Robust Control Toolbox™

Create uncertain frequency response data (ufrd) object, or convert another model type to ufrd model

Syntax

• usysfrd = ufrd(usys,frequency) 
  usysfrd = ufrd(usys,frequency,'Units',units) 
  usysfrd = ufrd(sysfrd) 
  usys = ufrd(response,frequency) 
  usys = ufrd(response,frequency,Ts) 
  usys = ufrd(response,frequency,RefSys) 
  usys = ufrd(response,frequency,'Units',units,Ts) 
  usys = ufrd(response,frequency,'Units',units,Ts,RefSys) 
  

Description

Uncertain frequency response data (ufrd) models result from the conversion of an uncertain state-space (uss) system to its uncertain frequency response. ufrd models also result when frequency response data models (frd) are combined with uncertain matrices (umat).

usysfrd = ufrd(usys,frequency,'Units',units) converts a uss model usys to a ufrd model usysfrd by frequency response.'Units' specifies the units of the frequencies in frequency, which can be 'rad/s' or 'Hz'. If the last two arguments are omitted, the default for frequency units is 'rad/s'.

Any of the previous syntaxes can be followed by property name/property value pairs.

usysfrd = ufrd(usys,frequency,'Units',units,'P1',V1,'P2',V2,...) sets the properties P1, P2, ... to the values V1, V2, ...

usys = ufrd(response,frequency) creates a ufrd from the response and frequency arguments. response should be a umat array, whose first array dimension (i.e., size(response,3)) aligns with the frequency. Note that you are unlikely to use this option.

usysfrd = ufrd(sysfrd) converts an frd model sysfrd to a ufrd model usysfrd with no uncertain elements.

Example

In the first example, you create a continuous-time uncertain system with both parametric uncertainty and unmodeled dynamics uncertainty. Compute the uncertain frequency response and plot the Bode plot, using 20 random samples, with a color choice of red for random samples, and blue for nominal.

• p1 = ureal('p1',5,'Range',[2 6]); 
  p2 = ureal('p2',3,'Plusminus',0.4); 
  p3 = ultidyn('p3',[1 1]); 
  Wt = makeweight(.15,30,10); 
  A = [-p1 0;p2 -p1]; 
  B = [0;p2]; 
  C = [1 1]; 
  usys = uss(A,B,C,0)*(1+Wt*p3); 
  usysfrd = ufrd(usys,logspace(-2,2,60)); 
  bode(usysfrd,'r',usysfrd.NominalValue,'b+') 
  

Example 2

In this example, you convert a not-uncertain frd model to ufrd without uncertainties. You can verify the equality of the nominal value of the ufrd and simplified representation to the original system.

• G = frd(tf([1 2 3],[1 2 3 4]),logspace(-2,2,40)); 
  usys = ufrd(G) 
  UFRD: 1 Output, 1 Input, Continuous System, 40 Frequency points 
  isequal(usys.NominalValue,G) 
  ans = 
       1 
  isequal(simplify(usys,'class'),G) 
  ans = 
       1 
  

See Also
frd         Creates or converts to frequency response data model

ss          Creates or converts to state-space model

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