[PPT] - ELECTROMECHANICAL SYSTEM Oct 27, 2014 MARIAN STYER & TAMANNA PowerPoint Presentation

SLIDE 1

ELECTROMECHANICAL SYSTEM

MARIAN STYER & TAMANNA ISLAM URMI

Oct 27, 2014

SLIDE 2

OVERVIEW

Introducing the experiment Relevant Background Theory:

 Transfer functions & Bode plots  Lorentz Force Damping  Measuring Deflection (different force application location)

Experimental Procedure Details
Results & Discussion
Conclusion

Tamanna Urmi, Marian Styer

SLIDE 3

EM SYSTEM AT A GLANCE

Tamanna Urmi, Marian Styer

SLIDE 4

EXPERIMENTAL SETUP (GENERAL)

Current Amplifier Oscilloscope FASTAR

Output DAC OUT ACHO BNC 1 BNC 2

ELVIS Electro-Mechanical System Coil Input

Coil Input

1 2

Tamanna Urmi, Marian Styer

SLIDE 5

OBJECTIVES

Explore 3 methods of system identification for the system

resulting transfer function resulting system parameters

Identify benefits and drawbacks of each method
Find the most descriptive model for the experimental set-

up

Tamanna Urmi, Marian Styer

SLIDE 6

SECOND-ORDER SYSTEMS, TRANSFER FUNCTIONS, AND BODE PLOTS

Generalized Transfer Function of a System
For a Second-Order System:
Bode plots relate frequency of system to magnitude and phase

𝐼 𝑡 = 𝛽 ∗ 𝜕𝑜 2 𝑡2 + 2𝜂𝜕𝑜𝑡 + 𝜕𝑜 2 𝑦 + 2𝜂𝜕𝑜𝑦 + 𝜕𝑜 2𝑦 = 𝑔(𝑢)

𝐻 𝑡 = 𝐵 (𝑡 + 𝑨𝑜)𝑏𝑜 (𝑡 + 𝑞𝑜)𝑐𝑜 𝑞𝑝𝑚𝑓𝑡 𝑏𝑢: 𝑡 = −𝑞𝑜 𝑨𝑓𝑠𝑝𝑓𝑡 𝑏𝑢: 𝑡 = −𝑨𝑜

Tamanna Urmi, Marian Styer

SLIDE 7

MEASURING DEFLECTION AT A DIFFERENT LOCATION FROM FORCE APPLICATION

Length factor equation

Ltotal= length of beam + coil assembly y = position of element of interest

Deflection:

Effective mass for individual elements: Effective mass for cantilevered beam Mb with uniform density:

𝑀. 𝐺. (𝑧) = 𝑧 𝑀𝑢𝑝𝑢𝑏𝑚

2

∗ 3 − 𝑧 𝑀𝑢𝑝𝑢𝑏𝑚 2 𝑌(𝑧) = 𝑌𝑓𝑜𝑒 ∗ 𝑀. 𝐺. (𝑧) 𝑁𝑓𝑔𝑔 𝑧 = 𝑁 𝑧 ∗ ( 𝑀. 𝐺. (𝑧))2 𝑁𝑐𝑓𝑔𝑔 = 33 140 𝑁𝑐 ≈ 0.23𝑁𝑐

Tamanna Urmi, Marian Styer

SLIDE 8

EXPERIMENTAL SETUP: IMPULSE RESPONSE

Current Amplifier Oscilloscope FASTAR

Output DAC OUT ACHO BNC 1 BNC 2

ELVIS Electro-Mechanical System Coil Input

Coil Input

1 2 adapter

Tamanna Urmi, Marian Styer

SLIDE 9

IMPULSE RESPONSE METHOD

Short, quick, and fast impulses were put on the beam by flicking it upwards
The impulse response was observed in LABVIEW
The response waveform was fitted to a transfer function to find the characteristic

parameters of the impulse response

Tamanna Urmi, Marian Styer

SLIDE 10

RESULT FROM IMPULSE RESPONSE

Parameter Value Natural Frequency 43.8733 rad/s Gain 1.81252 mm/N Damping Ratio 0.0253558

Below is the results obtained from the no adapter situation
K and M values cannot be found because without knowing the input amplitude,

the gain values does not make sense

Tamanna Urmi, Marian Styer

SLIDE 11

RESULT FROM IMPULSE RESPONSE

Used to observe electrical

method of damping

The damping ratio decrease

logarithmically as the resistance increases

V=IR. As R increases with V

being constant, the I decreases causing a damper oscillation.

y = -0.073ln(x) + 0.3669

0.1 0.2 0.3 0.4 0.5 0.6

10 20 30 40 50 60 70 80 90 Damping Ratio Resistance of adapter Damping Ratio Infinite Resistance Damping Ratio

