Project 2 - Speed Control of a Direct Current (DC) motor

Aim: To design a model to control the speed of a direct current DC motor.

Software used : Matlab (Simulink )

Specification : Controlling dc motor using PID controller kp- proportional gain, kd- derivative gain, ki-integral gain.

Theory :

• Mathematical modeling from the first principles

Legend:
uS – field winding voltage
uR – armature winding voltage
iS – field winding current
iR – armature winding current
RS – field winding resistance
RR – armature winding resistance
LS – field coil inductance
LR – armature coil inductance
MSR – mutual inductance
ωm – angular speed of the engine rotation
mC, mm – moment of conversion and load
Jm – total engine inertia torque
Bm – coefficient of viscous friction

• Modeling an Electrical Engineering system

A direct current (DC) motor is a type of electric machine that converts electrical energy into mechanical energy. DC motors take electrical power through direct current, and convert this energy into mechanical rotation.

• Here the Speed control of a DC motor is either done manually by the operator or by means of an automatic control device.
• This is different to speed regulation where the speed is trying to be maintained or regulated against the natural change in speed due to a change in the load on the shaft

• so the speed can be varied by changing:

  1. The terminal voltage of the armature V
  2. The external resistance in armature circuit R_a
  3. The flux per pole

• So Terminal voltage and external resistance involve a change that affects the armature circuit while flux involves a change in the maginetic field

• so Therefore speed control of DC motor can be classified into:

  1. Armature Control Methods
  2. Field Control Methods

Simulink model :

• Here first we need to creat simulink model of the DC motor and make it as subsytem called the DC motor
• So next the subsytem of DC motor is connected to the discrete PID controller which helps in maintaining the desired speed

• J=0.01; %moment of inertia

  Bf=0.1; %friction and viscous constant

  km=0.01; %Back EMF

  kt=0.01; % Torque

  Ra=1; %Armature resistance

  La= 0.5; %Inductance

Here we consider the PID control paramters as :

Kp =1 ;

ki = 1;

kd =0;

Blocks used for modelling

• Transfer function
• constant
• gain
• mux
• scope
• clock
• To workspace

Results : With continuous steps.

1. Supply Voltage

2. Armature current

3. Torque - At start there is high start torque then it stablise the torque at 3.5 sec

4. Speed

now changing with the values of PID control as

kp=31.5;

ki=82.3;

kd=2.3;

Results :

1.supply voltage

2.Armature current

3. Torque

Back EMF : Some amount of back emf generated with the motoring option

4. Speed: This waveform says that we can operate our desire speed control with the use of PID controller and it proves this model.

• Here by observing the above two graphs we change the desired speed .
• As the armature control changes the speed of the motor can be controlled .

Conclusion:

We have design Simulink model for the DC motor and also we Use 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 and successfully estalished.