Modelling of a motor
Approaches to motor identification
• Go to the data sheets from the manufacturer
and obtain the relevant motor performance
characteristics
• Use a step input to a physical motor and find
the time constant and gain of the system and
model it as a first order system
Experimental
• Using a fully instrumented system that
measures the voltage applied to the motor
and the rotational velocity produced by the
motor at regular time intervals
• Apply a step input to a physical motor and find
the time constant and gain of the system and
model it as a first order system
Experimental determination of
inductance and resistance
• Using a fully instrumented system that
measures the voltage applied to the motor
and the rotational velocity produced by the
motor at regular time intervals
• Connect a motor up to a resistance and
inductance meter.
• The following physical quantities of the DC Motor need to
be measured to determine its transfer function:
• Armature resistance: Ra [ohms]
• Armature inductance: La [Henries]
• Torque constant: KT [N-m/amp]. Proportionality constant
that relates
• Back EMF constant: Kb [volts-s/rad]. Proportionality
constant that relates
• Angular velocity and back e.m.f. Please refer to equation 2
on the previous slide.
• Viscous friction coefficient: B [N-m-s/rad]
• Rotor moment of inertia: J [kg-m²]
Locked rotor test
• Under locked rotor conditions there is no back
EMF, so the back EMF drops out of the equations
that describe a motors performance.
• Apply a step input to the motor and when the
motor reaches steady state with under locked
rotor conditions read the inductance and
resistance from the inductance resistance meter.
• Repeat this process by apply different voltage
step inputs.
• Take the average inductance and resistance
measurement from the set of data collected.
Armature inductance
•
•
•
•
Consider equation 1 again
We lock the rotor again
We apply a resistor in series with the motor.
We now use equaton 1 and equation 2
• Use an inductance meter to determine the
inductance of the motor under locked rotor
conditions.
• Repeat the experiment at different serial
resistance values
• Obtain an average for the inductance value
Back EMF constant
• Compute the back – EMF constant (Kb).
• The motor will be permitted to spin freely and
measurements will be taken when the system
has reached its steady state.
• Once steady state is reached, Ia will be
constant, therefore, its derivative will be zero.
• Substituting Equation 2 into Equation 1 yields
Equation 4:
• The angular velocity ( ω ) can be found by
measuring the tachometer voltage.
Viscous friction coefficient
• Since Kb = KT finding Kb will give KT.
• At steady state conditions, combining
Equation 5 and Equation 6 yields Equation 7,
which allows us to compute the viscous
Friction Coefficient (B).
Motor rotor moment of inertia J
• The motors moment of inertia can be
calculated from the motor time constant.
• The motor’s moment of inertia (J) and the
friction coefficient (B) establish the angular
velocity decay rate once current to the motor
has been cut.
• With B known, we can find J. (τ =J/B).