### Sensorless Control of a Hybrid Stepper Motor

Electrical drives are widely used in todayâ€™s society. They can be found in both
household products and in the industry. One application where electrical drives
are used is in robots for mowing lawns. In the studied robots the motors in the
electrical drives used for propulsion are Brush Less Direct Current motors, BLDC-
motors. The BLDC-motor has its maximum torque at high speeds and therefore
a gearbox is needed. The gearbox is space consuming, add costs and consists of
mechanical parts that wear during use. Of interest is therefore to investigate if
there are other electrical drives which can be used for propulsion.
A motor who has its maximum torque at low speeds is the Stepper motor, and
therefore it is of interest to investigate if a stepper motor could replace the BLDC-
motor. A drawback with the stepper motor is that it always consumes maximum
current and therefore a current controller is beneficial. Together with current
control, speed control is needed to make the robot run at desired speed. To be
able to perform an accurate current and speed control feedback from the motor is
needed. Information about the rotor angle and velocity can be used for the speed
control and the load angle can be used for the current control since the current is
proportional to the load torque.
To estimate the rotor angle and velocity a model has been developed. The
model is based on fundamental electrical and mechanical equations and neglects
the current and position dependence of the inductance and flux linkage. To com-
plete the model three motor parameters, the maximum detent torque Tdm , the
maximum flux linkage Ïˆm and the friction constant B was determined. Parameter
determination was done by linear regression and by using an Extended Kalman
Filter, EKF. The result of the parameter determination were Tdm = 0.2152 Nm,
Ïˆm = -0.002854 Vs/rad and B = 0.01186 Nms/rad.
The model is used in an EKF to estimate the rotor angle and angular velocity.
The result of the implemented EKF seems promising. When making the rotor
take a step in velocity from 3.927 rad/s to 7.85 rad/s the EKF estimates the states
with only a small bias: 0.02 rad for the angle, 0.3 rad/s for the velocity, 0.005 A
for phase a current and 0.0004 A for phase b current.
To estimate the load angle the Sliding Discrete Fourier Transform is used. The
expected relation between the load torque and load angle is sinusoidal. The load
angle is calculated from data where the external load is between 0-2.5 Nm. In
that area the load angle shows the expected sinusoidal appearance and the load
angle is in the area between 0.1 and 0.45 rad. At 3 Nm the rotor stalls and it is
shown that the load angle varies between 0 and 2Ï€ rad when the rotor is stalled.

*Lina Karlsson*

**2016**

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Last updated: 2019-12-17