Full Report Motor Speed

7/26/2019 Full Report Motor Speed

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NAME : MUHAMAD SHAIFULLAH EFENDI BIN JAWAHIR

MATRIC NUMBER : F57-213-0026

NAME : MUHAMMAD KHALID BIN YAHAYA

MATRIC NUMBER : F56-213-0002

CLASS : TAKI

TEACHER : SENSEI ISMAIL BIN JUSOH

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MARA-JAPAN INDUSTRIAL

INSTITUTE

FEEDBACK CONTROL SYSTEMDFE 3223!

DC MOTOR SPEED

INTRODUCTION


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A common actuator in control systems is the DC motor. It

directly provides rotary motion and, coupled with wheels ordrums and cables, can provide translational motion. Theelectric equivalent circuit of the armature and the free-bodydia ram of the rotor are shown in the followin ! ure. "or thise#ample, we will assume that the input of the system is thevolta e source $ V % applied to the motor&s armature, while theoutput is the rotational speed of the shaft d$ theta %'dt. The rotorand shaft are assumed to be ri id. (e further assume a viscous

friction model, that is, the friction torque is proportional to shaftan ular velocity.

)


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The physical parameters for our e#ample are*

$+% moment of inertia of the rotor . 1 .m ) $b% motor viscous friction constant .1 /.m.s $0e% electromotive force constant . 1 'rad'sec $0t% motor torque constant . 1 /.m'Amp $2% electric resistance 1 3hm $4% electric inductance .5 6

7ystem 8quation *

Transfer "unction *

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Desi n 2equirements *

7ettlin time less than ) seconds 3vershoot less than 5:

7teady-state error less than 1:

;

MATLAB ANALYSIS


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"rom the plot we see that when 1 olt is applied to thesystem the motor can only achieve a ma#imum speed of

.1 rad'sec, ten times smaller than our desired speed.Also, it ta es the motor ). = seconds to reach its steady-state speed> this does not satisfy our ) second settlintime criterion.

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PID CONTROLLER DESI"N


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@ID Controller Desi n Transfer "unction.

@roportional Control *

=


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"rom the plot above we see that both the steady-stateerror and the overshoot are too lar e. 2ecall from theIntroduction* @ID Controller Desi n pa e that increasin

the proportional ain Kp will reduce the steady-state error.6owever, also recall that increasin Kp often results inincreased overshoot, therefore, it appears that not all ofthe desi n requirements can be met with a simpleproportional controller.

@ID Control (ith 7mall 0i And 7mall 0d
http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction&section=ControlPIDhttp://ctms.engin.umich.edu/CTMS/index.php?example=Introduction&section=ControlPID


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Inspection of the above indicates that the steady-stateerror does indeed o to Bero for a step input. 6owever, thetime it ta es to reach steady-state is far lar er than therequired settlin time of ) seconds.

@ID Control (ith 4ar e 0i And 7mall 0d *


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As e#pected, the steady-state error is now eliminatedmuch more quic ly than before. 6owever, the lar e Ki has

reatly increased the overshoot. 4et&s increase Kd in anattempt to reduce the overshoot. o bac to the m-!leand chan e Kd to 1 as shown in the followin . 2erun yourm-!le and the plot shown below should be enerated.

@ID Control (ith 4ar e 0i And 4ar e 0d *

1


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As we had hoped, the increased Kd reduced the resultin

overshoot. /ow we now that if we use a @ID controller

with Kp E 1 , Ki E ) , and Kd E 1 , all of our desi n

requirements will be satis!ed.

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DISCUSSION


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In this e#periment we have discussed on how to !nd thetransfer function based on the modellin iven. 3ther than that

also we also have discussed on to apply step input in yoursystem and shows the output response. "urthermore, we alsohave analyse our system in term of time constant, pea time,rise time, settlin time, overshoot and also stability. /e#t, wealso have discussed on how to use

Full Report Motor Speed

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