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

ELECTROMECHANICAL SYSTEM Oct 27, 2014 MARIAN STYER & TAMANNA ISLAM URMI

Tamanna Urmi, Marian Styer 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 EM SYSTEM AT A GLANCE

Tamanna Urmi, Marian Styer EXPERIMENTAL SETUP (GENERAL) Oscilloscope Current Amplifier Input Coil 1 2 FASTAR Output DAC OUT ACHO ELVIS BNC 1 Coil BNC 2 Input Electro-Mechanical System

Tamanna Urmi, Marian Styer 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 SECOND-ORDER SYSTEMS, TRANSFER FUNCTIONS, AND BODE PLOTS -Generalized Transfer Function of a System ( 𝑡 + 𝑨 𝑜 ) 𝑏 𝑜 𝐻 𝑡 = 𝐵 ( 𝑡 + 𝑞 𝑜 ) 𝑐 𝑜 𝑞𝑝𝑚𝑓𝑡 𝑏𝑢 : 𝑡 = −𝑞 𝑜 𝑨𝑓𝑠𝑝𝑓𝑡 𝑏𝑢 : 𝑡 = −𝑨 𝑜 -For a Second-Order System: 𝑦 + 2 𝜂𝜕 𝑜 𝑦 + 𝜕 𝑜 2 𝑦 = 𝑔 ( 𝑢 ) 𝛽 ∗ 𝜕 𝑜 2 𝐼 𝑡 = 𝑡 2 + 2 𝜂𝜕 𝑜 𝑡 + 𝜕 𝑜 2 -Bode plots relate frequency of system to magnitude and phase

Tamanna Urmi, Marian Styer MEASURING DEFLECTION AT A DIFFERENT LOCATION FROM FORCE APPLICATION  Length factor equation 2 𝑧 𝑧 𝑀𝑢𝑝𝑢𝑏𝑚 ∗ 3 − 𝑀𝑢𝑝𝑢𝑏𝑚 𝑀 . 𝐺 . ( 𝑧 ) = 2 Ltotal= length of beam + coil assembly y = position of element of interest -Deflection: 𝑌 ( 𝑧 ) = 𝑌𝑓𝑜𝑒 ∗ 𝑀 . 𝐺 . ( 𝑧 )  Effective mass for individual elements: 𝑁𝑓𝑔𝑔 𝑧 = 𝑁 𝑧 ∗ ( 𝑀 . 𝐺 . ( 𝑧 )) 2  Effective mass for cantilevered beam M b with uniform density: 𝑁 𝑐 𝑓𝑔𝑔 = 33 140 𝑁 𝑐 ≈ 0.23 𝑁 𝑐

Tamanna Urmi, Marian Styer EXPERIMENTAL SETUP: IMPULSE RESPONSE Oscilloscope Current Amplifier Input Coil 1 2 FASTAR Output DAC OUT ACHO ELVIS adapter BNC 1 Coil BNC 2 Input Electro-Mechanical System

Tamanna Urmi, Marian Styer 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 RESULT FROM IMPULSE RESPONSE - 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 Parameter Value Natural Frequency 43.8733 rad/s Gain 1.81252 mm/N Damping Ratio 0.0253558

Tamanna Urmi, Marian Styer RESULT FROM IMPULSE RESPONSE -Used to observe electrical 0.6 Damping Ratio method of damping Infinite Resistance Damping Ratio 0.5 Log. (Damping Ratio) -The damping ratio decrease logarithmically as the 0.4 resistance increases Damping Ratio -V=IR. As R increases with V 0.3 being constant, the I decreases causing a y = -0.073ln(x) + 0.3669 0.2 damper oscillation. 0.1 0 0 10 20 30 40 50 60 70 80 90 Resistance of adapter

Tamanna Urmi, Marian Styer EXPERIMENTAL SETUP: STEP RESPONSE Oscilloscope Current Amplifier Input Coil 1 2 FASTAR Output DAC OUT ACHO ELVIS BNC 1 Coil BNC 2 Input Electro-Mechanical System

Tamanna Urmi, Marian Styer TECHNIQUE #2: STEP FUNCTION RESPONSE Damper Filled with Water vs Damper Filled with Glycerol Step Input Step Input System Response System Response Force (N); Position (mm) Force (N); Position (mm)

