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1

Control of a 2.4MW Linear Synchronous Motor

for launching roller-coasters

A. Veltman(1,2), P. van der Hulst (2), M.C.P. Jonker(3), J.P. van Gurp(3)

(1) Eindhoven Univertsity of Techn., P.O. Box 513, 5600 MB Eindhoven, Netherlands.

(2) Piak Electronic Design b.v., Markt 49, 4101 BW Culemborg, the Netherlands.

t: +31-345-534126, f: +31-345-534127, www.piak.nl

(3) GTI Electroproject b.v., P.O. Box 441, 1500 EK Zaandam, the Netherlands.

t :+31756811111, www.electroproject.nl

Author Information : a.veltman@piak.nl

Keywords

LSM, current control, sensor-less control, switched stators

Abstract

To accelerate a heavy roller-coaster train to a speed of 25m/s in less than 3 seconds requires a lot of

thrust. A 2.4MW Linear Synchronous Motor is applied for this function. Optimal thrust implies

optimal current control. Because of the increasing velocity along the track, the stator configuration

changes continuously during a launch (sequentially switched stator). A strategy to control 3kA of

current during abrupt changes in stator inductance, while maintaining thrust, is presented.

1 System configuration

A 2.4 MW Linear Synchronous Motor (LSM) is used to accelerate a roller-coaster train from

standstill to a final speed of 25m/s within a travelled distance of about 40m in a little less than 3

seconds. Initial acceleration is about 1.5g. The acceleration reduces beyond the velocity of maximum

power, yielding an economic constant power operation for the main part of the launch.

The LSM is of the long-stator type. It

consists of wound stators mounted on the

track (the stator) with a length of about 60m.

Permanent magnets are mounted on the

pusher-car that pushes the roller-coaster

train from underneath. After the pusher-car

reaches the required speed of 25m/s, the

train continues in a passive fashion, leaving

the pusher-car behind. The 6m long pusher-

car decelerates to standstill in about 1

second and then returns to the starting

position to launch the next train.

The long stator is fed by a group of parallel

inverters able to deliver 2.4MW using a

1000V DC-link voltage. The developed

current controller drives the gate signals of the IGBT’s in a direct fashion. The standard modulators in

the inverter are not used.

In order to waste as little voltage as possible, the long stator is divided into sections with a length of 3

meters each, all connected in series. Each of the sections can be shorted by means of heavy-duty

thyristors. By shorting all sections except the 3 (partly) covered by the magnets of the pusher-car,

inductance and resistance are minimised. Sections are shorted after the pusher-car has passed and

‘opened’ just before the pusher-car enters a new section. Since all stator sections are different to allow

optimal constant power operation, large abrupt (asymmetric) steps in inductance and resistance occur.

The equivalent circuit in fig. 5 shows all relevant electrical components. The voltage Us represents the

inverter voltage of all three inverters in parallel, Lr represents the coupling inductors to allow

Figure 1 2.4MW inverter under construction

2

paralleled inverters to share current. The effective

inductance L(thy) depends on the status of the thyristor

switches as does the effective stator resistance Rs.

These large parameter changes occur abruptly in a step-

wise fashion and make precise control of the motor current

(up to 3kA) a challenge. A system based on Hall sensors is

used for position measurement, the set-point for the

current vector is based on the actual position, velocity and

acceleration. We are presently working on a sensor-less

position estimator: first results in figures 6 and 7. Figure 1

shows the inside of the power converter under

construction, figure 3 depicts the test track of the LSM

launch system with thyristor switch boxes adjacent to the

track. Figure 4 shows the construction of the stator with

two-sided NeFeB magnets and airgaps of approximately

1cm.

Figure 2 Accelerating pusher-car without train.

Figure 3 Test track of LSM, stators and

guiding fin are visible. Pusher-car

is underneath the train. Thyristors

in boxes on left side.

Figure 4 Magnet-stator-magnet sandwich

on either side of pusher-car,

vertical guide-rail in centre.

Figure 5 Simplified equivalent per phase circuit of LSM

with switched stator.

3

Figure 2 shows an accelerating pusher-car

in the final set-up. Figures 6 and 7 show a

close-up measurement of a launched

train.

2 Synchronous frame

hysteresis controller

Requirements for the motor current

controller are:

1. Smooth thrust during fast

acceleration.

2. Accurate current control during

switching of thyristors: unbalanced

load and stepwise parameter changes.

3. Keep current when maximum voltage

is reached.

4. Use low switching frequency (max

1kHz at 3kA)

5. Minimise acoustic noise

Since most conventional current

controllers are based on a motor model

with constant parameters, these goals are

hard to achieve. Requirements 2 and 4

seem to contradict each other since fast

control needs high bandwidth and thus a

high switching frequency.

The presented synchronous-frame

hysteresis controller does show excellent

dynamics, even at low switching

frequencies (see figures 6 and 7). A

hysteresis current controller is inherently

insensitive to parameter variations, and

generates a more random-noise-like

acoustic spectrum than carrier-based

PWM modulators. The relations between voltage, its mathematical integral flux, and current that are

present in the equivalent circuit in figure 5 are explained in figure 8.

