nyquistplot

For this example, use the plot handle to change the phase units to radians and to turn the grid on.

Generate a random state-space model with 5 states and create the Nyquist diagram with plot handle h.

rng("default")
sys = rss(5);
h = nyquistplot(sys);

Change the phase units to radians and turn on the grid. To do so, edit properties of the plot handle, h using setoptions.

setoptions(h,'PhaseUnits','rad','Grid','on');

The Nyquist plot automatically updates when you call setoptions.

Alternatively, you can also use the nyquistoptions command to specify the required plot options. First, create an options set based on the toolbox preferences.

plotoptions = nyquistoptions('cstprefs');

Change properties of the options set by setting the phase units to radians and enabling the grid.

plotoptions.PhaseUnits = 'rad';
plotoptions.Grid = 'on';
nyquistplot(sys,plotoptions);

You can use the same option set to create multiple Nyquist plots with the same customization. Depending on your own toolbox preferences, the plot you obtain might look different from this plot. Only the properties that you set explicitly, in this example PhaseUnits and Grid, override the toolbox preferences.

Create a Nyquist plot of a dynamic system model and store a handle to the plot.

sys = tf(100,[1,2,1]);
h = nyquistplot(sys);

Change the plot title to read "Nyquist Plot of sys." To do so, use getoptions to extract the existing plot options from the plot handle h.

opt = getoptions(h)

opt =

                         FreqUnits: 'rad/s'
                          MagUnits: 'dB'
                        PhaseUnits: 'deg'
                   ShowFullContour: 'on'
          ConfidenceRegionNumberSD: 1
    ConfidenceRegionDisplaySpacing: 5
                        IOGrouping: 'none'
                       InputLabels: [1x1 struct]
                      OutputLabels: [1x1 struct]
                      InputVisible: {'on'}
                     OutputVisible: {'on'}
                             Title: [1x1 struct]
                            XLabel: [1x1 struct]
                            YLabel: [1x1 struct]
                         TickLabel: [1x1 struct]
                              Grid: 'off'
                         GridColor: [0.1500 0.1500 0.1500]
                              XLim: {[-20 100]}
                              YLim: {[-80 80]}
                          XLimMode: {'auto'}
                          YLimMode: {'auto'}

The Title option is a structure with several fields.

opt.Title

ans = struct with fields:
         String: 'Nyquist Diagram'
       FontSize: 11
     FontWeight: 'bold'
      FontAngle: 'normal'
          Color: [0 0 0]
    Interpreter: 'tex'

Change the String field of the Title structure, and use setoptions to apply the change to the plot.

opt.Title.String = 'Nyquist Plot of sys';
setoptions(h,opt)

Plot the Nyquist frequency response of a dynamic system. Assign a variable name to the plot handle so that you can access it for further manipulation.

sys = tf(100,[1,2,1]);
h = nyquistplot(sys);

Zoom in on the critical point, (–1,0). You can do so interactively by right-clicking on the plot and selecting Zoom on (-1,0). Alternatively, use the zoomcp command on the plot handle h.

zoomcp(h)

Compare the frequency responses of identified state-space models of order 2 and 6 along with their 1-std confidence regions rendered at every 50th frequency sample.

Load the identified model data and estimate the state-space models using n4sid. Then, plot the Nyquist diagram.

load iddata1
sys1 = n4sid(z1,2); 
sys2 = n4sid(z1,6);
w = linspace(10,10*pi,256);
h = nyquistplot(sys1,sys2,w);

Both models produce about 76% fit to data. However, sys2 shows higher uncertainty in its frequency response, especially close to Nyquist frequency as shown by the plot. To see this, show the confidence region at a subset of the points at which the Nyquist response is displayed.

setoptions(h,'ConfidenceRegionDisplaySpacing',50,...
             'ShowFullContour','off');

To turn on the confidence region display, right-click the plot and select Characteristics > Confidence Region.

For this example, consider a MIMO state-space model with 3 inputs, 3 outputs and 3 states. Create a Nyquist plot, display only the partial contour and turn the grid on.

Create the MIMO state-space model sys_mimo.

J = [8 -3 -3; -3 8 -3; -3 -3 8];
F = 0.2*eye(3);
A = -J\F;
B = inv(J);
C = eye(3);
D = 0;
sys_mimo = ss(A,B,C,D);
size(sys_mimo)

State-space model with 3 outputs, 3 inputs, and 3 states.

Create a Nyquist plot with plot handle h and use getoptions for a list of the options available.

h = nyquistplot(sys_mimo);

p = getoptions(h)

p =

                         FreqUnits: 'rad/s'
                          MagUnits: 'dB'
                        PhaseUnits: 'deg'
                   ShowFullContour: 'on'
          ConfidenceRegionNumberSD: 1
    ConfidenceRegionDisplaySpacing: 5
                        IOGrouping: 'none'
                       InputLabels: [1x1 struct]
                      OutputLabels: [1x1 struct]
                      InputVisible: {3x1 cell}
                     OutputVisible: {3x1 cell}
                             Title: [1x1 struct]
                            XLabel: [1x1 struct]
                            YLabel: [1x1 struct]
                         TickLabel: [1x1 struct]
                              Grid: 'off'
                         GridColor: [0.1500 0.1500 0.1500]
                              XLim: {3x1 cell}
                              YLim: {3x1 cell}
                          XLimMode: {3x1 cell}
                          YLimMode: {3x1 cell}

Use setoptions to update the plot with the required customization.

setoptions(h,'ShowFullContour','off','Grid','on');

The Nyquist plot automatically updates when you call setoptions. For MIMO models, nyquistplot produces an array of Nyquist diagrams, each plot displaying the frequency response of one I/O pair.