Coning motion stability of spinning missiles with strapdown seekers

2016 ◽  
Vol 120 (1232) ◽  
pp. 1566-1577 ◽  
Author(s):  
S. He ◽  
D. Lin ◽  
J. Wang
Keyword(s):  
Stability Analysis ◽  
Scaling Factor ◽  
Guidance System ◽  
Necessary Condition ◽  
Stability Conditions ◽  
Motion Stability ◽  
Model Derivation ◽  
The Stability ◽  
Stability Issues ◽  
Sufficient And Necessary Condition

ABSTRACTThis paper investigates the problem of coning motion stability of spinning missiles equipped with strapdown seekers. During model derivation, it is found that the scaling factor error between the strapdown seeker and the onboard gyro introduces an undesired parasitic loop in the guidance system and, therefore, results in stability issues. Through stability analysis, a sufficient and necessary condition for the stability of spinning missiles with strapdown seekers is proposed analytically. Theoretical and numerical results reveal that the scaling factor error, spinning rate and navigation ratio play important roles in stable regions of the guidance system. Consequently, autopilot gains must be checked carefully to satisfy the stability conditions.

scholarly journals Iterative stability analysis for general polynomial control systems

2021 ◽  
Author(s):  
Bo Xiao ◽  
Hak-Keung Lam ◽  
Zhixiong Zhong
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Control Systems ◽  
Polynomial System ◽  
Stability Conditions ◽  
General Polynomial ◽  
Main Challenge ◽  
Detailed Simulation ◽  
Feasible Solutions ◽  
The Stability

AbstractThe main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.

The stability analysis using Lyapunov exponents for high-DOF nonlinear vehicle plane motion

2021 ◽  
pp. 095440702110433
Author(s):  
Shuming Shi ◽  
Fanyu Meng ◽  
Minghui Bai ◽  
Nan Lin
Keyword(s):  
Stability Analysis ◽  
Quantitative Analysis ◽  
Lyapunov Exponents ◽  
Plane Motion ◽  
Vehicle Model ◽  
Motion Stability ◽  
Motion System ◽  
Nonlinear Vehicle Model ◽  
The Stability ◽  
Different Characteristics

The Lyapunov exponents method is an excellent approach for analyzing the vehicle plane motion stability, and the researchers demonstrated the effectiveness under 2-DOF vehicle model. However, whether the Lyapunov exponents approach can effectively reveal the characteristics of high-DOF nonlinear vehicle model is the key problem at present. In this paper, the Lyapunov exponents is applied to quantitatively analyze the stability of the nonlinear three and five degree of freedom vehicle plane motion system. The different characteristics between 2-DOF and high-DOF model are revealed and explained by using Lyapunov exponents. It illustrates the feasibility of using Lyapunov exponents to analyze the stability of high-DOF vehicle models, which supplements and perfects the existing quantitative analysis conclusion.

Consensus Problem of Singular Multi-Agent Systems with Continuous-Time and Fixed Topology

2013 ◽  
Vol 278-280 ◽  
pp. 1687-1691
Author(s):  
Tong Qiang Jiang ◽  
Jia Wei He ◽  
Yan Ping Gao
Keyword(s):  
Continuous Time ◽  
Spanning Tree ◽  
Undirected Graph ◽  
Necessary Condition ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Fixed Topology ◽  
The Stability ◽  
Sufficient And Necessary Condition

The consensus problems of two situations for singular multi-agent systems with fixed topology are discussed: directed graph without spanning tree and the disconnected undirected graph. A sufficient and necessary condition is obtained by applying the stability theory and the system is reachable asymptotically. But for normal systems, this can’t occur in upper two situations. Finally a simulation example is provided to verify the effectiveness of our theoretical result.

A Simplified Stability Criterion for Nonconservative Systems

1979 ◽  
Vol 46 (2) ◽  
pp. 423-426 ◽  
Author(s):  
I. Fawzy
Keyword(s):  
Dynamic Stability ◽  
Stability Criterion ◽  
Degrees Of Freedom ◽  
Necessary Condition ◽  
Matrix Methods ◽  
Nonconservative System ◽  
Nonconservative Systems ◽  
The Stability ◽  
Lyapunov’S Theorem ◽  
Sufficient And Necessary Condition

Dynamic stability of a general nonconservative system of n degrees of freedom is investigated. A sufficient and necessary condition for the stability of such a system is developed. It represents a simplified criterion based on the famous Lyapunov’s theorem which is proved afresh using λ-matrix methods only. When this criterion is adopted, it reduces the number of equations in Lyapunov’s method to less than half. A systematic procedure is then suggested for the stability investigation and its use is illustrated through a numerical example at the end of the paper.

