Advanced input shaping filter 3D virtuallaboratory

Martin Cech, Martin Goubej, Jan Reitinger

June 21, 2013

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Content

• Virtual laboratories• 3-platforms idea• Input shaping filters• Mathematical model of control system• The laboratory development cycle• Final laboratory• Conclusion

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Virtual laboratoriesAdvantages• Low cost maintenance• High efficiency in training• Making mass of experiments simultaneously• Often more demonstrative than real experiment

Commonly used approachesMatlab engine + GUI in LabView• Internet connection is needed• Non-monolithic application

Models in Easy Java Simulations• Described only by equations• Not compatible with

Matlab/SimulinkDrawback• The build-in algorithm cannot be usually directly used for

controlling real plant or machine• In our lab solved with 3-platforms idea

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3-platforms idea• Simulation and development platform• Real-time platform• Java applet platform

The control schemes are fully compatible with block algorithms, inputs,outputs and parameters.

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Input shaping filterProcess model

P(s) =ω2

n

s2 + 2ξωn + ω2n; ξ < 1, ωd = ωn

√1− ξ2,

• ωn – natural frequency• ξ – damping coefficient• ωd – damped frequency

Weighted sum of time delays

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Main advantages of IS filters

• Finite impulse response• Guaranteed stability• Monotone step response• Completely parameterized by ωn and ξ

Main types of IS filters

• ZV (Zero Vibration)• ZVD (Zero Vibration Derivative)• ZVDD• UEI (Extra Insensitive)• UTHEI

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Mathematical model of controled system• x1, y1 – cart coordinates• x1, y1, z1 – load coordinates• α – viscous friction• m – mass of the pendulum• l – length of the pendulum• g – gravitational acceleration• λ – Lagrange multiplier

Differential equations

x2 =−αx2 + 2λx2

m− x1,

y2 =−αy2 + 2λy2

m− y1,

z2 =−αz2 + 2λz2

m− g,

λ =−m(x2

2 + y22 + z2

2 − x1x2 − y1y2 − gz2 − l2 − l l) + α(x2x2 + y2y2 + z2z2)

2(x22 + y2

2 + z22 )

.

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The laboratory development cycle• Mathematical model deriving• Control scheme designing

• Export mdl→ java• 3D model creating

• CAD with VRML output• Construction of labs GUI

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Figure : 1 – SP with the filtration, 2 – motion control, 3 – pendulum model

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The final laboratory

Figure : 1 – control, 2 – interactive scheme, 3 – 3D model, 4 – trendsMartin Cech, Martin Goubej, Jan Reitinger Advanced input shaping filter 3D virtual laboratory June 21, 2013 10 / 12

Conclusion

• Proposed a novel approach for creating virtual labs• Presented vibration damping with the input shaping filter• Assembled virtual lab for presenting advanced input shaping filter• All shaping filter features may be evaluated on 3D gantry crane

model

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AcknowledgementThis work was supported by the Technology Agency of the CzechRepublic – project No. TA02010152 and by the European RegionalDevelopment Fund (ERDF), project NTIS New Technologies forInformation Society, European Centre of Excellence,CZ.1.05/1.1.00/02.0090. The support is gratefully acknowledged.

AvailableThis laboratory can be tested at www.contlab.eu.

Thank you for attention.

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