Aim

  To study the open loop characteristics of DC motor and experiment it with Matlab simulation File

The electric circuit of the armature and the free body diagram of the rotor for the DC motor are shown in the following figure:

For this system, we have the following physical parameters:

• moment of inertia of the rotor (J)
• damping ratio of the mechanical system (b)
• electromotive force constant ( = = K )
• armature resistance (R)
• armature inductance (L)
• input (V): source Voltage
• output (): rotating speed

Assumptions in Modelling a DC Motor:

• Demagnetizing effect of armature is neglected.
• Magnetic Circuit is assumed linear (no hysteresis and saturation).As a result all inductances (which came into play in dynamic analysis) are regarded as constant.
• The rotor and shaft is assumed to be rigid.

The motor torque, T, is related to the armature current, i, by a constant factor. The back emf, e, is related to the rotational velocity by the following equations:

In SI units, (torque constant) is equal to (Motor constant).Put, = = K


From the figure above we can write the following equations based on Newton's law combined with Kirchhoff's law:




The time-domain model for dc motor is given below:

The transfer function of the dc motor system is given by:


The block diagram of dc motor in s-domain is given below:

The impulse response and step response for an open loop dc motor system is given below. The dc motor is assumed to have the following parameters:

• moment of inertia of the rotor (J) =0.75e-07 Kg m2
• damping ratio of the mechanical system (b) = 1e-08 Nm/rad/s
• electromotive force constant ( = = K ) = 0.0033 (in SI units)
• armature resistance (R)= 1.27 ohm
• armature inductance (L)= 0.000035 H

The step response for an open loop dc motor system is given below.

The Bode diagram of the system is shown in the figure below:

The Nyquist diagram of the system is shown in the figure below:

The DC motor model for open loop step response and impulse response can be created using Matlab/Simulink.

• Open loop impulse response
• Open loop step response

PLEASE NOTE THAT THE MATLAB/SIMULINK VERSION USED IS 7.10.0.499 (R2010a)

The images of the models along with the corresponding speed profiles are given below.

Simulink Model for Open loop impulse response of DC motor:




Simulink Model for Open loop step response of DC motor: