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3 edition of Stability margins for multilinear interval systems via phase conditions found in the catalog.

Stability margins for multilinear interval systems via phase conditions

Stability margins for multilinear interval systems via phase conditions

a unified approach

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  • 16 Currently reading

Published by National Aeronautics and Space Administration, National Technical Information Service, distributor in [Washington, DC, Springfield, Va .
Written in English

    Subjects:
  • Automatic control.

  • Edition Notes

    Statementby L.H. Keel, S.P. Bhattacharyya.
    Series[NASA contractor report] -- NASA CR-192893., NASA contractor report -- NASA CR-192893.
    ContributionsBhattacharyya, S. P., United States. National Aeronautics and Space Administration.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL14694305M

    Characterizations of positive definiteness, positive semidefiniteness, and Hurwitz and Schur stability of interval matrices are given. First it is shown that an interval matrix has some of the four properties if and only if this is true for a finite subset of explicitly described matrices, Cited by: stability) or, sometimes more strictly, the system outputs tend to an equilibrium state of interest (the so-called as-ymptotic stability). Conceptually, there are different kinds of stabilities, among which three basic notions are the main concerns in nonlinear dynamics and control systems: the stability of a system with respect to its.

    Finding Phase Margin of Feedback Systems from Closed Loop AC Simulations Agustin Ochoa, Jr. and Howard Tang Xtreme Spectrum, Inc. Greenway Greenbelt Maryland Abstract: The stability of a feedback system is generally characterized with a point variable, the system phase margin. Phase Margin is a function of the system loop gain and is not. Due to the concept of matrix-valued function developed in the book, the direct Liapunov method becomes yet more versatile in performing the analysis of nonlinear systems dynamics. The possibilities of the generalized direct Liapunov method are opened up to stability analysis of solutions to ordinary differential equations, singularly perturbed.

    Assessing Gain and Phase Margins. For linear feedback systems, stability can be assessed by looking at the poles of the closed-loop transfer function. Consider for example the SISO feedback loop: the loop gain can increase % before you lose stability. Gain and Phase Margins. Changes in the loop gain are only one aspect of robust. ECE Bode Plot Example #2 Gain and Phase Margins. As described in Nyquist Example #3, gain margin and phase margin are two measures of relative bestwesternkitchenerwaterloo.com measure how "close" a system is to crossing the boundary between stability and instability, in one direction or the other.


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Stability margins for multilinear interval systems via phase conditions Download PDF EPUB FB2

Stability margins for multilinear interval systems by way of phase conditions: A unified approach Article (PDF Available) · February with 11 Reads How we measure 'reads'. Get this from a library.

Stability margins for multilinear interval systems via phase conditions: a unified approach. [L H Keel; S P Bhattacharyya; United States. National Aeronautics and. Stability margins for multilinear interval systems via phase conditions: A unified approach This paper gives a simple way of checking the stability with respect to an arbitrary stability region of a family of polynomials containing a vector of parameters varying within prescribed bestwesternkitchenerwaterloo.com by: 3.

The results can be used to determine various stability margins of control systems containing interconnected interval subsystems. These include the gain, phase, time-delay, H ¿ and nonlinear sector bounded stability margins of multilinear interval systems.

These include the gain, phase, time-delay, H¿> and nonlinear sector bounded stability margins of multilinear interval systems. The gain margin Gm is defined as 1/G where G is the gain at the phase crossing. The gain margin in dB is derived by Gm_dB = 20*log10(Gm) The phase margin Pm is in degrees.

The loop gain at Wcg can increase or decrease by this many dBs before losing stability. In this article necessary and sufficient conditions for the stability of time-varying discrete interval systems are studied and the corresponding stability margins are obtained.

Our analysis heavily employs the Perron—Frobenius theorem for nonnegative matrices and its extensions to a class of interval bestwesternkitchenerwaterloo.com: Karel Sladký.

Consequently, the optimal system that set of segments systems, the extremal margins over the interval plant produces m a x i m u m gain or phase m a r g i n over an interval Cited by: Phase margin: Stability is preserved when the phase increases or decreases by up to the phase margin value in each channel of the feedback loop.

