OPEN LOOP CHARACTERISTICS OF DC MOTOR


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 has been created using Matlab/Simulink.



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: