MIMO cascaded system stability analysis method based on impedance return-ratio matrix

Abstract

The invention discloses an MIMO cascaded system stability analysis method based on an impedance return-ratio matrix. The MIMO cascaded system stability analysis method regards a high-speed rail train network cascaded system as an object, and comprises the steps of deducing and calculating equivalent pre-stage output impedance of the system, deducing equivalent post-stage input admittance of the system, calculating a system integral transfer function and acquiring a return-ratio matrix, estimating feature values of the return-ratio matrix and limiting a distribution region of the feature values, setting a forbidden region in the feature value distribution region, and acquiring MIMO system stability criterion with low conservative property. The deduction and calculation of the equivalent pre-stage output impedance and the equivalent post-stage input admittance of the system are the premises for acquiring the system integral transfer function, and are essential conditions for further acquiring the return-ratio matrix of the cascaded system; and the Gerschgorin circle theorem is the basis for setting the forbidden region to limit and avoid the matrix feature value range, and further reducing the conservative property of the criterion. The criterion method is suitable for stability analysis of the MIMO cascaded system, can analyze stability of the MIMO cascaded system simply and effectively, and has lower conservative property than that of the existing singular value criterion, norm criterion and the like.

Description

technical field [0001] The invention relates to the field of automatic control and system stability analysis, in particular to a multiple-input multiple-output (MIMO) cascaded system stability analysis method based on an impedance-response ratio matrix. Background technique [0002] There are various types of automatic control systems in actual production applications, but they can only work normally when they meet the stability conditions. Therefore, system stability analysis is a crucial issue in the field of automatic control. [0003] Methods in classical control theory, such as Nyquist criterion, Bode diagram analysis, etc., can analyze the stability of single-input single-output (SISO) systems. Middlebrook proposed a stability criterion based on the impedance ratio function for the cascaded SISO system. Later, many scholars promoted the Middlebrook impedance criterion based on the concept of forbidden area, which reduced the conservatism of the criterion. Most of the ...

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Problems solved by technology

Belkhayat et al. extended the impedance stability analysis method of SISO cascade system to MIMO cascade system, and proposed methods such as singular value criterion and norm criterion, which are simpler than the method of linear system theory, but such criterion More conservative

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