Inverted Pendulum Stabilization of Submarines in Free Positive Buoyancy Ascent

1994 ◽  
Vol 38 (01) ◽  
pp. 71-82
Author(s):  
Fotis A. Papoulias ◽  
Brian D. McKinley

The problem of steady-state vertical ascent of a submarine with excess buoyancy is analyzed. All possible vertical plane solutions are computed and their stability is established in both in-plane and out-of-plane perturbations. Divergence of trajectories, sensitivity of solutions to initial conditions, and stable inverted pendulum configurations are shown to exist for certain ranges of parameters.

1968 ◽  
Vol 35 (2) ◽  
pp. 322-326 ◽  
Author(s):  
W. D. Iwan

The steady-state response of a system constrained by a limited slip joint and excited by a trigonometrically varying external load is discussed. It is shown that the system may possess such features as disconnected response curves and jumps in response depending on the strength of the system nonlinearity, the level of excitation, the amount of viscous damping, and the initial conditions of the system.


2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Hazem I. Ali

In this paper the design of robust stabilizing state feedback controller for inverted pendulum system is presented. The Ant Colony Optimization (ACO) method is used to tune the state feedback gains subject to different proposed cost functions comprise of H-infinity constraints and time domain specifications. The steady state and dynamic characteristics of the proposed controller are investigated by simulations and experiments. The results show the effectiveness of the proposed controller which offers a satisfactory robustness and a desirable time response specifications. Finally, the robustness of the controller is tested in the presence of system uncertainties and disturbance.


1992 ◽  
Vol 290 ◽  
Author(s):  
Eric Clément ◽  
Patrick Leroux-Hugon ◽  
Leonard M. Sander

AbstractWe have previously given an exact solution [1] for the steady state of a model of the bimolecular reaction model A+B→ 0 due to Fichthorn et al. [2]. The dimensionality of the substrate plays a central role, and below d=2 segregation on macroscopic scales becomes important: above d=2 saturation sets in for finite size systems. Here we extend our treatment to give an exact account of the dynamics and show how various initial conditions develop into the segregated and saturated regimes. In certain conditions we find logarithmic relaxation which is related to the dimensionality.


2021 ◽  
Author(s):  
Hai Zhou ◽  
Haiping Wu ◽  
Jian Xu ◽  
Hongbin Fang

Abstract Origami-inspired structures and materials have shown remarkable properties and performances originating from the intricate geometries of folding. Origami folding could be a dynamic process and origami structures could possess rich dynamic characteristics under external excitations. However, the current state of dynamics of origami has mostly focused on the dynamics of a single cell. This research has performed numerical simulations on multi-stable dual-cell series Miura-Ori structures with different types of inter-cell connections based on a dynamic model that does not neglect in-plane mass. We introduce a concept of equivalent constraint stiffness k* to distinguish different types of inter-cell connections. Results of numerical simulations reveal the multi-stable dual-cell structure will exhibit a variety of complex nonlinear dynamic responses with the increasing of connection stiffness because of the deeper energy well it has. The connection stiffness has a strong effect on the steady-state dynamic responses under different excitation amplitudes and a variety of initial conditions. This effect makes us able to adjust the dynamic behaviors of dual-cell series Miura-Ori structure to our needs in a complex environment. Furthermore, the results of this research could provide us a theoretical basis for the dynamics of origami folding and serve as guidelines for designing dynamic applications of origami metastructures and metamaterials.


Author(s):  
Isaac Esparza ◽  
Jeffrey Falzarano

Abstract In this work, global analysis of ship rolling motion as effected by parametric excitation is studied. The parametric excitation results from the roll restoring moment variation as a wave train passes. In addition to the parametric excitation, an external periodic wave excitation and steady wind bias are also included in the analysis. The roll motion is the most critical motion for a ship because of the possibility of capsizing. The boundaries in the Poincaré map which separate initial conditions which eventually evolve to bounded steady state solutions and those which lead to unbounded capsizing motion are studied. The changes in these boundaries or manifolds as effected by changes in the ship and environmental conditions are analyzed. The region in the Poincaré map which lead to bounded steady state motions is called the safe basin. The size of this safe basin is a measure of the vessel’s resistance to capsizing.


1992 ◽  
Vol 29 (02) ◽  
pp. 418-429 ◽  
Author(s):  
Hideaki Takagi

Generalized M/G/1 vacation systems with exhaustive service include multiple and single vacation models and a setup time model possibly combined with an N-policy. In these models with given initial conditions, the time-dependent joint distribution of the server's state, the queue size, and the remaining vacation or service time is known (Takagi (1990)). In this paper, capitalizing on the above results, we obtain the Laplace transforms (with respect to time) for the distributions of the virtual waiting time, the unfinished work (backlog), and the depletion time. The steady-state limits of those transforms are also derived. An erroneous expression for the steady-state distribution of the depletion time in a multiple vacation model given by Keilson and Ramaswamy (1988) is corrected.


2009 ◽  
Vol 46 (02) ◽  
pp. 363-371 ◽  
Author(s):  
Offer Kella

In this paper we generalize existing results for the steady-state distribution of growth-collapse processes. We begin with a stationary setup with some relatively general growth process and observe that, under certain expected conditions, point- and time-stationary versions of the processes exist as well as a limiting distribution for these processes which is independent of initial conditions and necessarily has the marginal distribution of the stationary version. We then specialize to the cases where an independent and identically distributed (i.i.d.) structure holds and where the growth process is a nondecreasing Lévy process, and in particular linear, and the times between collapses form an i.i.d. sequence. Known results can be seen as special cases, for example, when the inter-collapse times form a Poisson process or when the collapse ratio is deterministic. Finally, we comment on the relation between these processes and shot-noise type processes, and observe that, under certain conditions, the steady-state distribution of one may be directly inferred from the other.


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