.70	46.3	6.91	2.87	895-00	895	134.492
8	100,78.2	0.53,9.81	55.1	7.75	2.34	895-00	895	169.178
9	122,102.6	0.57,9.82	46.8	7.2	3.96	1011-740	271	164.94
10	122,102.7	0.57,9.9	57.8	8.5	3.6	1057-728	329	240.34

For a given value of motor voltage as the Electromagnet Current was increased stopping time was decreased. This was because braking depends on the EM current as larger EM current means more magnetic field of EM and braking is produced by the interaction of induced eddy currents in the disc and magnetic field of EM. Material of disc also plays a very important role in amount of braking produced as the amount of eddy current braking produced varies directly with the electrical conductivity of the material of disc.

Improved braking performance in terms of stopping time and stopping distance was achieved by using LM6 Aluminium alloy disc in place of EN31 MS alloy disc due to better electrical conductivity of LM6 Alloy because of which more eddy currents are produced in it. Fuzzy Controller helps in achieving precise control and desired results as per requirement. Figure 8 shows the variation of braking torque with initial disc speed. Figure 9 shows the variation of braking torque with EM current. It can be seen that LM6 alloy disc gives much better braking performance as compared to EN31 alloy disc.

Fig.8

(a) Braking torque versus initial disc speed for EN31 alloy disc (b) Braking torque versus initial disc speed for LM6 alloy disc.

Fig.9

(a) Braking torque versus EM current for EN31 alloy disc (b) Braking torque versus EM current for LM6 alloy disc.

Figure 10 shows comparison of values of EM current for different values of drop in speed for EN 31 Alloy disc and LM6 Alloy disc. The value of EM current and hence braking torque was higher when ANN was applied as compared to the value obtained with FLC and hardware.

Fig.10

(a) Variation of EM current with change in speed for ANN controller, fuzzy logic controller output and experimental value for EN31 alloy disc (b) Variation of EM current with change in speed for ANN controller, fuzzy logic controller output and experimental value for LM6 alloy disc.

6.1 Comparative study

Using Fuzzy Logic Controller (FLC) gives enhanced system performance as shown in the comparative study in Tables 6 and 7. Value of EM current gets increased for same value of drop in speed by the use of FLC which results in greater braking torque and hence gives improved braking performance. Table 6 shows the comparative study table for EN31 alloy disc showing comparison between experimental, FLC and ANN results. Table 7 shows the same for LM6 alloy disc. Greater braking torque using FLC results in better braking performance in terms of better braking control, desired stopping distance, desired stopping time. But there was a major drawback with FLC is that it is unable to give the output for the certain sample period of time so as to get more precise value that’s why ANN controller has been used to remove the drawback associated with FLC.It gives more precise value of higher EM Current under a given time interval for any sample duration of time.

Table 6
Comparative study table for EN31 alloy disc

Sr. No. Method Drop in Speed (rpm) Rate of change of speed EM Current(A) T_b (KNm)

1 Experimental 440 162.96 6.96 0.369

FLC 440 162.96 9 0.618

ANN 10(440-430,430-420…) – 9.2 0.645

2 Experimental 488 305 7.6 0.488

FLC 488 305 7.6 0.488

ANN 10(488-478,478-468…) – 7.9 0.528

3 Experimental 658 217.16 7 0.559

FLC 658 217.16 9 0.924

ANN 10(658-648,648-638…) – 9.2 0.965

4 Experimental 729 202.5 8.8 0.979

FLC 729 202.5 9 1.024

ANN 10(729-719,719-709…) – 9.3 1.093

5 Experimental 846 253.29 6.91 0.7

FLC 846 253.29 9 1.188

ANN 10(846-636,836-826…) – 9.3 1.268

Sr. No.	Method	Drop in Speed (rpm)	Rate of change of speed	EM Current(A)	T_b (KNm)
1	Experimental	440	162.96	6.96	0.369
FLC	440	162.96	9	0.618
ANN	10(440-430,430-420…)	–	9.2	0.645
2	Experimental	488	305	7.6	0.488
FLC	488	305	7.6	0.488
ANN	10(488-478,478-468…)	–	7.9	0.528
3	Experimental	658	217.16	7	0.559
FLC	658	217.16	9	0.924
ANN	10(658-648,648-638…)	–	9.2	0.965
4	Experimental	729	202.5	8.8	0.979
FLC	729	202.5	9	1.024
ANN	10(729-719,719-709…)	–	9.3	1.093
5	Experimental	846	253.29	6.91	0.7
FLC	846	253.29	9	1.188
ANN	10(846-636,836-826…)	–	9.3	1.268

Table 7

Comparative study table for LM6 alloy disc

Sr. No.	Method	Drop in Speed (RPM)	Rate of change of speed	EM Current(A)	T_b (KNm)
1	Experimental	540	257.14	6.96	82.32
	FLC	540	257.14	7.5	95.42
	ANN	10(540-530,530-520…)	–	7.7	100.76
2	Experimental	588	490	7.69	111.18
	FLC	588	490	8	118.22
	ANN	10(588-578,578-568…)	–	8.2	124.437
3	Experimental	740	296	7	114.11
	FLC	740	296	7.5	130.76
	ANN	10(740-730,730-720…)	–	7.9	145.346
4	Experimental	800	310	6.97	122.09
	FLC	800	310	7.5	141.37
	ANN	10(800-790,790-780…)	–	7.9	157.13
5	Experimental	895	382.47	6.91	134.49
	FLC	895	382.47	7.5	158.16
	ANN	10(895-885,885-875…)	–	7.8	171.368

7. Conclusion

Hardware model implementation of ECBS has been shown. Experimental results have been carried out on the developed hardware model of ECBS which gives an adequate amount of braking torque for a certain value of EM Current which was not sufficient. Now the similar concept of braking applied to Fuzzy logic controller which gives better performance in terms of high braking torque but only for a long-time period. So, the problem of analysing the high braking torque for a certain sample period of time has been solved by using ANN controller which results in reliable, smooth, sufficient amount of high braking torque. It has been shown that by using intelligent controllers overall braking performance of ECBS can be improved.

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