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Control of a 2.4 MW Linear Synchronous Motor for launching roller-coasters

  • Piak Electronic Design bv

Abstract and Figures

2) Piak Electronic Design b.v., Markt 49, 4101 BW Culemborg, the Netherlands. t: +31-345-534126, f: +31-345-534127, (3) GTI Electroproject b.v., P.O. Box 441, 1500 EK Zaandam, the Netherlands. t :+31756811111, Author Information : 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.
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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,
(3) GTI Electroproject b.v., P.O. Box 441, 1500 EK Zaandam, the Netherlands.
t :+31756811111,
Author Information :
LSM, current control, sensor-less control, switched stators
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
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
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.
Figure 2 shows an accelerating pusher-car
in the final set-up. Figures 6 and 7 show a
close-up measurement of a launched
2 Synchronous frame
hysteresis controller
Requirements for the motor current
controller are:
1. Smooth thrust during fast
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 *
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
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
time [s]
i [A]
Figure 7 Measured data: start of launch with controlled build
up to 2200A, sensor-less position.
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 *
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 *
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 *
is leading the magnet flux by angle
The best way
to orient the switching box is to align it to *
. 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
. (e) Load
angle correction of error box.
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
is leading m
Φ by 90°. To achieve maximum force
per ampère, *
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
U to lead the current by load-angle
. Load angle
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
As set points we use *
i and *
i. As discussed above, we will for now assume that 0
i. In case
there is insufficient DC link voltage to realize *
i, a negative value of *
ican buy force at the expense
of more stator losses as is shown in figure 9.
With the measured dq
two error values can be distinguished, (see figure 8(d)):
By using an estimate of load-angle
, the switching rules can be applied to a transformation of
according to:
dq i
By applying the switching rules in figure 8(b) to the transformed error vector 2dq
, 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.
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
inductance [mH
1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08
1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08
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
position [m]
0 10 20 30 40 50 60 70 80
position [m]
speed [m/s]
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
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
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
time [s]
iq [Arms]
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
time [s]
speed [m/s]
Figure 12 Launch with train to 25m/s. Current and speed versus time.
Figure 13 Final result.
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... We also use the finite element software FEMM [11], connected to Matlab ® in order to simulate the functioning of the motor in controlled loop, using the Hall-effect sensors method ( Figure 1). This method consists in computing a sector variable from the binary combination of the three Hall sensors outputs (1). Then, the coils that are fired are determined according to this variable. ...
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... The main challenge of sensorless control of such an LSM is to deal with fast changing parameters, an high acceleration at speeds from standstill up to 25m/s (0-125Hz electrical).Figure 1 A position estimation method is presented which uses ripple components in the currents and voltages , implicitly generated by current controller the inverter [5], to estimate the motor impedance. This information is then used to extract the angle of the rotor with high precision, even during fast acceleration and stepwise switching motor parameters. ...
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MB Eindhoven, the Netherlands 2 Piak Electronic Design b.v., Markt 49, 4101 BW Culemborg, the Netherlands t: +31-345-534126, f: +31-345-534127, 3 GTI Electroproject b.v., P.O. Box 441, 1500 EK Zaandam, the Netherlands t :+31756811111, Author Information : Abstract An accurate method for estimating the position of a large Linear Synchronous Motor, based on on-line measured phase currents and voltages is shown. Synchronous frame filters remove the fundamental component from these signals effectively, even during fast accelera-tion. The proposed correlators estimate local parameter values, inductance and resistance, from the remaining switching ripple signals with high bandwidth, able to follow the abrupt changes caused by block switching of the long stator. Experimental results show that a controlled start from standstill is possible.
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