Characteristic‐varying systems in the D‐Module: Their properties of existence, realization, and stability

Abstract

SUMMARYSignal processing based on frequency polarity has been attracting wide attention due to its potential applications to industry. It is popular to employ two vector rotators for such signal processing. However, it has very recently been reported that an equivalent signal processing effect can be attained in a much simpler manner using two-input two-output filters in the D-module. This paper further investigates a class of characteristic-varying systems in the D-module, which contains the filters in the D-module as a special case, and gives new analytical results on their properties from the viewpoints of existence, realization, and stability. If the results are applied to filter problems, n-th order filters in the D-module in new forms can be easily and directly obtained, whose stability and response equivalent to the associated filters with vector rotators are guaranteed. If the results are applied to AC motor modeling problems, dynamic models and block diagrams of AC motors in general reference frame are easily and directly obtained. Very general and useful analyses are given for a newly proposed class of characteristic-varying systems in the D-module that have potential usefulness in various industrial applications including control of magnetic bearing system, analyses and active compensations of power systems, and sensorless drives of AC motors.

“Disturbance observers in D‐module” for sensorless drive of synchronous motors—new phase estimation with zero phase lag

“…Existing specific two-input/output D-module systems such as a D-module filter [1,2], D-module dynamic models for AC motors [2][3][4], a D-module vector controller [5], and a state observer in a D-module for permanent-magnet synchronous motors [6] confirm the very useful properties of the D-module. In particular, in sensorless vector control of synchronous motors, D-module systems are utilized in the following ways.…”

“…Here It has been shown analytically that the 2n-th order D-module filter has the following attractive features [1,2].…”

“…In addition, consider the following two-input/output 2n-th order D-module filter F(D(s, ω)) with the same filter parameters [1,2]:…”

“…The D-module and the D-module system (two-input two-output system described by D-module) were proposed and analyzed by Shinnaka, and the general structure and transfer characteristics of the D-module have been explained elsewhere [1][2][3][4][5][6]. Existing specific two-input/output D-module systems such as a D-module filter [1,2], D-module dynamic models for AC motors [2][3][4], a D-module vector controller [5], and a state observer in a D-module for permanent-magnet synchronous motors [6] confirm the very useful properties of the D-module.…”

A new sensorless vector control method using high‐order filters with speed‐varying bandwidth for permanent magnet synchronous motors

“…Such a speed-varying bandwidth high-order filter is composed of two one-input one-output filters connected in parallel [10]. On the other hand, a speed-varying bandwidth high-order filter can also be configured in the quasi-synchronous frame of reference γδ so as to obtain synchrony free of phase shift at rotor pole N. This can be done by formal replacement of the Laplace operator in the αβ frame of reference by the D-module [19,20]. That is, a speed-varying bandwidth high-order filter in the γδ frame of reference is a single two-input two-output D-module filter.…”