This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Generate Samples of Uncertain Systems

Use the usample function to randomly sample an uncertain model, returning one or more non-uncertain instances of the uncertain model.

Generating One Sample

If A is an uncertain object, then usample(A) generates a single sample of A.

For example, a sample of a ureal is a scalar double.

A = ureal('A',6); 
B = usample(A) 
B = 

Create a 1-by-3 umat with A and an uncertain complex parameter C. A single sample of this umat is a 1-by-3 double.

C = ucomplex('C',2+6j); 
M = [A C A*A]; 
ans = 
   5.9785             1.4375 + 6.0290i  35.7428          

Generating Many Samples

If A is an uncertain object, then usample(A,N) generates N samples of A.

For example, 20 samples of a ureal gives a 1-by-1-20 double array.

B = usample(A,20); 
ans = 
     1     1    20 

Similarly, 30 samples of the 1-by-3 umat M yields a 1-by-3-by-30 array.

ans = 
     1     3    30 

See Create Arrays with usample for more information on sampling uncertain objects.

Sampling ultidyn Elements

When sampling an ultidyn element or an uncertain object that contains a ultidyn element, the result is always a state-space (ss) object. The property SampleStateDimension of the ultidyn class determines the state dimension of the samples.

Create a 1-by-1, gain bounded ultidyn object with gain bound 3. Verify that the default state dimension for samples is 1.

del = ultidyn('del',[1 1],'Bound',3);
ans =


Sample the uncertain element at 30 points. Verify that this creates a 30-by-1 ss array of 1-input, 1-output, 1-state systems.

delS = usample(del,30);
30x1 array of state-space models.
Each model has 1 outputs, 1 inputs, and 1 states.

Plot the Nyquist plot of these samples and add a disk of radius 3. Note that the gain bound is satisfied and that the Nyquist plots are all circles, indicative of 1st order systems.

hold on;
theta = linspace(-pi,pi);
hold off;

Change SampleStateDimension to 4, and repeat entire procedure. The Nyquist plots satisfy the gain bound and as expected are more complex than the circles found in the 1st-order sampling.

del.SampleStateDimension = 4;
delS = usample(del,30);
hold on;
theta = linspace(-pi,pi);
hold off;

See Also


Related Examples

Was this topic helpful?