Log. (Damping Ratio)

Tamanna Urmi, Marian Styer

SLIDE 12

EXPERIMENTAL SETUP: STEP RESPONSE

Current Amplifier Oscilloscope FASTAR

Output DAC OUT ACHO BNC 1 BNC 2

ELVIS Electro-Mechanical System Coil Input

Coil Input

1 2

Tamanna Urmi, Marian Styer

SLIDE 13

TECHNIQUE #2: STEP FUNCTION RESPONSE

Damper Filled with Water vs Damper Filled with Glycerol

Force (N); Position (mm) Step Input System Response Force (N); Position (mm) Step Input System Response

Tamanna Urmi, Marian Styer

SLIDE 14

STEP FUNCTION RESPONSE METHOD

Mathcad and LabView were used to apply a step input function of 0.4 N
ver 0.5 seconds and record the response of the beam
Mathcad was then used to find the system parameters (gain, natural

frequency, damping) via least square fit

Mathcad calculated the corresponding M, C, and K where:

𝐿 = 𝑀. 𝐺. 𝛽 𝑁 = 𝑀. 𝐺. 𝛽 ∗ 𝜕𝑜 2 𝐷 = 2 ∗ 𝜂 ∗ 𝑀. 𝐺. 𝛽 ∗ 𝜕𝑜

L.F. = Length Factor=0.668 for position transducer

Tamanna Urmi, Marian Styer

SLIDE 15

SYSTEM ID RESULTS FROM TECHNIQUE #2

Parameter Damper Filled with Water Damper Filled with Glycerol

Gain (α) 1.662 ± 4.2E-3 mm/N 1.6670 ± 5.4E-3 mm/N Damping Ratio (ζ) 0.019 ± 0.00 0.178 ± 0.022 Natural Frequency (ωn) 43.73 ± 0.15 rad/s 43.11 ± 0.37 rad/s Beam Stiffness (K) 402.2 ± 1.3 N/m 401.0 ± 1.4 N/m Effective Mass (M) 210.2 ± 1.5 g 215.8 ± 4.2 g Damping constant (C) 0.3525 ± 6.2E-3 N*s/m 3.30 ± 0.43 N*s/m Calculated theoretical K & M values for comparison: K = 441 ± 12 N/m M = 203.10 ± 0.26 grams

Tamanna Urmi, Marian Styer

SLIDE 16

COMPARING TRANSFER FUNCTION MODELS OF THE SYSTEMS

Position (mm)

Damper with water Damper with Glycerol

Tamanna Urmi, Marian Styer

SLIDE 17

EXPERIMENTAL SETUP: SWEPT SINE RESPONSE

Current Amplifier Oscilloscope FASTAR

Output DAC OUT ACHO BNC 1 BNC 2

ELVIS Electro-Mechanical System Coil Input

Coil Input

1 2

Tamanna Urmi, Marian Styer

SLIDE 18

RESULTS FROM SWEPT SINE RESPONSE

The low frequency transfer function for the

waveform is:

1062.26 𝑡2+19.7043𝑡+1948.31

Parameters:

𝛽 = 1.745 mm/N,
𝜕𝑜 = 44.545 rad/s,
ζ = 0.223

Parameter Theoretical Experimental

Stiffness of beam, K [N/m] 440.68 ±11.919 383.077 Effective mass, Meff [kg] (203.1±0.26)x10-3 (193.05)x10-3

The magnitude of force applied to the beam is controlled by ELVIS
The swept was initiated by “Swept Sine” program in LABVIEW and ran for

about 12 minutes. It stopped after creating a loud sound at the resonant frequency.

𝐼 𝑡 = 𝛽 ∗ 𝜕𝑜 2 𝑡2 + 2𝜂𝜕𝑜𝑡 + 𝜕𝑜 2

Tamanna Urmi, Marian Styer

SLIDE 19

BODE PLOT OBTAINED FROM SWEPT SINE

The primary resonance
ccurs at 7.09 Hz or

44.545 rad/s as can be seen in the bode plot

Number of poles : 2
Number of zeroes : 0

Tamanna Urmi, Marian Styer

SLIDE 20

COMPARING THE 3 METHODS

Impulse response can only be used to find damping ratio
Step response with water gives more accurate K and M values

Parameter Theoretical Impulse Response Step Response (Glycerol) Step Response (Water) Swept Sine Response K [N/m] 440.68 ±11.919 Cannot be found 401.04±1.36 402.24±1.29 383.077 Meff [kg] (203.1±0.26)x10-3 Cannot be found (215.75±4.18)x10-3 (210.25 ±1.52 )x10-3 (193.05)x10-3 𝛽 Cannot be found 1.6670±5.4x10-3 1.662±4.2x10-3 1.745 𝜕𝑜 43.8733 43.11±0.37 43.73±0.15 44.545 ζ 0.02536 0.178±0.022 0.019±0.00 0.223

