DESIGN ,ANALYSIS

&COMPARISON OF VARIOUS

CONTROLLERS FOR DC

MOTOR SPEED CONTROL

Presented By

VARUN Kvarunkpa@gmail.com

INTRODUCTION

• A DC motor is any of a class of electrical machines that converts direct current electrical power into mechanical power.

• Applications: Lathes ,Drills, Boring mill, shapers, Spinning and Weaving machines, Electric traction, Cranes etc.

• How to choose DC motor: 1.How fast we want to move

2.Weight,size

3.cost and size

• Parameters:

b)Torque a)Rated speed

MODELLING

MODELLING

MODELLING

BLOCK DIAGRAM

DC MOTOR CHARACTERISTICS

• J=0.01 kgm2

• B=0.1 Nms

• Kb=0.01

• Kt=1.25

• R=1 ohm

• L=0.5 H

• Operating Voltage:12-15v

• speed:140-160rpm (1V12 rpm)

1.25

0.005 s^2 + 0.06 s + 0.1125OT=w(s)/Va(s)=

OPEN LOOP step response(m)

Tr=0.991secTs=1.8003 secMp=0%

CLOSED LOOP SYSTEM• Implementation of speed to voltage converter

• Gain of S to V Converter=0.25

(Reference speed =140rpm)

DESIRED OUTPUT

TACHOMETER

1

S-V converter

CLOSED LOOP STEP RESPONSE(m)

Tr= 0.215secTs=0.652 secMp=6.77%Ess=26.5%

COMPARISON

OPEN LOOP

• RiseTime: 1.3290sec

• SettlingTime: 1.8003sec

• Overshoot: 0%

• Steady state: 11.1078

CLOSED LOOP

• RiseTime: 0.215sec

• SettlingTime: 0.652sec

• Overshoot: 6.77%

• Steady state : 0.735

OBSERVATIONS: Transient Response improvement

Tr reducedTs reducedMp introducedEss increased

STATE SPACE MODEL(m)-ss()• a =

• x1 x2

• x1 -12 -5.625

• x2 4 0

•

• b =

• u1

• x1 8

• x2 0

•

• c =

• x1 x2

• y1 0 7.813

•

• d =

• u1

• y1 0

• a =

• x1 x2

• x1 -12 -10.63

• x2 8 0

•

• b =

• u1

• x1 2

• x2 0

•

• c =

• x1 x2

• y1 0 3.906

•

• d =

• u1

• y1 0

CONTROLLER DESIGN

P PROPORTIONAL CONTROLLER(m)

AIM: set input =1 output= 1.It never happens If it happens plant gets switched off. So always there is a Ess in closed loopProportional controller is used to raise the steady state output.Designed for various values of Ki

Kp %Mp Ϛ Tr

1 6.7 0.65 0.3

0.5 1.14 0.85 0.346

.25 0 >=1 0.521

P controllerKp=1

Kp=0.5

Kp=0.25

OBSERVATIONS(m) As Kp , Ϛ , overshoot ,Tr becomes over damped.Never achieves the steady state.Existence of steady state error.

I INTEGRAL CONTROLLER(m)

Accumulation of past errorsIncreases the order of the system.

Ki Tr %Mp Ts Ϛ

1 0.5 33.2 4.65 0.33

0.5 1.01 12.6 3.41 0.55

0.25 2.11 0.74 3.39 0.91

I controller

Ki=0.25

Ki=0.5

Ki=1

OBSERVATIONS(m)

If Ki Steady state error eliminates. Rise time reduces. Peak over shoot increases. Settling time increases. Damping factor increases Over damped responses

Why not Differential controller???Amplifies High frequency noiseDerivative of sudden changes creates impulsesDerivative action deceases rise time and oscillations

PI Controller(m)

Root locus methodTr<0.3 sec, Ts<0.6sec,%Mp<5%.Kp=2.14, Ki=18.4.Rise time condition satisfied and Ess=0.Settling time and overshoot is heavyKp makes small change in settling time, increase in overshoot.Ki Ts, %Mp.

Step response(m)

Tr=0.10secTs=2.31sec%Mp=66.5Ess=0

Root locus method

Tr<0.3 sec, Ts<0.6sec,%Mp<5%.

Kp=10,Kd=0.858

Ts, %mp reduced drastically

Overshoot error=4%.

PD Controller(m)

Step response(m)

Tr=0.037secTs=0.059sec%Mp=1%Ess=4%

PID controller(m)

• Root locus

• Combining the requirements. Tr<0.3 sec, Ts<0.6sec,%Mp<5%.

• Kp=6.914 Ki=18.53 Kd=0.3104

• Ts

• Tr

• Ess=0

Step response

Tr=248 msecTs=926 msec%Mp=7.48 %Ess=0

Tr Ts %Mp %Ess

open 0.991sec 1.8003sec 0 8.3

closed 0.215sec 0.652sec 6.77 0.735

P 0.07sec 0.61sec 33.6 6

I 0.59sec 4.65sec 33.2 0

PI 0.1sec 2.31sec 66.5 0

PD 0.037sec 0.059sec 1 4

PID 0.248 sec 0.926 sec 7.48 0

COMPARISON

Open loop locus root locus

With PID controller Root locus

Gain Margin – Phase MarginGain Margin: additional gain that makes the

system on the verge of instability /gain

perturbation that makesthe system marginally stable.Phase Margin: Additional phase lag that makes the system on the verge of

instability/negative phase perturbation

that makes the system marginally stable.

Why should we consider GM,PM?

• Different rotor Inertia(diff size load) –Gain

• Temperature sensitive(Back emf) Power –Gain

• More drag in Bearings –Gain and Phase

• Slower digital computer(Sensor)-Phase

You cannot know of all these things, So we should define everything in margin.

Bode plot-without controller

PM=43.3 degGM=inf

Bode plot-with PID controller

PM=69.3 degGM=inf

Simscape Model DC-Motor