Motor inductance, or more appropriately “electrical time constant”, value affects servo drives in many ways. While high inductance values may limit the system bandwidth, low inductance values can lead to control loop instabilities, inaccuracies in current readings, increased power losses and other problems. These issues are especially critical in high speed brushed motors with very low friction and fast dynamics.
Attention with low inductance motors
Low inductance motors may be uncontrollable with most off-the-shelf servo drives or may require hardware / firmware modifications for proper operation. Always check with the manufacturer if the driver is appropriate. The problem is more notorious with brushed DC motors.
This page highlights the principal effects of high and low motor inductance values on the whole servo drive system and how to deal with these effects.
Understanding the effects of low inductance motors
Simplified motor electrical model
An electric motor can be modeled with an equivalent electric circuit that can be used to calculate required voltages (for multiphase motors this circuit would be a single phase representation):
The resistance R is due to the copper wire used to create the windings, the inductance L is due to the magnetic circuit formed by the primary and secondary circuit and is greatly affected by winding and core construction. The voltage E (the back EMF voltage) is due to the induced voltage from the secondary circuit and is proportional to the change in magnetic field (linked to motor speed). In the case of stepper motors and brushless permanent magnet motors the back EMF (Electro Motive Force) is due to the magnets on the rotor. In the case of brushed DC motors it is due to the permanent magnets on the stator or the field winding.
[latex]v(t)=R\times i(t) + L\frac{di(i)}{d(t)}+e(t)[/latex]
This a simplified model based on well understood electrical components such as inductors and resistors. The reality is more complex and can only be understood using advanced electromagnetic simulations.
By the way, depending on the rotor construction method (surface mounted permanent magnet or interior permanent magnet), the inductance will not be always constant, it varies depending on rotor position and the construction of stator and rotor.
Because the magnetic material has a much less relative permeability than the surrounding iron, the reluctance difference for flux flowing through the magnet is greater than reluctance of the iron path. As the rotor’s angle advances, the reluctance has a periodic variation. If the inductance is measured on a coil of the stator, it will look something like below.
Effects of the motor inductance on the servo drive
Current ripple may be big, specially at low speeds
The electrical equation of a motor is given by:
[latex]v=L \frac{di}{dt}+I R+K_{e}\omega[/latex]
Where:
- v is the motor applied voltage (generated by the driver)
- L is the phase inductance of the motor (H)
- [latex]\frac{di}{dt}[/latex] is the rate of change of the current (A/s)
- R is the phase resistance of the motor (Ω)
- I is the current through the motor (A)
- [latex]K_{e}[/latex] is the motor voltage constant (v/RPM)
- ω is the speed of the motor (RPM)
The current variation with time can be expressed:
[latex]\frac{di}{dt}=(v - IR - K_{e}\omega)/L[/latex]
The maximum ripple in a PWM modulated driver is obtained with minimum I·R product and zero motor speed. Motor voltage will be assumed to be equal to bus voltage. Therefore, solving the differential equation and using system values.
[latex]\Delta i_{max} \approx \frac{VBUS}{R} \bigg( 1-e^{\displaystyle-\frac{R}{2Lf_{PWM}}} \bigg)[/latex]
Parameter | Name | Effect on current ripple and conclusions |
L | Motor phase Inductance | Low inductance motors will lead to higher current ripple. |
[latex]f_{PWM}[/latex] | PWM frequency | Low PWM frequency means higher ripple, increasing the PWM will reduce the current ripple. Typically, Ingenia servo drives have PWM frequencies of 20 kHz or 40 kHz, consult the exact value with the datasheet or HW configuration file. A linear servo drive would have an “infinite” PWM frequency and therefore zero ripple. |
[latex]V_{bus}[/latex] | DC bus voltage | High DC bus voltage means higher ripple, reduce the DC bus voltage to the motor nominal whenever possible. |
R | Motor phase resistance | Low resistance motors have lower current ripple. |