Tamanna Urmi, Marian Styer STEP FUNCTION RESPONSE METHOD -Mathcad and LabView were used to apply a step input function of 0.4 N over 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 . L.F. = Length Factor=0.668 𝛽 for position transducer 𝑀 . 𝐺 . 𝑁 = 𝛽 ∗ 𝜕 𝑜 2 𝐷 = 2 ∗ 𝜂 ∗ 𝑀 . 𝐺 . 𝛽 ∗ 𝜕 𝑜

Tamanna Urmi, Marian Styer 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 ( ω n ) 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 COMPARING TRANSFER FUNCTION MODELS OF THE SYSTEMS Damper with water Damper with Glycerol Position (mm)

Tamanna Urmi, Marian Styer EXPERIMENTAL SETUP: SWEPT SINE RESPONSE Oscilloscope Current Amplifier Input Coil 1 2 FASTAR Output DAC OUT ACHO ELVIS BNC 1 Coil BNC 2 Input Electro-Mechanical System

Tamanna Urmi, Marian Styer RESULTS FROM SWEPT SINE RESPONSE - 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. -The low frequency transfer function for the Parameter Theoretical Experimental 1062.26 waveform is: 𝑡 2 +19.7043𝑡+1948.31 𝛽 ∗ 𝜕 𝑜 2 Stiffness of beam, K 440.68 ±11.919 383.077 𝐼 𝑡 = 𝑡 2 + 2 𝜂𝜕 𝑜 𝑡 + 𝜕 𝑜 2 [N/m] Parameters: Effective mass, M eff (203.1±0.26)x10 -3 (193.05)x10 -3 - 𝛽 = 1.745 mm/N, [kg] - 𝜕 𝑜 = 44.545 rad/s, - ζ = 0.223

Tamanna Urmi, Marian Styer BODE PLOT OBTAINED FROM SWEPT SINE - The primary resonance occurs 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 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 Step Response (Water) Swept Sine (Glycerol) Response K [N/m] 440.68 ±11.919 Cannot be found 401.04±1.36 402.24±1.29 383.077 (203.1±0.26)x10 -3 (215.75±4.18)x10 -3 (210.25 ±1.52 )x10 -3 (193.05)x10 -3 M eff [kg] Cannot be found Cannot be found 1.6670±5.4x10 -3 1.662±4.2x10 -3 𝛽 1.745 43.8733 43.11±0.37 43.73±0.15 𝜕 𝑜 44.545 0.02536 0.178±0.022 0.019±0.00 ζ 0.223

Tamanna Urmi, Marian Styer MASSES FOUND BY DIFFERENT METHODS M eff [kg] 2.50E-01 2.16E-01 2.10E-01 2.03E-01 1.93E-01 2.00E-01 1.50E-01 1.00E-01 5.00E-02 0.00E+00 Theoretical Step Response (Glycerol) Step Response (Water) Swept Sine Response

Tamanna Urmi, Marian Styer BEAM STIFFNESS FOUND BY DIFFERENT METHODS K [N/m] 500 440.68 402.24 401.04 383.077 400 300 200 100 0 Theoretical Step Response (Glycerol) Step Response (Water) Swept Sine Response

Tamanna Urmi, Marian Styer 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 M eff [kg] K [N/m] 2.50E-01 500 2.00E-01 400 1.50E-01 300 1.00E-01 200 5.00E-02 100 0.00E+00 0 Theoretical Step Response Step Response Swept Sine Theoretical Step Response Step Response Swept Sine Response (Glycerol) (Water) Response (Glycerol) (Water)

Tamanna Urmi, Marian Styer 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 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 QUESTIONS?

Tamanna Urmi, Marian Styer BONUS SLIDES! GAIN VS RESISTANCE OF ADAPTER 12 Gain Infinite Resistance Gain Power (Gain) 10 8 Gain 6 4 y = 4.3172x -0.308 2 0 0 10 20 30 40 50 60 70 80 90 Resistance of Adapter

Tamanna Urmi, Marian Styer BONUS SLIDES! HIGHER FREQUENCY BODE PLOT - The secondary resonance occurs 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