In MIMO systems, the gain or phase can change in all channels at once, and by a different amount in each channel. Jun 05,  · Further, it is proved that the existing results of Anderson et al.

[2] on the stability of low-order interval systems using Kharitonov’s theorem are only applicable for absolute stability of the interval system and it is not applicable for relative stability of the interval systems, i.e., for phase margin.

The proposed technique and stability analysis for low-order interval systems are verified Cited by: The closed characteristic equation of the system is loop 6(s,a,b)= Figure 3: Graphical prediction of limit cycle 5. STABILITY MARGIN COMPUTATION A main problems in robustness of control systems is to find the maximum allowable perturbation bounds of parameters of a system while preserving bestwesternkitchenerwaterloo.com by: 2.

Stability Margins for Multilinear Interval Systems via Phase Conditions: A Unified Approach L.H. Keel CenterofExcellenceinInformationSystems TennesseeStateUniversity Nashville,TN DepartmentofElectricalEngineering TexasA&M University CollegeStation,TX Abstract Thispapergivesasimplewayofcheckingthestabil.

STABILITY MARGIN VIA REFLECTION VECTORS gain and phase margin in frequency domain, minimal distance from imaginary axis (or unit circle) in pole domain, stability radius in system parameter domain.

For interval or polytopic type of parametric uncertainties some kind of stability margin can be obtained by the Kharitonov the. Stability Criteria - (Gain Margin and Phase Margin) Think of both of these as safety margins for an open-loop system which you would like to make closed-loop.

That is, if you are walking next to a cliff, you want a positive space or "margin" of safety between you and a big disaster. The phase at kHz is °. Thus, the phase margin of this system is °. Although this method is acceptable for simulated devices, in real systems it creates many problems.

For example, many devices with control systems cannot tolerate the wide range of. Description [cm,dm,mm] = loopmargin(L) analyzes the multivariable feedback loop consisting of the loop transfer matrix L (size N-by-N) in negative feedback with an N-by-N identity matrix. cm, or classical gain and phase margins, is an N-by-1 structure corresponding to loop-at-a-time gain and phase margins for each channel.L is an LTI model.

Consider a closed loop system with the loop transfer function L(s). The closed loop poles are the zeros of the function f(s) = 1+L(s) To flnd the number of zerosin the right half plane we investigate the winding number of the function f(s) = 1+L(s) as smoves along the Nyquist con- tour ¡ in the clockwise direction.

Jun 03,  · In this paper, It is showed that however we can mention the guaranteed gain margin of -6 to +∞ and also phase margin of -〖60〗^° to +〖60〗^° for single input systems as the well-known robustness properties of linear quadratic regulators (LQR).

But determining the robustness of closed-loop system from the range of gain and phase margins is not corrected. Phase margin of 45 degrees is a somewhat common compromise between good step response and stability and a step response which overshoots and has ringing. Makers of OpAmps like to push gain bandwidth of their products and that reduces phase margin (PM).

For a minimum-phase system, the gain and phase margins must be positive for the system to be stable. This system has two poles at the origin, and hence is not minimum-phase.

Thus it can be stable even if the gain or phase margins are negative. Computation of Time Delay Margins for Stability of a Single-Area Load Key-Words: Load Frequency Control System, Time Delay, Stability, Delay Margin. essential to determine conditions on the delay such that the LFC system will be stable.

The stability is.Phase margin and its important companion concept, gain margin, are measures of stability in closed-loop, dynamic-control systems. Phase margin indicates relative stability, the tendency to oscillate during its damped response to an input change such as a step function.GAIN-MARGINS AND PHASE-MARGINS OF MULTIVARIABLE TIME-DELAY SYSTEMS.

Tsung-Huang Ma1, Chih-Min Lin1, Fei Chao2, Chun-Fei Hsu. 3, Jih-Gau Juang4, and Ching-Hung Lee5. Key words: gain-margin, phase-margin, MIMO system, time-delay, robustness. ABSTRACT. In this paper, the gain-phase-margin tester method is ap.