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

SPEED CONTROL OF A DC MOTOR:

*Using kirchoffs voltage law one can derive

vs = Ra ia + La di/dt + vb

*Back EMF,angular velocity, and torque are related by
vb = Km D0/dt Toque = Kt i

*Here Km and Kt are the back EMF and torque constants respectively

*Angular velocity = theta dot

*The open-loop transfer function for the motor with the speed omega and supply voltage(Vs) can be derived as

w(s)/Vs(s) = Kt/[JLas^2 + (JRan + BLa)s + (BRa + KtKm) ]

*A proportional,integral, and Derivative(PID) controller design is demonstrated to obtain the desired angular speed using the appropriate supply voltage.

PID DESIGN FOR SPEED CONTROL OF A DC MOTOR:

Parameters

*J - Moment of inertia of the rotor - 0.01 kgm^1
*B - Motor viscous friction constant - 0.1 Nms
*Km - Back EMF constant - 0.01V/radians/s
*Kt - Motor torque constant - 0.01 Nm/Ampere
*Ra - Armature resistance - 1 Ohm
*La - Armature inductance - 0.5 Henry

CONTROL DESIGN OBJECTIVES:

*Setting time < 2s
*Overshoot < 5%
*Steady state error < 1%

MATLAB AND SIMULINK MODEL:

*A new script was opened and given a name and the following script was written.

J = 0.01;% Moment of inertia of the rotor in kg-m^2

B = 0.1; % Motor viscous friction constant in N-M-s

*Then the model for speed control of a DC motor was designed using various blocks and the file has been pasted for the reference.

*The above image is the designed model.

*The model is finally saved and run.

*The plots have been made to observe the output.

*The output graphs has been pasted for reference.

*Thus the stability of the system has been analysed from this graph.