scholarly journals Modelling and Stability Analysis for a Magnetically Levitated Slice Motor (MLSM) with Gyroscopic Effect and Non-Collocated Structure Based on the Extended Inverse Nyquist Stability Criterion

Machines ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 201
Author(s):  
Lingling Li ◽  
Yang Yu ◽  
Liang Hu ◽  
Xiaodong Ruan ◽  
Rui Su ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Stability Criterion ◽  
Mimo System ◽  
Loop Model ◽  
Gyroscopic Effect ◽  
Nyquist Stability ◽  
Magnetically Levitated ◽  
The Stability ◽  
Slice Motors ◽  
Nyquist Stability Criterion

Stability of the rotor motion is the precondition for the reliable operation of magnetically levitated slice motors (MLSMs). However, with gyroscopic effect and non-collocated structure existing simultaneously, its stability analysis faces a tremendous challenge, because the torsional motions couple with the radial translational ones, making MLSM a multiple-input and multiple-output (MIMO) system with high order. Therefore, in this paper, we first establish a novel MIMO rotor dynamics closed-loop model and further convert it into an equivalent single-input and single-out (SISO) feedback control system by constructing complex variables, meanwhile reducing the system order by half. Beneficial from the equivalence between the MIMO and SISO systems, the sufficient and necessary conditions of the absolute stability of MLSM are derived by the extended inverse Nyquist stability criterion in the complex domain. Additionally, the effectiveness of the proposed modelling and stability analysis method is evaluated by simulation and experimental results. Thus, apart from PID parameters, this paper demonstrates that the stability of MLSM is also affected by the coupling of gyroscopic effect and non-collocated structure, which should serve as an essential guideline for system regulation of MLSM.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

An Improved Delay-Dependent Stability Criterion for a Class of Lur’e Systems of Neutral Type

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
K. Ramakrishnan ◽  
G. Ray
Keyword(s):  
Stability Analysis ◽  
Stability Criterion ◽  
Time Derivative ◽  
Neutral Type ◽  
Linear Matrix ◽  
Lur’E Systems ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Nonlinearity ◽  
Delay Dependent Stability

In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

scholarly journals Complex-Coefficient Frequency Domain Stability Analysis Method for a Class of Cross-Coupled Antisymmetrical Systems and Its Extension in MSR Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yuan Ren ◽  
Jiancheng Fang
Keyword(s):  
Stability Analysis ◽  
Frequency Domain ◽  
Stability Criterion ◽  
Mimo System ◽  
Multiple Input Multiple Output ◽  
Complex Coefficient ◽  
Analysis Method ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Domain Stability

This paper develops a complex-coefficient frequency domain stability analysis method for a class of cross-coupled two-dimensional antisymmetrical systems, which can greatly simplify the stability analysis of the multiple-input multiple-output (MIMO) system. Through variable reconstruction, the multiple-input multiple-output (MIMO) system is converted into a single-input single-output (SISO) system with complex coefficients. The pole locations law of the closed-loop system after the variable reconstruction has been revealed, and the controllability as well as observability of the controlled plants before and after the variable reconstruction has been studied too, and then the classical Nyquist stability criterion is extended to the complex-coefficient frequency domain. Combined with the rigid magnetically suspended rotor (MSR) system with heavy gyroscopic effects, corresponding stability criterion has been further developed. Compared with the existing methods, the developed criterion for the rigid MSR system not only accurately predicts the absolute stability of the different whirling modes, but also directly demonstrates their relative stability, which greatly simplifies the analysis, design, and debugging of the control system.

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