Integration of observer equations used in AC motor drives by zero and First Order Hold discretization

The paper discusses the problem of integrating the equations of state observers associated with direct field orientation (DFO) of AC motor drives and shows the results when the quasi-low pass filters used for integration are discretized based on the Zero Order Hold method (ZOH) and the First Order Hold method (FOH). In a typical observer implementation, the equations are discretized using the Euler method - this is a simple, straightforward approach. Integration is accurate only if the sampling time is small. However, in certain cases, it may not be possible to use a small sampling time. At higher sampling time and under special conditions (if the signals to be integrated are of high frequency), the integration process becomes more inaccurate because the Euler approximation starts losing significant area from under the curve. For a given sampling time, the integral output could be improved by using a more accurate integration method, for example, trapezoidal integration - this solution was already studied. The paper presents the results obtained when the observer equations are integrated with filters that are discretized using the ZOH and the FOH methods. The resulting integral outputs are compared with the ones of the Euler and trapezoidal methods. For illustration, a state observer for the permanent magnet synchronous motor is studied. The theoretical developments are supported with simulation results.