High FluxDrive Coils

Top & bottom

Laser FeedbackSensorsTop & bottom

LaserConditioningElectronics

Provides high resolutionposition measurement

Rare EarthMagnets

NbFeB, one or twoat a time for SISO

or MIMOLow Friction

GuidePrecision ground& polished glass

MagnetStorage

Safely stows highstrength magnets

Model 730MagLev

ApparatusF a c t S h e e t

m g

Attractive LevitationOpen Loop Unstable

Repulsive LevitationOpen Loop Stable

mg

Ic

y

m2 gm1

Ic2

Ic1

S

NS

N

S

N

N

S

y1

y2

MIMO Levitation, LocallyOpen Loop Stable

MIMO Levitation,Open Loop Unstable

F = (y + d)Ncm

kcmIc ,c1m

my+cy = F - mgc2mmy+cy = Fc1

- mgm

my' +cy' +ky' =

I 'ckF my' +cy' - ky' = I 'ckF

"'"denotes value relative to some equilibrium pt. kcm, d, & Ncm are positive constants, (Ncm ≈ 4)

Educational Control Products

m1y1+cy1 = Fc1m1+Fm1m2

+Fc2m1+ m1g

m2y2+cy2 = Fc1m2+Fm1m2

+Fc2m2+ m2g

Fc1m1 = kcmIc1

(y1+dc1m1

)Ncm

Fm1m2 = kmm

(y1-y2+dm1m2)Nmm

Fc2m1= kcmI

2

(y1+dc2m1

)Ncm

Fc1m2= -kcmI

1

(y2- dc1m2

)Ncm

c Fc2 m2= -kcmI

2

(y2- dc2m2

)Ncm

c

m1y1+cy1' '+ (k + k - k )y - k y'1'

21 2 23 = +I 'ckF 111

I 'ckF 221

F = (d- y)Ncm

kcmIcc2m

Stable ∀ (k1+k2)≤ k3 and (k2+k5)≤ k4

m1y1+cy1 = Fc1m1- Fm1m2

+Fc2m1+ m1g

m2y2+cy2 = Fc1m2- Fm1m2

+Fc2m2+ m2g

m1s2+cs +(k

1+k

2-k

3) -k 2

-k2

m2s2+cs +(k

2+k

5-k

4)

Y1

Y2

= kF

1 1kF

1 2

kF2 1

kF2 2

I 1

I 2

m2y2+cy2' ' '2'

12 4 25 = +I 'ckF 112

I 'ckF 222

+(k - k + k )y - k y

m1y1 +cy1' '+ (k - k - k )y + k y'1'

21 2 23 = +I 'ckF 111

I 'ckF 221

m2y2 +cy2' '- (k + k - k )y + k y'2' 12 4 25 = +I 'ckF 112

I 'ckF 222

Stable ∀ k1 ≥ (k2+k3) and k5 ≥ (k2+k4)

YI 'c

= kF

ms2+cs +k

Notation similar to thatfor SISO (Nmm ≈ 4)

ECP's unique MagLev appa-ratus dramatically demon-strates closed loop levitationof permanent and ferromagneticelements. The apparatus in-cludes laser feedback and highflux magnetics to affect large dis-placements and provide visuallystimulating tracking and regulationdemonstrations. The system is quicklyset up in the open loop stable and un-stable (repulsive and attractive fields)configurations shown. By adding a sec-ond magnet and driving both actuators,MIMO control is studied. The inherent magnetic field nonlinearities may be inverted via provided real-time algorithms for linearcontrol study or the full system dynamics may be examined. Disturbances may be introduced via the second drive coil for demon-strating system regulation in SISO operation. An optional turntable accessory provides graphic demonstration of induced field levi-tation - the principal used in high speed bullet trains!

TF of above leftstable system

TF of above leftsystem; stabilityassumed

Configur-ation

Equationsof Motion

LinearizedForms

TransferFunction

Notation

(about some coilcurrent / gravity

equilibrium)

(selected linear-ized plant)

Ic

y

("c" is very small frictionmodeled as viscous)

N

S

S

N N

S

S

N

Fc1m Fc2m Coil #1 (c1)

Coil #2 (c2)

m2

gm1

Ic2

Ic1

S

NS

N

S

N

N

S

y1

y2

Provides A Variety Of SISO & MIMO, Stable & Unstable Plant Configurations

Attachment For TurntableOptional, demonstrates induced field levitation

Quality Components Provide High System PerformanceRange of Motion

Magnets

Sensors

Drive Coils

Drive Amplifiers

Size & Weight

Turntable Accessory

Accessory Sensor & Actuator

Accessory Size & Weight

15 cm total. 6 cm indefinitely 10 cm momentarily ea. actuator

Very high flux, rare earth NdFeB, with laser reflective coating

Laser light amplitude with low noise, stray light rejection circuitry

Low inductance, high field constant, air core

Linear range ± 40V out, 500 Hz current loop bandwidth

36x36x30 cm. (14x14x12 in.), 5.1 kg. (11 lb.)

