Lower bounds for the stability margin of discrete two-dimensional systems based on the two-dimensional Lyapunov equation

1988 ◽  
Vol 35 (6) ◽  
pp. 745-749 ◽  
Author(s):  
P. Agathoklis
Keyword(s):  
Lower Bounds ◽  
Stability Margin ◽  
Lyapunov Equation ◽  
Two Dimensional ◽  
The Stability

Computation of the stability margin of two-dimensional discrete systems

1992 ◽  
Vol 37 (6) ◽  
pp. 824-827 ◽  
Author(s):  
A. Kanellakis ◽  
S.G. Tzafestas ◽  
N. Theodorou
Keyword(s):  
Stability Margin ◽  
Discrete Systems ◽  
Two Dimensional ◽  
The Stability

Distributed Control of Two Dimensional Vehicular Formations: Stability Margin Improvement by Mistuning

2009 ◽  
Author(s):  
He Hao ◽  
Prabir Barooah ◽  
Prashant G. Mehta
Keyword(s):  
Distributed Control ◽  
State Space Model ◽  
Stability Margin ◽  
Two Dimensional ◽  
Pde Model ◽  
Asymptotic Formulae ◽  
Control Objective ◽  
Spatio Temporal ◽  
The Stability ◽  
Computation Of Eigenvalues

We consider distributed control of a large two-dimensional (planar) vehicular formation. An individual vehicle in the formation is assumed to be a fully actuated point mass. The control objective is to move the formation with a constant pre-specified velocity while maintaining constant inter-vehicle separation between any pair of nearby vehicles. The control law is distributed in the sense that the control action at each vehicle depends on the relative position measurements with nearby vehicles and its own velocity measurement. For this problem, a partial differential equation (PDE) model is derived to describe the spatio-temporal evolution of velocity perturbations for large number of vehicles, Nveh. The PDE model is used to deduce asymptotic formulae for the stability margin (absolute value of the real part of the least stable eigenvalue). We show that the stability margin of the closed loop decays to 0 as the number of vehicles increases, but the decay rate in 2D formation is much slower than in 1D platoons. In addition, the PDE is used to optimize the stability margin using a mistuning-based approach, in which the control gains of the vehicles are changed slightly from their nominal values. We show that the mistuning design reduces the loss of stability margin significantly even with arbitrarily small amount of mistuning. The results of the analysis with the PDE model are corroborated with numerical computation of eigenvalues with the state-space model of the vehicular formation.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

scholarly journals Stability-Guaranteed and High Terrain Adaptability Static Gait for Quadruped Robots

Sensors ◽  
2020 ◽  
Vol 20 (17) ◽  
pp. 4911
Author(s):  
Qian Hao ◽  
Zhaoba Wang ◽  
Junzheng Wang ◽  
Guangrong Chen
Keyword(s):  
Impedance Control ◽  
Stability Margin ◽  
Planning Method ◽  
Legged Robots ◽  
Gait Planning ◽  
Quadruped Locomotion ◽  
Quadruped Robots ◽  
Adjustment Strategy ◽  
Compliant Behavior ◽  
The Stability

Stability is a prerequisite for legged robots to execute tasks and traverse rough terrains. To guarantee the stability of quadruped locomotion and improve the terrain adaptability of quadruped robots, a stability-guaranteed and high terrain adaptability static gait for quadruped robots is addressed. Firstly, three chosen stability-guaranteed static gaits: intermittent gait 1&2 and coordinated gait are investigated. In addition, then the static gait: intermittent gait 1, which is with the biggest stability margin, is chosen to do a further research about quadruped robots walking on rough terrains. Secondly, a position/force based impedance control is employed to achieve a compliant behavior of quadruped robots on rough terrains. Thirdly, an exploratory gait planning method on uneven terrains with touch sensing and an attitude-position adjustment strategy with terrain estimation are proposed to improve the terrain adaptability of quadruped robots. Finally, the proposed methods are validated by simulations.

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