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DESIGN ,ANALYSIS
&COMPARISON OF VARIOUS
CONTROLLERS FOR DC
MOTOR SPEED CONTROL
Presented By
VARUN [email protected]
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
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)=
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
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
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
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
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.
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)
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
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
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.