Download presentation

Presentation is loading. Please wait.

Published bySawyer Houff Modified over 2 years ago

1
Nyquist (1) Hany Ferdinando Dept. of Electrical Engineering Petra Christian University

2
Nyquist (1) - Hany Ferdinando 2 General Overview Relation between Magnitude and Phase Angle Relation between Magnitude and Phase Angle Freq. response can be analyzed also via Polar Plot (the polar plot is also called as Nyquist plot) Freq. response can be analyzed also via Polar Plot (the polar plot is also called as Nyquist plot) Advantages and disadvantages Advantages and disadvantages How to plot Nyquist using Matlab is discussed here How to plot Nyquist using Matlab is discussed here

3
Nyquist (1) - Hany Ferdinando 3 What? Bode diagram uses two plots to show the frequency response of plants Bode diagram uses two plots to show the frequency response of plants Nyquist combines both plots into a single plot in polar coordinate as is varied from 0 to One must have knowledge in using complex number both in general notation and in phasor form Nyquist combines both plots into a single plot in polar coordinate as is varied from 0 to One must have knowledge in using complex number both in general notation and in phasor form

4
Nyquist (1) - Hany Ferdinando 4 Polar Coordinate? There are two parameters: There are two parameters: Radius, measured from the originRadius, measured from the origin Angle (from positive real axis)Angle (from positive real axis) Positive angle is counter clock wise Positive angle is counter clock wise Negative angle is clock wise Negative angle is clock wise For reference, students can study the general concept for algebra and geometry For reference, students can study the general concept for algebra and geometry

5
Nyquist (1) - Hany Ferdinando 5 Advantage and Disadvantage Advantage: Advantage: It shows the frequency response characteristic of a system over the entire freq. range in a single plotIt shows the frequency response characteristic of a system over the entire freq. range in a single plot Disadvantage: Disadvantage: It does not clearly indicate the contribution of each individual factor of the open-loop transfer functionIt does not clearly indicate the contribution of each individual factor of the open-loop transfer function

6
Nyquist (1) - Hany Ferdinando 6 How to plot it? The idea is presented in: Integral/derivative factor Integral/derivative factor First order factor First order factor Quadratic factor Quadratic factor Students have to exercise themselves how to plot the nyquist plot for other factors!!!

7
Nyquist (1) - Hany Ferdinando 7 Derivative/integral factors (j ) ±1 Polar plot of (j) -1 is negative imaginary axis Polar plot of (j) -1 is negative imaginary axis Polar plot of (j) is positive imaginary axis Polar plot of (j) is positive imaginary axis

8
Nyquist (1) - Hany Ferdinando 8 1 st -order factors (1+j ) ±1 (1+j) -1 (1+j) -1 For = 0 1 angle 0 oFor = 0 1 angle 0 o For = 1/T 1/ 2 angle -45 oFor = 1/T 1/ 2 angle -45 o For = 0 angle -90 oFor = 0 angle -90 o

9
Nyquist (1) - Hany Ferdinando 9 1 st -order factors (1+j ) ±1

10
Nyquist (1) - Hany Ferdinando 10 1 st -order factors (1+j ) ±1 (1+j) -1 (1+j) -1 For = 0 1 angle 0 oFor = 0 1 angle 0 o For = 1/T 2 angle 45 oFor = 1/T 2 angle 45 o For = angle 90 oFor = angle 90 o

11
Nyquist (1) - Hany Ferdinando 11 1 st -order factors (1+j ) ±1

12
Nyquist (1) - Hany Ferdinando 12 Quadratic Factor [1+2(j/ n )+(j/ n ) 2 ] -1 [1+2(j/ n )+(j/ n ) 2 ] -1 For 0, G(j) = 1 angle 0 oFor 0, G(j) = 1 angle 0 o For, G(j) = 0 angle -180 oFor, G(j) = 0 angle -180 o

13
Nyquist (1) - Hany Ferdinando 13 Quadratic Factor

14
Nyquist (1) - Hany Ferdinando 14 Quadratic Factor [1+2(j/ n )+(j/ n ) 2 ] [1+2(j/ n )+(j/ n ) 2 ] For 0, G(j) = 1 angle 0 oFor 0, G(j) = 1 angle 0 o For, G(j) = angle 180 oFor, G(j) = angle 180 o

15
Nyquist (1) - Hany Ferdinando 15 Quadratic Factor

16
Nyquist (1) - Hany Ferdinando 16 General Shapes of Polar Plot Type 0 systems: the starting point (=0) is finite on positive real axis. The tangent to polar plot at =0 is perpendicular to the real axis. The terminal point (=) is at the origin and the curve is tangent to one of the axes Type 0 systems: the starting point (=0) is finite on positive real axis. The tangent to polar plot at =0 is perpendicular to the real axis. The terminal point (=) is at the origin and the curve is tangent to one of the axes

17
Nyquist (1) - Hany Ferdinando 17 General Shapes of Polar Plot Type 1 systems: at =0, the magnitude is infinity and phase angle is -90 o. At =, the magnitude is zero and the curve converges to the origin and is tangent to one of the axes Type 1 systems: at =0, the magnitude is infinity and phase angle is -90 o. At =, the magnitude is zero and the curve converges to the origin and is tangent to one of the axes

18
Nyquist (1) - Hany Ferdinando 18 General Shapes of Polar Plot Type 2 systems: at =0, the magnitude is infinity and the phase angle is -180 o. At = the magnitude becomes zero and the curve is tangent to one of the axes Type 2 systems: at =0, the magnitude is infinity and the phase angle is -180 o. At = the magnitude becomes zero and the curve is tangent to one of the axes

19
Nyquist (1) - Hany Ferdinando 19 Polar plot of type 0, 1 and 2 = Type 0 Type 1 Type 2

20
Nyquist (1) - Hany Ferdinando 20 Polar Plot of high freq. range n-m = 1

21
Nyquist (1) - Hany Ferdinando 21 Nyquist in Matlab Use [re,im,w]=nyquist(sys) Use [re,im,w]=nyquist(sys) sys may be filled with (num,den) or transfer function or (A,B,C,D) in state space sys may be filled with (num,den) or transfer function or (A,B,C,D) in state space In Nyquist, it is important to see the direction of the curve In Nyquist, it is important to see the direction of the curve

22
Nyquist (1) - Hany Ferdinando 22 Next… The Nyquist plot is already discussed, the subjects are to plot several general equation in Nyquist and how to use Matlab to plot nyquist. The next class is Nyquist stability criterion and phase-gain margin. Students have to prepare themselves for this topic.

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google