Sample Uncertain Systems

The command usample randomly samples the uncertain system at a specified number of points. Randomly sample an uncertain system at 20 points in its modeled uncertainty range. This gives a 20-by-1 ss array. Consequently, all analysis tools from Control System Toolbox™ are available.

p1 = ureal('p1',10,'Percentage',50); 
p2 = ureal('p2',3,'PlusMinus',[-.5 1.2]); 
p3 = ureal('p3',0); 
A = [-p1 p2; 0 -p1]; 
B = [-p2; p2+p3]; 
C = [1 0; 1 1-p3]; 
D = [0; 0]; 

sys = ss(A,B,C,D) % Create uncertain state-space model

Uncertain continuous-time state-space model with 2 outputs, 1 inputs, 2 states.
The model uncertainty consists of the following blocks:
  p1: Uncertain real, nominal = 10, variability = [-50,50]%, 2 occurrences
  p2: Uncertain real, nominal = 3, variability = [-0.5,1.2], 2 occurrences
  p3: Uncertain real, nominal = 0, variability = [-1,1], 2 occurrences

Type "sys.NominalValue" to see the nominal value and "sys.Uncertainty" to interact with the uncertain elements.

manysys = usample(sys,20); 
size(manysys)

20x1 array of state-space models.
Each model has 2 outputs, 1 inputs, and 2 states.

stepplot(manysys)

The command stepplot can be called directly on a uss object. The default behavior samples the uss object at 20 instances, and plots the step responses of these 20 models, as well as the nominal value.

The same features are available for other analysis commands such as bodeplot, bodemag, impulse, and nyquist.