Vibration stability analysis of dual motor harmonic synchronous excitation nonlinear vibration conveyer

2018 ◽  
Vol 42 (4) ◽  
pp. 419-426 ◽  
Author(s):  
Xiaohao Li ◽  
Yuanyuan Sun ◽  
Tao Shen
Keyword(s):  
Stability Analysis ◽  
Nonlinear Vibration ◽  
Vibration Machine ◽  
Nonlinear Dynamical ◽  
Motion Stability ◽  
Practical Applications ◽  
Nonlinear Force ◽  
The Stability ◽  
Parameter Perturbation Method ◽  
Compensation Function

To enhance the stability of a harmonic vibration synchronous conveyer, this paper establishes a nonlinear dynamical model for this kind of vibration machine, and the effects and compensation function on the stability produced by the nonlinearity of a master vibration spring have been analyzed. A small parameter perturbation method has been used to analyze the effects of a nonlinear force on the conveyer when a fluctuating impact was loaded onto the machine. The reaction between motion stability of the vibration conveyer and the synchronization of the two motors was also investigated. The results of experiments and practical applications demonstrated the correctness of the motion stability analysis of this nonlinear vibration conveyer and its application validity. In conclusion, significant reference values for design, dynamic analysis, testing, and application of the nonlinear vibration conveyer, with harmonic synchronous vibration, actuated by two motors have been achieved.

On Stability Analysis of Switched Linear Time-Delay Systems under Arbitrary Switching

2015 ◽  
pp. 480-515 ◽  
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Lyapunov Function ◽  
Continuous Time ◽  
Delay System ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Delay Systems ◽  
Arbitrary Switching ◽  
The Stability

This chapter focuses on the stability analysis problem for a class of continuous-time switched time-delay systems modelled by delay differential equations under arbitrary switching. Then, a transformation under the arrow form is employed. Indeed, by using a constructed Lyapunov function, the aggregation techniques, the Kotelyanski lemma associated with the M-matrix properties, new delay-dependent sufficient stability conditions are derived. The obtained results provide a solution to one of the basic problems in continuous-time switched time-delay systems. This problem ensures asymptotic stability of the switched time-delay system under arbitrary switching signals. In addition, these stability conditions are extended to be generalized for switched systems with multiple delays. Noted that, these obtained results are explicit, simple to use, and allow us to avoid the problem of searching a common Lyapunov function. Finally, two examples are provided, with numerical simulations, to demonstrate the effectiveness of the proposed method.

Development of Fuzzy Controllers with Dynamics Regarding Stability Conditions and Sensitivity Analysis

2004 ◽  
Vol 8 (5) ◽  
pp. 499-506 ◽  
Author(s):  
Radu-Emil Precup ◽  
◽  
Stefan Preitl ◽  
Péter Korondi ◽  
Keyword(s):  
Sensitivity Analysis ◽  
Control System ◽  
Stability Analysis ◽  
Stability Conditions ◽  
Fuzzy Controllers ◽  
Electrical Drives ◽  
Points Of View ◽  
The Stability ◽  
Predictive Effect

The paper presents development techniques for fuzzy controllers with dynamics and with predictive effect dedicated to some electrical drives with variable inertia. The development techniques are presented regarding the stability analysis based on programs developed in Matlab & Simulink. In addition, it presents points of view regarding the sensitivity analysis on the basis of some sensitivity models associated to the control system.

scholarly journals Hierarchical B-spline complexes of discrete differential forms

2018 ◽  
Vol 40 (1) ◽  
pp. 422-473 ◽  
Author(s):  
John A Evans ◽  
Michael A Scott ◽  
Kendrick M Shepherd ◽  
Derek C Thomas ◽  
Rafael Vázquez Hernández
Keyword(s):  
Stokes Problem ◽  
Differential Forms ◽  
Spatial Dimension ◽  
Necessary Condition ◽  
Two Dimensional ◽  
B Spline ◽  
Discrete Differential Forms ◽  
The Stability ◽  
Local Exactness ◽  
Sufficient And Necessary Condition

Abstract In this paper we introduce the hierarchical B-spline complex of discrete differential forms for arbitrary spatial dimension. This complex may be applied to the adaptive isogeometric solution of problems arising in electromagnetics and fluid mechanics. We derive a sufficient and necessary condition guaranteeing exactness of the hierarchical B-spline complex for arbitrary spatial dimension, and we derive a set of local, easy-to-compute and sufficient exactness conditions for the two-dimensional setting. We examine the stability properties of the hierarchical B-spline complex, and we find that it yields stable approximations of both the Maxwell eigenproblem and Stokes problem provided that the local exactness conditions are satisfied. We conclude by providing numerical results showing the promise of the hierarchical B-spline complex in an adaptive isogeometric solution framework.

Stability of Internal Modes in Circularly Cylindrical MDH Equilibria

1980 ◽  
Vol 35 (1) ◽  
pp. 75-79
Author(s):  
D. Lortz ◽  
J. Nührenberg
Keyword(s):  
Stability Analysis ◽  
Pressure Gradient ◽  
Plasma Boundary ◽  
Cylindrical Symmetry ◽  
Magnetic Axis ◽  
Marginal Stability ◽  
Stability Conditions ◽  
The Stability

Abstract The stability of internal modes, i.e. modes which leave the plasma boundary unperturbed, is discussed for magnetohydrostatic equilibria in circularly cylindrical symmetry. Stability analysis can be performed analytically by expansion near the magnetic axis. Marginal stability conditions relating the pressure gradient and the shear are determined.

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