# It is a presentation on Simulation & Analysis of speed control of separately excited DC motor using PID controller

**OBJECTIVES**

1. Applying armature control method to control speed of separately excited dc motor using PID controller.

2. Modeling of full control system of the DC motor.

3. Matlab and simulink has been used for performance analysis of the control system.

**BASIC IDEA**

Equation of speed,

*N = (V - I*

_{a}*R*

_{a})/*φ*

Where

N = Speed of the DC motor

V = Armature voltage

Ia = Armature current

Ra = Armature resistance

φ = Flux

__CHARACTERISTICS OF DC MOTOR__

This is a basic characteristic of the motor; it is a linear relationship and is used to calculate the no-load speed and the start-up torque of the motor.

**Speed, torque and power characteristics of separately excited DC motor**

**PID CONTROLLER**

The transfer function of the PID controller looks like the following:

K

_{p}= Proportional gain
K

_{I}= Integral gain
K

_{D}= Derivative gain**EFFECTS OF INCREASING PARAMETERS**

Parameter | Rise Time | Overshoot | Settling Time | Steady state error |

Kp | Decrease | Increase | Small Change | Decrease |

Ki | Decrease | Increase | Increase | Eliminate |

Kd | Small Change | Decrease | Decrease | Small Change |

Tachometer is a kind of sensor which is electromechanical devices that converts mechanical energy into electrical energy.

Fig: DC tachometer

The induced voltage is given by

Vo=K_{tac}.ω

1. Vo is output voltage,

2. ω is angular velocity,

3. K

_{tac}is proportional constant.**Separately excited DC motor**

Ra: the armature resistance

La: the armature inductance

i

_{a}: the armature current
i

_{f}: the field current
e

_{a}: the input voltage
e

_{b}: the back electromotive force (EMF)
T

_{m}: the motor torque
ω: an angular velocity of rotor

J: rotating inertial measurement of motor bearing

B: a damping coefficient

**Block diagram of separately excited DC motor**

The transfer function of the DC motor

*G(s) = Ω(s) / Ea(s) = KT / {(Ra + Las)(B + Js) + KbKT}*

La can be neglected due to its small value in practice, then,

*Ω(s) / Ea(s) = KT / {Ra (B + Js) + KbKT} = {(KT/RaB) + KbKT} / {1 + (RaJs/RaB) + KbKT}*

ð

*Ω(s) / Ea(s) = Km / (**τ**s + 1)**Km = KT / (RaB + KbKT)*– is a motor gain,

*τ*

*= (RaJ/RaB) + KbKT*– is a motor time constant

**Block diagram of control system for the DC motor**

**The closed loop transfer function of DC motor speed control system expresses as follows**

**Specification**

*Experimental separately excited DC motor*
K

_{T }= 0.06 Nm/A
K

_{b }= 0.06 Vs/rad
Jm = 6.2 x 10

^{-4}Nms^{2}/rad
ω

_{max }= rad/s
I

_{max }= 2 A
ω

_{NL }= rad/s
P

_{max }= 54 Watt
R

_{a}= 1.2 Ω
B

_{m}= 1 x 10^{-4}Nms/rad

**Labvolt DC motor****(model 8211-0A)**
K

_{T }= 2.161 Nm/A
K

_{b }= 2.161 Vs/rad
Jm = 0.47 Nms

^{2}/rad
ω

_{max }= = 101.108 rad/s
I

_{max }= 1.5 A
ω

_{NL }= = 111.051 rad/s
P

_{max }= 472.643 Watt
R

_{a}= 30.467 Ω
B

_{m}= 0.046 Nms/rad**DC motor (Experimental)**

**SIMULINK MODEL**

Labvolt DC motor (8211-0A)

**CONCLUSION**

- Mainly armature voltage is varied where the field current, armature circuit resistance is kept constant.
- Suddenly applied mechanical load causes high armature current due to decrease of the EMF.
- When the torque developed by the motor is exactly equal to the torque imposed by the mechanical load, and then the speed will remain constant.

**Submitted by SAMIR DAS and SURUPAM CHAND DEV at July, 2009**

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