Robust Control Toolbox™

Substitute given values for uncertain elements of uncertain objects

Syntax

• B = usubs(M,atomname1,value1,atomname2,value2,...) 
  B = usubs(M,{atomname1;atomname2;...},{value1;value2;...}) 
  B = usubs(M,StrucArray) 
  

Description

usubs is used to substitute a specific value for an uncertain element of an uncertain object. The value can itself be uncertain. It needs to be the correct size, but otherwise can be of any class, and can be an array. Hence, the result can be of any class. In this manner, uncertain elements act as symbolic placeholders, for which specific values (which can also contain other placeholders too) can be substituted.

B = usubs(M,atomname1,value1,atomname2,value2,...) sets the atoms in M, identified by atomname1, atomname2, etc., to the values in value1, value2, etc., respectively.

B = usubs(M,ElementName1,value1,ElementName2,value2,...) sets the elements in M, identified by ElementName1, ElementName2, etc., to the values in value1, value2, etc. respectively.

The names and values can also be grouped in cell arrays, as

• B = usubs(M,atomname1,value1,...) 
  

In this case, if the value cell is 1-by-1, then that value is substituted for all the listed atoms. For this situation, it is not required that the value be in a cell array.

value can also be the string 'NominalValue' or 'Random' (or only partially specified) in which case the nominal value, or a random instance of the atom is used.

Combinations of the above syntaxes are also allowed, so that

• B = usubs(M,{atomname1;atomname2},{value1;value2}) 
  

is allowed.

The names and values can also be grouped in a structure, with its field names constituting the Names, and the field values constituting the Values. In the following function call, StrucArray is a structure with field names and values.

• B = usubs(M,StrucArray)
  

Robustness analysis commands such as wcnorm, wcgain and robuststab return the offending uncertain element values in this manner. usample, which randomly samples uncertain objects, also returns the sample points in this manner.

Examples

Create an uncertain matrix and perform identical substitution in two different manners.

• p = ureal('p',5); 
  m = [1 p;p^2 4]; 
  size(m) 
  ans = 
       2     2 
  m1 = usubs(m,'p',5) 
  m1 = 
       1     5 
      25     4 
  NamesValues.p = 5; 
  m2 = usubs(m,NamesValues) 
  m2 = 
       1     5 
      25     4 
  m1 - m2 
  ans = 
       0     0 
       0     0 
  

You can make an array-valued substitution using the structure-based syntax,

• NamesValues.p = rand(1,1,6); 
  m3 = usubs(m,NamesValues);  % 2-by-2-by-6 
  size(m3) 
  ans = 
       2     2     6 
  

You can use usubs to substitute for individual uncertainties. Create three uncertain real parameters, and form a simple 2-by-2 uncertain matrix with the parameters

• a = ureal('a',5); b = ureal('b',3); c = ureal('c',1); 
  m = [a b;c a*b*c]; 
  

You can perform a single parameter substitution and check the results

• m1 = usubs(m,'a',10); 
  simplify(m1(1,1)) 
  ans = 
      10 
  simplify(10*m1(1,2)*m1(2,1) - m1(2,2)) 
  ans = 
       0 
  

You can replace one real parameter with a transfer function, and other parameters with doubles. You can do this using two different forms of the syntax and check that the results are identical.

• m2 = usubs(m,'a',tf([5],[1 1]),'b',2.6,'c',1.3); 
  nv.a = tf([5],[1 1]); 
  nv.b = 2.6; 
  nv.c = 1.3; 
  m3 = usubs(m,nv); 
  norm(m2-m3,'inf') 
  ans = 
       0 
  

In m, replace 'a' with 'b', obtaining 'b' directly from m :

• m4 = usubs(m,'a',m.Uncertainty.b); 
  

See Also
gridureal   Grids uncertain real parameters over their range

usample     Generates random samples of an atom

simplify    Simplify representation of uncertain objects

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