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: R a [ohms] Armature inductance: L a [Henries] Torque constant: K T [N-m/amp]. Proportionality constant that relates Back EMF constant: K b [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, I a 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 K b will give K T. 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).