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The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...
Liénard–Chipart criterion; Nyquist stability criterion; Routh–Hurwitz stability criterion; Vakhitov–Kolokolov stability criterion; Barkhausen stability criterion; Stability may also be determined by means of root locus analysis. Although the concept of stability is general, there are several narrower definitions through which it may be ...
To use the Hall circles, a plot of M and N circles is done over the Nyquist plot of the open-loop transfer function. The points of the intersection between these graphics give the corresponding value of the closed-loop transfer function. Hall circles are also used with the Nichols plot and in this setting, are also known as Nichols chart.
An explicit scheme of FDM has been considered and stability criteria are formulated. In this scheme, temperature is totally dependent on the old temperature (the initial conditions) and θ, a weighting parameter between 0 and 1. Substitution of θ = 0 gives the explicit discretization of the unsteady conductive heat transfer equation.
In addition to determining the stability of the system, the root locus can be used to design the damping ratio and natural frequency (ω n) of a feedback system. Lines of constant damping ratio can be drawn radially from the origin and lines of constant natural frequency can be drawn as arccosine whose center points coincide with the origin.
In nonlinear control and stability theory, the circle criterion is a stability criterion for nonlinear time-varying systems. It can be viewed as a generalization of the Nyquist stability criterion for linear time-invariant (LTI) systems .
These systems can be solved by powerful frequency domain mathematical techniques of great generality, such as the Laplace transform, Fourier transform, Z transform, Bode plot, root locus, and Nyquist stability criterion. Nonlinear control theory covers a wider class of systems that do not obey the superposition principle.
The small-gain theorem gives a sufficient condition for finite-gain stability of the feedback connection. The small gain theorem was proved by George Zames in 1966. It can be seen as a generalization of the Nyquist criterion to non-linear time-varying MIMO systems (systems with multiple inputs and multiple outputs).