Stability and Accuracy of the Robust System for Stabilizing the Rotor Flux-Linkage of an Asynchronous Electric Drive at Random Variations of the Uncertain Parameters Within the Specified Boundaries

Abstract

The aim is to investigate the stability and the accuracy of a robust system for stabilizing the rotor flux-linkage of an asynchronous electric drive at random variations of the uncertain parameters of the object and the regulator within the specified boundaries. Methodology. To make the research, the mathematical model of the rotor flux-linkage channel of the vector control system of an asynchronous electric drive with parametric uncertainty was applied. The transfer function of the Н ∞-suboptimal regulator was calculated using the mixed sensitivity method. This transfer function was used to construct the regulator structural scheme in the form of a connection of proportional and integrating links and several adders. Analytical dependences of the coefficients of the regulator's transfer function on the parameters of links of such a connection are determined. These dependences served to researching the influence of uncertain parameters of the regulator links and the object on the stability of the robust system and the accuracy of flux-linkage stabilization. Results. Investigations of the robust system stability and the accuracy of flux-linkage stabilization in the Robust Control Toolbox are done. The curves of the fluxlinkage transient processes and the Bode diagram for the open system at random variations of the indeterminate parameters of the object and the regulator links within the specified boundaries are constructed. A choice of variable parameters was carried out by the Monte Carlo method. By the scatter of the obtained curves of the transient processes, the accuracy of flux-linkage stabilization was determined, and according to the Bode diagram, stability reserves in the amplitude and the phase of the robust system were determined. A high accuracy of flux-linkage stabilization (deviation less than 1 %) in fairly wide ranges of changing the uncertain parameters of the object and the regulator, while maintaining the stability of the system with permissible reserves in amplitude and phase, is established. Originality. For the first time, analytical dependences of the coefficients of the transfer function of the Н ∞-suboptimal regulator on the parameters of its structural scheme, which represented in the form of a connection of proportional and integrating links, are obtained. The method for calculating the stability of a robust flux-linkage control system and the accuracy of its stabilization at random variations of the uncertain parameters of the object and the regulator links within the specified boundaries is developed. Practical value. The use of the proposed method allows, during the design of the regulator, to ensure the selection of its elements from standard series. References 10, figures 3.

Analysis and Verification of the Operation of the Stabilizing Robust Controller's Electrical Circuit of the Rotor Flux-Linkage Control System

“…First, a mathematical model of the control object was built and the transfer function of the controller was calculated, as in works [2][3][4]. Then this function was expanded into a continued fraction [4]. The coefficients of this fraction were used to construct a circuit diagram of the controller.…”

“…However, such an analysis cannot be carried out without determining the analytical relationships between the coefficients of the transfer function of the controller and the parameters of the resistors and capacitors of the circuit, which vary randomly within the specified boundaries. Due to the linearity of the mathematical model of the robust fluxlinkage control system [4], such formulas cannot be obtained exactly [6,7]. Therefore, it is necessary to quickly check the operation of the circuit.…”

“…The above approach allows solving the considered problem of analyzing and checking the operation of the electrical circuit of the controller. It was proposed by us in [4]. However, in this work, only the relationship between the coefficients of the transfer function of the controller and the parameters of its structural scheme was taken into account.…”

“…It contains negatrons of negative capacitance NC and negative resistance NR, designed to suppress interference, and differs from circuit [1] only in other designations of resistance and capacitance indexes. The choice of the resistances of the resistors and capacitances of the capacitors of the electrical circuit is carried out in the process of rounding the calculated values of the RC function coefficients (4) to the values of the standard series, and their permissible deviations are determined from the calculation of the stability of the robust rotor flux-linkage control system with random variations in the object parameters (1) and controller (4) within the specified boundaries. In this case, the resistances R4…R7 of the circuit resistors are selected from design considerations, and their accuracy from the same stability calculation.…”