The prime goal of the current controller is to realize a required value of *

q

i within the given

constraints of the inverter. The output voltage of the three phase inverter can be regarded as one of

23=8 possible states, of which six are called ‘active vectors’ and two (000 and 111) are called ‘zero

vectors’, see figure 8(c). The current controller makes a kind of pulse width modulated output such

that the required current is realized as quickly as possible by means of only four switching rules as

shown in figure 8(b). The strategy is straightforward: when the difference between reference and

actual current value is within the gray box, the present state of the inverter is maintained until one of

the boundaries is crossed. Each of the boundaries has a distinct effect on the switching state. Suppose

the inverter state is 110 (active vector at 60°, see figure 8(c)). A stop would mean switching to the

nearest zero vector which is 111. A stop causes a zero voltage on the motor terminals, hence the

integral of voltage, the terminal flux ΨT will hold position. A +60° transition would imply going to

010 and a -60° transition would imply going to 100, since voltage represents the direction of increase

of the flux ΨT, the flux orbit as seen in figure 8(a) gets an additional corner. All other active vectors

-4000 -3000 -2000 -1000 01000 2000 3000 4000

-3000

-2000

-1000

0

1000

2000

3000

iα [A] →

iβ [A] →

Figure 6 Measured data: current vector during launch in first

second, sensor-less position estimation

00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

time [s] →

i [A] →

iα

iβ

Figure 7 Measured data: start of launch with controlled build

up to 2200A, sensor-less position.

4

also have their own adjacent states that can be regarded as a +60°, a -60° and a zero vector. It is

evident that each boundary transition involves the change of only one phase, which makes this

strategy effective.

2.1 A 2-dimensional hysteresis controller

The voltage needed to realize *

q

i depends mainly on the velocity of the pusher-car, the total coupled

magnetic flux (depending on the number of active turns) and the present inductance. The latter two

strongly depend on the position on the launch track and the status of the thyristor switches along the

track respectively (also see figure 3).

The required inverter flux to generate *

q

i is depicted in figure 8(a). The flux across the inductance

equals L

⋅

i and the current is perpendicular to the magnet flux m

Φ, here the flux across the resistance

Rs is neglected for clarity. The terminal flux *

T

Ψ

r

is leading the magnet flux by angle

ρ

The best way

to orient the switching box is to align it to *

T

Ψ

r

. However, this flux is not known, because the

inductance L is not known to the current controller at every instant.

Figure 8 Asynchronous current control switching algorithm. (a) The switching box is aligned with the mean

stator flux. (b) Switching actions on crossing boundaries when assuming a reference for terminal

flux. (c) Definition of voltage vectors, mean terminal voltage vector and leading/lagging. (d) Vector

representation of voltages and current in synchronous motor operating at load angle

ρ

. (e) Load

angle correction of error box.

5

figure 8(b) shows the best orientation. figure 8(d) is the same situation but seen from the voltage point

of view. The Electro-motive force (emf) m

jΦ

ω

is leading m

Φ by 90°. To achieve maximum force

per ampère, *

q

i is parallel to the emf. The voltage drop in resistance Rs i is also parallel to the emf. The

voltage over series inductance L is leading the current by 90°, causing the required terminal voltage

*

Tdq

U to lead the current by load-angle

ρ

. Load angle

ρ

can be estimated in various ways, and should

be done with sufficient bandwidth to allow following fast impedance changes.

2.2 Implicit alignment to T

U

r

As set points we use *

q

i and *

d

i. As discussed above, we will for now assume that 0

*=

d

i. In case

there is insufficient DC link voltage to realize *

q

i, a negative value of *

d

ican buy force at the expense

of more stator losses as is shown in figure 9.

With the measured dq

i

r

two error values can be distinguished, (see figure 8(d)):

*

*

qTqq

dTdd

iii

iii

−=∆

−=∆ (1)

By using an estimate of load-angle

ρ

, the switching rules can be applied to a transformation of

dq

i

r

∆according to:

∆

∆

⋅

−

=

∆

∆

=∆

q

d

q

d

dq i

i

i

i

i

ρρ

ρρ

cossin

sincos

2

2

2

r

(2)

By applying the switching rules in figure 8(b) to the transformed error vector 2dq

i

r

∆, an excellent

switching behavior results. Experimental results are shown in various graphs in following sections.

2.2.1 Handling Voltage shortage

Conventional hysteresis controllers are usually of

the per-phase type with problems of limit cycles

(see [1]). The presented current controller uses a 2

dimensional vector approach with two criteria: one

for amplitude, one for angle as shown in figure

8(b,c). The robustness of this approach is depicted

in figures 6, 7 and 10. Figure 7 shows the very low

switching frequency during the start of the train,

figure 6 shows the control of the current-vector in a

stationary α and β reference frame. An interesting

detail can be seen in figure 10 where the inductance

reduces by a large amount at t=1.042s, as a

consequence the switching frequency goes up, but

the current vector is not noticeably affected. Note

that the inductance change of one of the delta

connected phases reduces from 1.1mH to 0.73mH

within a few milliseconds. The apparent inductance

change on the inverter terminals is 1/3 of this value

(∆-Y equivalent), hence the flux change involved

here is 3/Li ∆⋅=∆Ψ . The switching rules realize

this mutual amplitude and phase change of the terminal flux by directly shortening the time of active

vectors, which causes an increase in switching frequency [3].

