2 edition of **Passive stabilization in a linear MHD stability code** found in the catalog.

Passive stabilization in a linear MHD stability code

A. M. M. Todd

- 184 Want to read
- 40 Currently reading

Published
**1980**
by Dept. of Energy, Plasma Physics Laboratory, for sale by the National Technical Information Service] in Princeton, N.J, [Springfield, Va
.

Written in English

- Plasma instabilities.,
- Differential equations, Linear -- Numerical solutions.

**Edition Notes**

Statement | A. M. M. Todd, Plasma Physics Laboratory, Princeton University. |

Series | PPPL ; 1645, PPPL (Series) -- 1645. |

Contributions | United States. Dept. of Energy., Princeton University. Plasma Physics Laboratory. |

The Physical Object | |
---|---|

Pagination | 20 p. : |

Number of Pages | 20 |

ID Numbers | |

Open Library | OL17651178M |

1. Deﬁnitions of Stability and Instability 2. Basic Stability Theorems 3. Basic Instability Theorems 4. Converse Lyapunov Theorems 5. Exponential Stability Theorems 6. Specialization to Linear Systems 7. Stabilization of nonlinear systems 8. Circle criterion, absolute stability, Popov criterion Linearization by State Feedback Chapter 9 and LOCAL LINEAR STABILITY ANALYSIS INTRODUCTION Until the advent of high performance computers, local stability analysis was the standard approach to ﬂow instability. These days it is still useful although, as computers become more powerful, it is likely to be used more as a diagnostic tool than as a predictive tool.

Let us assume that the linear control system x˙ = Ax+Buis controllable. Then PA+BK; K∈ R m×n = Pn. Corollary If the linear control system x˙ = Ax+Buis controllable, there exists a linear feedback x→ u(x) = Kxsuch that 0 ∈ Rn is (globally) asymptotically stable for the . 12 Stability of linear systems Deﬂnition An autonomous system of ODEs is one that has the form y0 = f(y).We say that y0 is a critical point (or equilibrium point) of the system, if it is a constant solution of the system, namely if f(y0) = 0. Deﬂnition (Stability).File Size: 68KB.

ROBUST STABILITY AND STABILIZATION OF A CLASS OF NONLINEAR DISCRETE-TIME STOCHASTIC SYSTEMS WITH STATE AND CONTROLLER DEPENDENT NOISE S. Sathananthan, A. Strong, M. J. Knap, and L.H. Keely Abstract. A problem of robust state feedback stability and sta-bilization of nonlinear discrete-time stochastic processes is consid . which u() exists! If Xis a Banach space, we de ne stability in Xto mean that Xis chosen in all three places. The de nition must be modi ed for non-equilibrium solutions such as traveling waves (orbital stability). The de nition must be modi ed in case some solutions do not exist for all Size: KB.

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Get this from a library. Passive stabilization in a linear MHD stability code. [A M M Todd; United States. Department of Energy.; Princeton University. Plasma Physics Laboratory.]. The stability of a plasma is an important consideration in the study of plasma a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on stability of the system determines if the perturbations will grow, oscillate, or be damped out.

In many cases, a plasma can be treated. The STARWALL/CAS3D/OPTIM code package is a powerful tool to study the linear MHD stability of 3D, ideal equilibria in the presence of multiply-connected ideal and/or resistive conducting. A new linear MHD stability code, NOVA-W, is described and applied to the study of the feedback stabilization of the axisymmetric mode in deformable tokamak plasma.

The NOVA-W code is a modification of the non-variational MHD stability code NOVA that includes the effects of resistive passive conductors and active feedback circuits. Experimental results are closely compared with predictions of two numerical stability codes: the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code.

Other names for linear stability include exponential stability or stability in terms of first approximation. [1] [2] If there exist an eigenvalue with zero real part then the question about stability cannot be solved on the basis of the first approximation and we approach the so-called "centre and focus problem".

This paper addresses the problem of stabilization of a class of internally passive nonlinear dynamic systems using linear, time-invaxiant (LTI) passive controllers. Fundamental results on global asymptotic stability are obtained via Lyapunov-LaSalle method, using extensions of the Kalman-Yakubovich lemma.

Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of stability and feedback stabilization methods, which enables the reader to learn and understand major techniques used Cited by: Stability and Stabilization of Nonlinear Systems with Random Structures (Stability and Control: Theory, Methods and Applications Book 18) - Kindle edition by Martynyuk, A.A.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Stability and Stabilization of Nonlinear Systems with Random Format: Kindle. Linear Stability Analysis for Systems of Ordinary Di erential Equations Consider the following two-dimensional system: x_ = f(x;y); y_ = g(x;y); and suppose that (x; y) is a steady state, that is, f(x ; y)=0 and g(x; y)=0.

The question of interest is whether the steady state is stable or unstable. Consider a small perturbation from the steady. Problems of analysing stability of an equilibrium under specified forces and stabilization, with the possibility of adding control forces, are classical problems of mechanics; considerable importance is attached to them in the looks by Rumyantsev.1, 2, 3 If the positional forces are extremely non-linear, i.e., the expansion in a power series of the generalized coordinates begins with non Cited by: 5.

Linear Stability Analysis Dominique J. Bicout Biomath ematiques et Epid emiologies, EPSP - TIMC, UMRUJF - VetAgro Sup, Veterinary campus of Lyon. Marcy l’Etoile, France UE MMED, Joseph Fourier - Grenoble UniversityFile Size: KB.

Magnetohydrodynamic (MHD) stability and the microscopic and macroscopic effects of various classes of MHD instability underlie essentially all aspects of achievable plasma performance in tokamaks and determine the principal operational limits for tokamaks—maximum plasma current and plasma pressure (beta) and pressure gradient—and plays an important.

The National Spherical Torus Experiment Upgrade and both active and passive stabilization of global MHD modes through the passive conducting plate and applied 3D magnetic fields, along with production of favorable current profiles, will allow sustainment of high performance.

Final Report of the Committee on a Strategic Plan for U.S. for the following matrices A, classify the stability of the linear systems x=Ax as asymptotically stable, L-stable (but not asymptotically stable) or unstable and indicate whether it is a stable node, stable degenerate node, etc.

A consistent linear FDM such as (11) is convergent if and only if it is stable. In many problems of practical interest, we would like to study stability when t!1. To analyze stability for these problems, we need an alternative stability de nition. De nition 3: Absolute StabilityFile Size: 1MB.

Stronger versions of classical Rurnyantsev and Lyapunov - Malkin theorems on partial stability are considered. Its applications to problems of partial stability and stabilization for some mechanical systems (solid, gyrostat, point in gravitational field) are : Vladimir I.

Vorotnikov. Summary Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of stability theory and the theory of stabilization of nonlinear systems with random structure in terms of new developments in the direct Lyapunov's method.

Passivity and Feedback Stabilization Feedback Passivity Linear Systems Nonlinear Systems Exercises Notes and References 15 Partially Linear Cascade Systems LAS from Partial-State Feedback The Interconnection Term Stabilization by Feedback Passivation Stability of the Linear System solution is stable if all the eigenvalues of Ahave negative real part.

solution is unstable if at least one eigenvalue of Ahas positive real part. concern stability theory for linear PDEs. The two other parts of the workshop are \Using AUTO for stability problems," given by Bj orn Sandstede and David Lloyd, and \Nonlinear and orbital stability," given by Walter Strauss.

We will focus on one particular method for obtaining linear stability: proving decay of the associated semigroup. The asymptotic stability and stabilization problem of a class of fractional-order nonlinear systems with Caputo derivative are discussed in this paper.

By using of Mittag–Leffler function, Laplace transform, and the generalized Gronwall inequality, a new sufficient condition ensuring local asymptotic stability and stabilization of a class of fractional-order nonlinear Cited by: (integral) input to state stability is used instead of linear matrix inequalities to derive the results.

All proofs and results for the stability of linear and nonlinear two-dimensional systems in the time domain are given in a uniﬁed notation, studying systems with continuous and discrete independent variables simultaneously.