nicholschart

Arguments

modules

vector of real numbers: modules (in dB). Default values:

[-30:-10:Modmin -20 -15 -12 -9 -6 -3 -2 -1 -.5 -0.2 -0.1 0 0.1 0.2 0.5 1 2 3 6 12]

args

vector of real numbers: phases (in degree). Default values:

-[1 2 5 10 20 30 50 70 90 120 140 160 180]°

colors

vector of 1 or 2 components specifying the colors of the isogain and isophase sets of curves. If a single color is provided, it is used for both gains and phases. colors may be specified either

• by indices in the color map.
• named colors among the predefined ones.
• "#RRGGBB" hexadecimal case-insensitive strings starting with "#", like "#FA7B35".
• A 1x3 or 2x3 matrix of [r g b] intensities such that 0 <= r,g,b <= 1.

sh

Structure with 3 fields:

• .phaseLines: vector of handles of isophase lines. .phaseLines(i) is the line for args(i).
• .gainLines: vector of handles of isogain lines. .gainLines(i) is the line for modules(i).
• .gainLabels: vector of handles of isogain labels. .gainLabels(i) is the label for modules(i).

Description

plot the Nichols'chart: iso-module and iso-argument contours of y/(1+y) in y phase/gain plane.

nicholschart may be used in conjunction with black.

To use the default value of an input argument, just skip it, as in nicholschart(modules,,colors).

Examples

//Nichols chart
clf
subplot(1,2,1)
nicholschart();
subplot(1,2,2)
mod = [-35:5:-10 -6 -3 -1 -0.2 1 2 3 6];
nicholschart(mod, -[1 20 40 80 160 180],["khaki" "paleturquoise"]);

//Black diagram with Nichols chart as a grid
s = poly(0,'s');
Plant = syslin('c',16000/((s+1)*(s+10)*(s+100)));

//two degree of freedom PID
tau = 0.2;
xsi = 1.2;
PID = syslin('c',(1/(2*xsi*tau*s))*(1+2*xsi*tau*s+tau^2*s^2));
clf
black([Plant;Plant*PID ],0.01,100,["Plant";"Plant and PID corrector"]);

//move the caption in the lower right corner
gca().children(1).legend_location="in_lower_right";

// Add the Nichols frame and tune its labels color
h = nicholschart(,,'wheat');
h.gainLabels.font_foreground = color("orange");

See also

• hallchart — Draws a Hall chart
• sgrid — draws a s-plane grid
• zgrid — zgrid plot
• bode — Bode plot
• black — Black-Nichols diagram of a linear dynamical system
• nyquist — nyquist plot
• svplot — singular-value sigma-plot
• color_list — list of named colors

History