PPT-ME190L Nyquist Stability Criterion

UC Berkeley Fall 2010 httpjaggermeberkeleyedupackme190L Copyright 200710 Andy Packard This work is licensed under the Creative Commons Attribution ShareAlike License To view a copy of this license visit . It is known as Nyquist stability criterion It is based on the complex analysis result known as Cauchys principle of ar gument Note that the system transfer function is complex function By applying Cauchys principle of ar gument to the openloop syste N Puri ECE Department Rutgers University 1 Nyquist Theorem Given a closed loop system rt ct KG KG 1 KG KN KN The order of denominator polynomial KG Open Loop Transfer Function Open Loop Characteristic polynomial with unstable roots unstab Mapping If we take a complex number on the splane and substitute into a function an other complex number results eg substitut ing 4 3 into 2 1 yields 16 30 Contour Consider a collection of points called a contour A Contour A can be mapped Nyquist olar plots olar plot of the frequency resp onse pro duces curv with frequency as parameter relating the oin ts on the olar plot to the appropriate oin ts on the Bo de plots see Fig 1 The Nyquist plot con tains the same information as the Bo An alternative to factoring the denominator polynomial Rouths stability criterion determines the number of closed loop poles in the righthalf plane Algorithm for applying Rouths stability criterion The algorithm described below like the stability cr The 64257rst criterion was that each pulse is zero at the sampling time of other pulses 0 kT k Harry Nyquist Certain topics in telegraph transmission t heory Trans AIEE Apr 1928 EE 179 May 16 2014 Lecture 20 Page 1 brPage 2br Pulse Shaping sinc December 4 2002 1993 Thomas H Lee All rights reserved Page 1 of 12 The Nyquist Stability Test 10 Introduction With negative feedback the closedloop transfer function approaches the reciprocal of the feedback gain as the magnitude of increases Thi DIGITAL COMMUNICATION. In Binary:. Each pulse holds 1 bit. 1 bit per . T. 0. . .  . . bit . per sec. (bit rate. ). .  . .  . To . increase the data rate by . k . .  . .  . is equal to the number of open-loop poles in the right-half plane. !!The closed-loop system which is open-loop stable (no open-loop poles in RHP) is stable if and only if there are no encirclements of S-Plane: Poles and Zeros . A linear system can be represented by the following transfer function: . Zeros: . z. i. (the roots of the numerator) . Poles: p. i. (the roots of the denominator or of the system or . Routh . Herwitz. Stability Criterion. Routh-Hurwitz Stability Criterion. It . is a method for determining continuous system . stability.. It can tell whether there are roots in the RHP of the characteristic polynomial of a control system without solving it.. frequency-response studies. In practice, the performance of a control system is more realistically measured by its time-domain characteristics.. The reason is that the performance of most control systems is judged based on the time due to certain test signals. . Department of Mechanical, Industrial and Manufacturing Engineering. University of Toledo. Stability Margins. Outline of Today’s Lecture. Review. Open Loop System. Nyquist. Plot. Simple . Nyquist. Theorem. - Steven A. . Balbus. (1995). The Second Law. T . dS. = . dQ. = -. L. . dt. Where . L. . = cooling loss function (ergs/. s·g. ). The instability criterion. If . δ. S and . δ. (. L. /T) have the same sign, then the parcel of gas tends to return to the background entropy. If they have different signs, then the parcel continues to evolve away from the background condition..