Plot Bode frequency response with additional plot customization options (2024)

For this example, use the plot handle to change the frequency units to Hz and turn off the phase plot.

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

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

Change the units to Hz and suppress the phase plot. To do so, edit properties of the plot handle, h using setoptions.

setoptions(h,'FreqUnits','Hz','PhaseVisible','off');

The Bode plot automatically updates when you call setoptions.

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

p = bodeoptions('cstprefs');

Change properties of the options set by setting the frequency units to Hz and hide the phase plot.

p.FreqUnits = 'Hz';p.PhaseVisible = 'off';bodeplot(sys,p);

You can use the same option set to create multiple Bode 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 PhaseVisible and FreqUnits, override the toolbox preferences.

For this example, create a Bode plot that uses 15-point red text for the title and sets a custom title. When you specify plot properties explicitly using bodeoptions, the specified properties override the MATLAB session preferences. Thus, the plot looks the same regardless of the preferences of the MATLAB session in which it is generated.

First, create a default options set using bodeoptions.

opts = bodeoptions;

Next, change the required properties of the options set opts. Because opt.Title is a structure, specify the properties of the plot title by specifying the fields and values of that structure.

opts.Title.FontSize = 15;opts.Title.Color = [1 0 0];opts.Title.String = 'System Frequency Response';opts.FreqUnits = 'Hz';

Now, create a Bode plot using the options set opts.

bodeplot(tf(1,[1,1]),opts);

Because opts begins with a fixed set of options, the plot result is independent of the toolbox preferences of the MATLAB session.

For this example, create a Bode plot of the following continuous-time SISO dynamic system. Then, turn the grid on, rename the plot and change the frequency scale.

$$sys(s)=\frac{s^2+0.1s+7.5}{s^4+0.12s^3+9s^2}.$$

Create the transfer function sys.

sys = tf([1 0.1 7.5],[1 0.12 9 0 0]);

Next, create the options set using bodeoptions and change the required plot properties.

plotoptions = bodeoptions;plotoptions.Grid = 'on';plotoptions.FreqScale = 'linear';plotoptions.Title.String = 'Bode Plot of Transfer Function';

Now, create the Bode plot with the custom option set plotoptions.

bodeplot(sys,plotoptions)

bodeplot automatically selects the plot range based on the system dynamics.

For this example, consider a MIMO state-space model with 3 inputs, 3 outputs and 3 states. Create a Bode plot with linear frequency scale, specify frequency units in Hz 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 Bode plot with plot handle h and use getoptions for a list of the options available.

h = bodeplot(sys_mimo);p = getoptions(h)

p = FreqUnits: 'rad/s' FreqScale: 'log' MagUnits: 'dB' MagScale: 'linear' MagVisible: 'on' MagLowerLimMode: 'auto' PhaseUnits: 'deg' PhaseVisible: 'on' PhaseWrapping: 'off' PhaseMatching: 'off' PhaseMatchingFreq: 0 ConfidenceRegionNumberSD: 1 MagLowerLim: 0 PhaseMatchingValue: 0 PhaseWrappingBranch: -180 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: {6x1 cell} XLimMode: {3x1 cell} YLimMode: {6x1 cell}

Use setoptions to update the plot with the required customization.

setoptions(h,'FreqScale','linear','FreqUnits','Hz','Grid','on');

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

For this example, match the phase of your system response such that the phase at 1 rad/sec is 150 degrees.

First, create a Bode plot of transfer function system with plot handle h.

sys = tf(1,[1 1]); h = bodeplot(sys);

Use getoptions to obtain the plot properties. Change the properties PhaseMatchingFreq and PhaseMatchingValue to match a phase to a specified frequency.

p = getoptions(h); p.PhaseMatching = 'on'; p.PhaseMatchingFreq = 1; p.PhaseMatchingValue = 150;

Update the plot using setoptions.

setoptions(h,p);

The first bode plot has a phase of -45 degrees at a frequency of 1 rad/s. Setting the phase matching options so that at 1 rad/s the phase is near 150 degrees yields the second Bode plot. Note that, however, the phase can only be -45 + N*360, where N is an integer. So the plot is set to the nearest allowable phase, namely 315 degrees (or $$1*360-45=315^o$$).

For this example, compare the frequency responses of two identified state-space models with 2 and 6 states along with their 2 $$\sigma$$ confidence regions.

Load the identified state-space model data and estimate the two models using n4sid. Using n4sid requires a System Identification Toolbox license.

load iddata1sys1 = n4sid(z1,2); sys2 = n4sid(z1,6);

Create a Bode plot of the two systems.

bodeplot(sys1,'r',sys2,'b');legend('sys1','sys2');

From the plot, observe that both models produce about 70% fit to data. However, sys2 shows higher uncertainty in its frequency response, especially close to the Nyquist frequency. Now, use linspace to create a vector of frequencies and plot the Bode response using the frequency vector w.

w = linspace(8,10*pi,256);h = bodeplot(sys1,sys2,w);legend('sys1','sys2');

Use setoptions to turn on phase matching and to specify the standard deviation of the confidence region.

setoptions(h,'PhaseMatching','on','ConfidenceRegionNumberSD',2);

You can use the showconfidence command to display the confidence regions on the Bode plot.

showConfidence(h)

For this example, compare the frequency response of a parametric model, identified from input/output data, to a non-parametric model identified using the same data. Identify parametric and non-parametric models based on the data.

Load the data and create the parametric and non-parametric models using tfest and spa, respectively.

load iddata2 z2;w = linspace(0,10*pi,128);sys_np = spa(z2,[],w);sys_p = tfest(z2,2);

spa and tfest require System Identification Toolbox™ software. The model sys_np is a non-parametric identified model while, sys_p is a parametric identified model.

Create an options set to turn phase matching and the grid on. Then, create a Bode plot that includes both systems using this options set.

plotoptions = bodeoptions; plotoptions.PhaseMatching = 'on';plotoptions.Grid = 'on';bodeplot(sys_p,sys_np,w,plotoptions);legend('Parametric Model','Non-Parametric model');

h — Plot handle
handle object

Plot handle, returned as a handle object. Use the handle h to get and set the properties of the Bode plot using getoptions and setoptions. For the list of available options, see the Properties and Values Reference section in Customizing Response Plots from the Command Line.