The command usample is used to randomly sample an uncertain object, giving a not-uncertain instance of the uncertain object.
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
C = ucomplex('C',2+6j); M = [A C A*A]; usample(M) ans = 5.9785 1.4375 + 6.0290i 35.7428
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.
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;