Project - Speed Control of a Direct Current (DC) motor

Aim - This Project we make the with help mathematical eqution and make the DC Motor and Try to Maintain Desired Speed for the during the running condition with help of PID

Working -

Using Kirchoffs Voltage one Can

Vs= Ra*ia + La*dia/dt + Vb

Back Emf angular Velocity and Torque

Vb= Km d*theta/dt

Here Km and Kt are The Back Emf and Torque Contant

Design Parametre For the DC motor For the Motor Controlled

J -Moment Of Intertia Constant 0.01 kgm^2

B- Motor Viscous Fricition Constant - 0.1 Nms

Km- Back EMF Constant - 0.01 v/radins/s

KT-Motor torque Constant - 0.01 Nm/Ampere

Ra- Armature Resitance -1 ohm

La -Armature inductance- 0.5 H

With help of this parameter we make mathmatical equation of Motor

Now we have to Find Out the Kp and Ki and Kd for the Controlled the Motor speed

for we used the State Space Module

d/dt*[theta;i]=[-B/J KT/J; -km/La -Ra/La]*[theta ; i] + [0;1/La]*Vs

A=[-10 1; 0.02 2] B=[0 ; 2]

Now we used Pole placemnt

Fn= 1.0 ; Frequncy

wn= 2*pi*Fn Natural Frquncy

zeta=0.9 Underdamped Condition

p1= -zeta*wn+wn*sqrt(zeta^2-1)

p2=-zeta*wn-wn*sqrt(zeta^2-1)

P=[p1;p2];

K=Place(A,B,P)

Kp=13.2005

Kd=1.6549

Ki=1

Now Design the Model Of DC Motor and PID controller in Simulink

For Better Tracking Performace we Take

Kp=39.43

Kd=19.14

Ki=16

we take Input Supply As Step Function

then we take Three gain block for Ki ,Kd,Kp for the Kd we take derivative block and For the Ki we take the integrator block

then we take the tranfer function block for the dc motor parameter armature and Rotor Intertia and Frication

we calacualte the speed

Output Plot for the Tracking Performace of the Vechicle speed according to the desired speed and actule speed

Conclusion-

we try to maintain the speed of motor according to ref speed with help of PID Controller we get better tracking perfromace with find out the best Ki,Kp ,Kd for controlled speed