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Multivariable Control of Polymerization Reactors
Published in F. Joseph Schurk, Pradeep B. Deshpande, Kenneth W. leffew, Vikas M. Nadkarni, Control of Polymerization Reactors, 2017
Schurk F. Joseph, Deshpande Pradeep B.
The Nyquist stability criteria are developed around a Nyquist plot. A Nyquist plot depicts the real part of GUw) on the x axis and the imaginary part of GUw) on they axis. A typical Nyquist plot is shown in Fig. 9.6. A point on the Nyquist plot at a particular frequency gives the corresponding amplitude ratio and phase angle for that frequency, and, thus, Nyquist plots can be prepared from the familiar Bode plots. The Nyquist stability criterion states that a feedback control system will be unstable if the Nyquist plot of G(s) encircles the point (–1,0) on the negative real axis as the frequency increases from zero to infinity. The number of encirclements corresponds to the number of roots of the characteristic equation that lie in the right-half s plane assuming that the process is open-loop stable.
Linear Quadratic Optimal Control Systems II
Published in Desineni Subbaram Naidu, Optimal Control Systems, 2018
We recall that the gain margin of a feedback control system is the amount of loop gain (usually in decibels) that can be changed before the closed-loop system becomes unstable. Let us now apply the well-known Nyquist criterion to the unity feedback, optimal control system depicted in Figure 4.11. Here, we assume that the Nyquist path is clockwise (CW) and the corresponding Nyquist plot makes counter-clockwise (CCW) encirclements around the critical point −1 + j0. According to Nyquist stability criterion, for closed-loop stability, the Nyquist plot (or diagram) makes CCW encirclements as many times as there are poles of the transfer function Go(s) lying in the right half of the s-plane.
Stability of Digital Control Systems
Published in Anastasia Veloni, Nikolaos I. Miridakis, Digital Control Systems, 2017
Anastasia Veloni, Nikolaos I. Miridakis
The Nyquist stability criterion (Nyquist stability criterion—1932) is based on the graphical representation of the open-loop transfer function for a particular closed path in the complex frequency domain and provides information not only on the stability of the closed systems but for their relative stability as well. The special closed road is called Nyquist path or Nyquist plot and includes the right complex half plane. In Figure 5.7, Nyquist path ΓC is presented.
Vibration control techniques during turning process: a review
Published in Australian Journal of Mechanical Engineering, 2021
X. Ajay Vasanth, P. Sam Paul, G. Lawrance, A.S. Varadarajan
Above mentioned literatures reveal that SLD usually changes with the machine tool, work-piece material and tool geometry and from case to case, making it very difficult to apply in practical situation. In addition, any analytical technique used in obtaining SLD cannot describe high stability property at lower spindle speed due to the use of a static model of the turning process. This can be avoided by using Nyquist method (Eynian 2015). Nigm (1981) proposed Nyquist criterion, a method from feedback control theory which was accounting for the dynamics of the cutting process. Nyquist stability criterion is a graphical technique used to determine the stability of a dynamic system. Since it only looks at the parameters plot of a frequency response of the open loop systems, it can be applied without explicitly computing the poles and zeros of either the closed loop or open loop system. In general, this Nyquist stability criterion is for assessing the stability of the turning process with feedback. This method only requires plotting the operative reacceptance instead of plotting the open-loop frequency response locus and it also consumes less time.
PD–PID controller for delayed systems with two unstable poles: a frequency domain approach
Published in International Journal of Control, 2019
David Fernando Novella-Rodríguez, Basilio del Muro Cuéllar, Juan Francisco Márquez-Rubio, Miguel Ángel Hernández-Pérez, Martin Velasco-Villa
From the Nyquist stability criterion, the system QPD(jω) = CPD(jω)Gs(jω), has P = 2 unstable poles, then the Nyquist plot should encircle twice the critical point (−1, j0) in counter clockwise direction. Therefore, the selection of the derivative term must be done in order to obtain a Nyquist trajectory such that the closed-loop system is stable, as it is shown in Figure 2.