SLAU958A January 2025 – March 2025 MSPM0G3507
Model-based BEMF estimation methods are used to achieve position sensorless control of the IPMSM drive system when the motor runs at middle or high speeds. The model methods estimates the rotor position by the back-EMF or the flux linkage model. The sliding mode observer is an observer-design method based on sliding mode control. The structure of the system is not fixed but purposefully changed according to the current state of the system, forcing the system to move according to the predetermined sliding mode trajectory. Advantages include fast response, strong robustness, and insensitivity to both parameter changes and disturbances.

In a digital control application, a time discrete equation of the SMO is needed. The Euler method is the appropriate way to transform to a time discrete observer. The time discrete system matrix of motor model is given in stationary reference frame is given as in Equation 11.
where Fsmo and Gsmo are constants defined based on the Motor parameters as shown below.
and are sliding mode components and are defined as:
where Kslide is the constant sliding mode gain designed by Lyapunov stability analysis. The Kslide value can be tuned using the System Parameters. Having higher Kslide tracks the sliding surface current faster but having very high Kslide leads to errors in BEMF estimation due to switching noise.
Below equation represents the time discrete form of filtered BEMF. Low pass filter removes the high frequency sliding mode output, where the cutoff frequency is usually chosen as the fundamental frequency of stator current. This introduces a phase shift of 45 degrees which is compensated from the estimated rotor position.