Simulation & Analysis of speed control of separately excited DC motor using PID controller

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_aR_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 / (τs + 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 Nms²/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 Nms²/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

1. Mainly armature voltage is varied where the field current, armature circuit resistance is kept constant.
2. Suddenly applied mechanical load causes high armature current due to decrease of the EMF.
3. 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