Dynamically balanced spin platter, 0-500 RPM

Optical encoder, 12,000 counts/rev. Rare earth, servo motor

38x38x15 cm. (15x15x6in.), 4.3 kg. (9.5 lb.)

Turn-key Systems* for Easy Setup & Operation

Thought-provoking Experiments

Contact us For More Information1-800-486-0840

Toll-free in the US & Canada

www.ecpsystems.com

The MagLev system is furnished with a range of experi-ments that graphically demonstrate important theoreti-cal principles and applied control implementation.All experiments include detailed student procedures,supplementary exercises, and complete instructorsolutions. Also provided are plant dynamic models,Matlab® scripts for analysis and simulation, and op-tional exercises to taylor course content.Initial tests perform system identification to quantifythe plant parameters and measure the strongnonlinearities. Early experiments demonstrate appli-cation of simple linear closed loop control to stabilizeand regulate the closed loop system about somesetpoint. It is shown that for the open loop stableplant, (see front page) the system is stabilizable for allpositive gains but that for the unstable plant a mini-mum gain (bandwidth) is necessary for closed loopstability. Further tests vividly show the effect of thenonlinear dynamics on closed loop tracking control(see upper plots). By inverting these dynamics, rapidand precise tracking control is demonstrated.MIMO experiments are included that demonstrate arange of design approaches including LQR, poleplacement, and loop shaping methodologies. The systemis tested (lower plots) with the two magnets controlled in-dependently which produces much cross coupling intheir motion. By implementing a full multivariable controllaw, effective and uncoupled control is accomplished.Other exciting experiments including disturbance re-jection and induced field levitation using the optionalturntable are provided.

E-mail: Info@ ecpsystems.comPh: (818) 703-0802Fax: (818) 703-6040

Educational Control Products5725 Ostin Avenue

Woodland Hills, CA 91367

The MagLev system comes complete with all the hardware &software you need to efficiently perform a broad range of con-trol experiments. Setup requires only three simple steps: 1) In-stall DSP Board in standard PC slot, 2) Load software, 3) Plugin cables and begin. You can easily operate the system in min-utes and perform meaningful experiments the very first hour!

* "Plant Only" option available without DSP board & I/F software

• Rare earth magnets with ultra high flux density produce large levitation heights forgraphic trajectory tracking demonstrations

• Precision non-contacting laser sensors provide feedback over large range of mo-tion without introducing friction

• System may be operated over limited range to demonstrate linear system dynamics, orover large range to show inherent high nonlinearity (inverse fourth order with position)

• Magnets are easily added and removed to provide MIMO or SISO plants that areopen loop stable or unstable

• Adjustable scale for mechanical height reference and dual color LED for bipolar coilcurrent indication promote visualization of system states (available in real-time data)

• Durable plate and bar aluminum construction (guide rod is fracture resistantPyrex®), and ruggedized industrial grade electronics assure high-ly reliable operation

• Step-by-step instructions, intuitive interface software, and detailedexperiments with solutions assure productive use of laboratory time.

• Safety features such as amplifier thermal dissipation limit, over-current shutdown, and magnet overspeed protection assure equipmentdurability and a safe operating environment

• Bench top sized with quick connect cabling for easy transportabilityand reconnection to rest of system

Advanced System Features, Time-saving Benefits

Nonlinear Plant Compensation A simple closed loop linear controller reveals the strong plantnonlinearity which manifests as a low gain step response in the forward direction (underdamped, large s.s.error) and high gain response going negative. The control authority vs. position nonlinearity is addressedvia sensed position/control effort compensation to yield the well behaved bipolar step response at right.

Multi-variable control The plant is configured for 2 inputs and 2 outputs. In the first series, thesystem is controlled as two independent SISO systems and driven with repeated ramp and impulse inputs.Cross coupling due to magnetic interaction is clearly seen in both outputs. Full multivariable methodolo-gy is employed in the second case (right) to effectively control each magnet independent of the other's motion.