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

Aim

A Simulink model for the DC motor by using the Proportional, Integral, and Derivative (PID) control design knowledge gained in the training to design, develop and test a controller to maintain a desired speed for the motor.

Describtion

Simulink model of a dc motor by using PID control design

Steady state model :

Armature current =ia

Back emf =vb

voltage source=vs

Armature inductance =La

Armature Resistance=Ra

J=Rotational inertia

B= Viscous friction

T=Motor Torque

w=Motor speed

Tf=Motor friction torque

The equations are

Torque

Torque=Kt.ia-Tf N(m

Kvl(Armature circuit)

Ea=ia.Ra+eb.v

Ea=armature voltage

Eb=back emf

Ra=Armature resistance

Back emf

Eb=Ke.wm.V

Wm=shaft spped(rad/s)

Eb=Back emf

Ke=Back emf constant

Developed Power

P=wm.T W

P=Power shaft

SIMULINK BLOCK DIAGRAM OF DC MOTOR CONTROLLER SPEED

PID controller

Simulink block diagram of a dc motor output by scope :

Scope

The above Dc motor controlled are shown Armature circuit field circuit with mechanical load

Here the Ea and Eb are the inputs and i(t) is the output

The kvl equation is

Ea(t)=Ra.ia(t) +L.d ia(t)/dt+Eb(t)

Mechanical Dynamics

T(t)=Jm.dwm(t)/dt+Bm.wm(t)

The Electromechanical equations

Eb(t)=Ke.wm(t)

T(t)=Kt.ia(t)

The laplace transform of equation is

Ia(s)=[1/L.s+Ra].Ea(s)-Eb(s)

T(s)=[Jm.s+Bm].ohm sign (s)=ohm sign(s)=[1/Jm.s+Bm].T(s)

The motor shaft position is the integral of the motor velocity with respect to ti,me.To find shaft position,integrate velocity

To find the motor shaft position with respect with respect to armature voltage

Dc motor Transfer function

Back emf ,angular velocityand Torque

vb=Km.d(angular velocity)/dt

Torque =Kti

Km and Kt are back emf and torque constants are used.

MOTOR TRANSFER FUNCTION WITH SPEED CHANGER

Final value

The open loop Transform motor with speed (w) and supply volatage Vs

w(s)/vs(s)=KT/JLas^2+(JRa+BLa)s+(B.Ra+KT.Km)

desired angular speed using the applied supply voltage.