Figure 9 Introducing negative id to reduce

required voltage.

6

3 Roller-coaster performance

During a launch cycle, various stages can be distinguised. A full cycle is depicted in figure 11. A

cycle starts at a postion of about 6m. To avoid ‘whip-lash’ risk of the passengers on board, the launch

consists of a gradual increase of the thrust, as shown in figure 12. During the thrust build up, the

displacement of the train is about 0.2m. Figure 11 shows that speed increases rapidly in the first

meters of the track: after 4m of travelled distance, the speed already crosses 10m/s. The remaining

45m are needed to accelerate further from 10m/s to 25m/s. Once the required speed is reached, the

current is reduced to zero and

the pushercar soon enters the

eddy-current brakes between

60m and 75m. Figure 11

shows that the realized

current level is slightly

reduced due to lack of

voltage between 45 and 55m.

In the eddy current brakes the

decelleration is large,

between –20 and -30m/s2,

causing the pushercar alone

to stop within one second.

The train with the passengers

continues at a speed of 25m/s

for some meters before it

enters the first high looping

of the complex curved ride.

After delivering the train at

the requircd speed, the

pushercar decelerates in eddy

current brakes and returns to

the starting postion before

engaging with the next train.

1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08

0

0.5

1

inductance [mH

]

→

1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08

-500

0

500

u

β

[V]→

1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08

-4000

-2000

0

2000

4000

iα,i

β

[A]→

time [s]→

Figure 10 Measured data: stepwise change in inductance, switching frequency

increases, current shape unaffected.

0 10 20 30 40 50 60 70 80

−1000

0

1000

2000

3000

position [m] →

i

q

[A

rms

] →

0 10 20 30 40 50 60 70 80

−10

0

10

20

30

position [m] →

speed [m/s] →

launch

launch

return

return

Figure 11 Current and pushercar speed versus position during one cycle.

Cycle consists of start, launch with train, brake without train,

slow return through eddy current brakes and fast return to initial

position.

7

The return thru the eddy current

brakes should be done at low

speed to reduce excessive stator

heating. After the brakes are

passed, the acelleration is

increased until the speed of 12m/s

is reached, the rest of the return

between 45m and 12m is in free

wheeling mode. Mechanical

brakes stop the pushercar on the

return to base movement.

Both high speed and low speed

pushercar braking were tested

succesfully in various

experiments. During these

experiments additional brake choppers were placed on the DC link of the inverter to allow burning

over 1.2MW of regenerative power. The proposed current control method proved well capable of full

four quadrant operation. For safety reasons the practical roller coasters still use passive braking.

Mechanical wear of pneumatic brakes could be reduced when active braking would be implemented.

However, during the design of the present track layout, active braking was not considered. A more

economic launch track design might be possible when including the possibility of high power active

braking.

4 Conclusions

• An effective and robust current control strategy for a 2.4MW synchronous linear motor has been

designed and implemented, needing no actual motor parameters such as inductance. The method

allows controlling current straight thru step-wise inductance changes as do occur in switched-

stator linear motors (at 3m intervals in

this case, yielding 25/3=8.3 inductance

changes per second at top speed).

• The proposed current control strategy

allows very low asynchronous switching

frequencies (between 500Hz and

1000Hz) to control large currents of up

to 3kA at high acceleration (up to

75Hz/s) with high phase accuracy.

• Active braking of up to 1.2MW has

been succesfully tested, hence yielding

full 4-quadrant capability when a

sufficient brake chopper is installed.

• A sensorless position estimation

strategy [4] was succesfully tested on the

long LSM, using just measured voltages and currents of the inverter.

• The proposed current control makes it possible to repeatedly launch roller coaster trains up to

15m/s2, 0…90km/h in 3s, using low cycle times, with only local forced air cooling.

5 References

1. D.M Brod, D.W. Novotny, ‘Current control of VSI-PWM inverters’, IEEE Trans. Ind. Appl., IA-21, 1985.

2. G.W McLean, ‘Review of recent progress in linear motors’, IEE proceedings Vol. 135, Nov. 1988

3. A.Veltman, ‘The Fish Method : Interaction between AC-Machines and Switching Power Converters’, Phd

thesis, Delft University of Technology the Netherlands, 1994, ISBN 90-9006763-9

4. A.Veltman, ‘A method and a device for sensorless estimating the relative angular position of the rotor of a

three-phase synchronous motor’, Patent application, EP1162106, 2001-12-12.

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

0

1000

2000

3000

time [s] →

iq [Arms] →

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

0

10

20

30

time [s] →

speed [m/s] →

Figure 12 Launch with train to 25m/s. Current and speed versus time.

Figure 13 Final result.