Generate Samples of Uncertain Systems

The command usample is used to randomly sample an uncertain object, giving a not-uncertain instance of the uncertain object.

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 = 
    5.7298 

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]; 
usample(M) 
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); 
size(B) 
ans = 
     1     1    20 

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

size(usample(M,30)) 
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 SampleStateDim 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);
del.SampleStateDim
ans =

     1

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);
size(delS)
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.

nyquist(delS)
hold on;
theta = linspace(-pi,pi);
plot(del.Bound*exp(sqrt(-1)*theta),'r');
hold off;

Change the SampleStateDim 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.SampleStateDim = 4;
delS = usample(del,30);
nyquist(delS)
hold on;
theta = linspace(-pi,pi);
plot(del.Bound*exp(sqrt(-1)*theta),'r');
hold off;

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