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Eric Gilbertson, egilbert@mit.edu

Kavya K.Manyapu, kavyam@mit.edu

Lennon Rodgers, rodgers@mit.edu

2.14/2.140 Analysis and Design of Feedback Control

Systems

(Spring 2009 Term Project)

May 14th, 2009

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Objective & Motivation Problem Definition Technical Approach Theoretical Plant Model Controller Design Simulation Results Experimental Design Results Conclusions

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Electric Vehicles (EVs) could soon become atransportation option in the U.S.

EVs can be modeled and controlled using thetools learned in this class

SISO system The speed is controlled via asingle 0-5V signal (throttle)

www.electricmotion.org

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Accurate model of the motorcycle Add speed control to the electric motorcycle

Rise Time (~4 seconds) for step input of 13 m/s (~30 MPH) Zero Steady State Error

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Theoretical Motorcycle (Plant) Model Controller Choice PID

P = Good disturbance rejection I = Zero steady state error D = Faster response

SISO tools/Matlab ROM of gains Simulink to model and tune gains Validated the model using experimentation

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Equations of Motion

Vin = iR +Vemf + Ldi

dt

J= z Fwrw

mx = FwC( x + 2 xw + w

2) (+ Sin)mg

X=Vin

Ls+R

Ktz

J

rw

+mrw

s+Crw(1+ 2w)

+

Ktz

rw

(+ sin)mgr

w+Cw

2rw

J

rw+mr

w

s+C(1+ 2w)rw +

Kt2z

2

Ls+R( )rw

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Constant Description Method ValueL Inductance of the motor

Measured with inductance

meter50*106 Hen.

R Resistance of motor Measured with Ohm meter 0.12 Ohm

Kt Torque constantDetermined from

manufacturers data

0.187 Nm/Amp and Volt/

rad

mTotal mass of motorcycle

and driverCalculated/Estimated 295 kg

JCombined Moment of

Inertia for both front andrear wheels

Calculated/Estimated 1.4 kgm2

z Sprocket Ratio Fixed 6

rw Radius of the wheel Measured/Estimated 0.32 m

Cd Drag Coefficient Estimated 0.6

A Frontal Area of motorcycle Estimated 0.41 m2

Pw = Fw x =1

2ACd(20+ 2)

2+ mg

20

Pwmeter

= (Pmeter Plights) 0.88

Efficiency of motor

Tuned values of , A and Cd

(within uncertainty) to obtain:

Pw

meter= P

w

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PID gains estimated using SISOtools

Finalized using Simulink:KP = 3, KI = 1/2, Kd = 1/5

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Step Input, 13 m/s

13 m/s

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Analog Input: Throttle (05V)

Note: voltage divider was usedDigital Input: Speedometer pulses

Analog Output: Command signal (05V)

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Step Input, Open Loop

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Comm

and/PIDMotorVoltage

(V)

Step Input, Closed Loop

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Step Input, Closed Loop, Beacon HillStep Input, Open vs. Closed Exp., Flat

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Design and implementation of a PIDcontroller

Validation of the design through experiment Future work

Use plant model to predict power consumption andcompare to the experimental (power meter)

Lessons learned EM noise is a serious issue with power electronics Arduino microcontroller was a good final choice

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Gene F. Franklin, 2006, Feedback Control ofDynamic Systems, 5th Edition, Prentice Hall

Vittore Cossalter, Motorcycle Dynamics, 2ndEdition

Electric motorcycle design:www.electricmotion.org

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