Tamanna Urmi, Marian Styer

SLIDE 21

MASSES FOUND BY DIFFERENT METHODS

2.03E-01 2.16E-01 2.10E-01 1.93E-01 0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 2.50E-01

Theoretical Step Response (Glycerol) Step Response (Water) Swept Sine Response

Meff [kg]

Tamanna Urmi, Marian Styer

SLIDE 22

BEAM STIFFNESS FOUND BY DIFFERENT METHODS

440.68 401.04 402.24 383.077

100 200 300 400 500

Theoretical Step Response (Glycerol) Step Response (Water) Swept Sine Response

K [N/m]

Tamanna Urmi, Marian Styer

SLIDE 23

COMPARING ACCURACY OF K & M VALUES

Step Response using water gives greatest accuracy for K and M values,

however Step Response using glycerol does not give as good an accuracy

0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 2.50E-01 Theoretical Step Response (Glycerol) Step Response (Water) Swept Sine Response

Meff [kg]

100 200 300 400 500 Theoretical Step Response (Glycerol) Step Response (Water) Swept Sine Response

K [N/m]

Tamanna Urmi, Marian Styer

SLIDE 24

CONCLUSION

In general Method #2, Step Response (water), provides

“depth”

Method #3, Swept Sine, gives “breadth”
Further study: examine how each damping component

varies and which dominates under different conditions.

Tamanna Urmi, Marian Styer

SLIDE 25

REFERENCES & ACKNOWLEDGEMENTS

1 B. J. Hughey and I. W. Hunter, "Electro Mechanical System Experiment: Background," 2.671

Laboratory Instructions, MIT, Fall, 2014 (unpublished, accessed on 10/10/14 from https://wikis.mit.edu/confluence/display/2DOT671/Electromechanical+System+Experiment)

2 B. J. Hughey and I. W. Hunter, "Electro Mechanical System Experiment Procedure," 2.671

Laboratory Instructions, MIT, Fall, 2014 (unpublished, accessed on 10/10/14 from https://wikis.mit.edu/confluence/display/2DOT671/Electromechanical+System+Experiment)

We would like to thank Dr. Hughey for patiently answering our many questions, both via email and in person. We would also like to thank Dr. Milne and Dr. Hughey for their assistance while conducting the lab.

Tamanna Urmi, Marian Styer

SLIDE 26

QUESTIONS?

Tamanna Urmi, Marian Styer

SLIDE 27

BONUS SLIDES! GAIN VS RESISTANCE OF ADAPTER

y = 4.3172x-0.308

2 4 6 8 10 12

10 20 30 40 50 60 70 80 90

Gain Infinite Resistance Gain Power (Gain)

Resistance of Adapter Gain

Tamanna Urmi, Marian Styer

SLIDE 28

BONUS SLIDES! HIGHER FREQUENCY BODE PLOT

The secondary resonance
ccurs at 48.73 Hz or

306.18 rad/s as can be seen in the bode plot

Number of poles : 4
Number of zeroes : 4

Tamanna Urmi, Marian Styer

SLIDE 29

THEORY BEHIND DASHPOT DAMPING CONSTANT

Shear stress, τ = −µ𝑕𝑚𝑧𝑑 υ

δ

Viscous force exerted on the

plunger, 𝐺 = τ𝐵 = −µ𝑕𝑚𝑧𝑑

υ δ

π𝐸𝑞𝑚 = −𝐷𝑒𝑞υ Hence, 𝐷𝑒𝑞 =

µ𝑕𝑚𝑧𝑑π𝐸𝑞𝑚 δ

Correcting for the fact that force

and damping is applied at position

ther than the end of the beam,

𝐷 ≡ µ𝑕𝑚𝑧𝑑π𝐸𝑞𝑚 δ LengthFactor ydp ydp L

Tamanna Urmi, Marian Styer

SLIDE 30

DETAILED DESCRIPTION OF SYSTEM COMPONENTS

Position Transducer: composed of a high precision inductor and an aluminum plunger.

As beam moves, plunger moves through coil and FASTAR SP-300A signal

processor accurately measures change in coil inductance.

Lorentz Force Actuator: composed of copper coil surrounded by a pair

f magnets arranged in a quadrupole configuration.
Resulting Magnetic field is at 90degree angle to current flowing through coil.
Positive current produces an upward Lorentz force, deflecting beam up.

(Same direction as viscous mechanical damping force of plunger)

Tamanna Urmi, Marian Styer