Robust Control Toolbox™

Compute normalized distance between uncertain atom nominal value and specified value

Syntax

• NDIST = actual2normalized(A,V)
  

Description

NDIST = actual2normalized(A,V) is the normalized distance between the nominal value of the uncertain atom A and the given value V. If A is a ureal, then NDIST may be positive or negative, reflecting that V is greater than, or less than the nominal value. If A is any other class of uncertain atom, then ndist is nonnegative.

If V is an array of values, then NDIST is an array of normalized distances.

The robustness margins computed in robuststab and robustperf serve as bounds for the normalized distances in NDIST. For example, if an uncertain system has a stability margin of 1.4, this system is stable when the normalized distance of the uncertain element values from the nominal is less than 1.4.

Examples

Uncertain Real Parameter with Symmetric Range

For uncertain real parameters whose range is symmetric about their nominal value, the normalized distance is intuitive, scaling linearly with the numerical difference from the uncertain real parameter's nominal value

Create uncertain real parameters with a range that is symmetric about the nominal value, where each end point is 1 unit from the nominal. Points that lie inside the range are less than 1 unit from the nominal, while points that lie outside the range are greater than 1 unit from the nominal.

• a = ureal('a',3,'range',[1 5]); 
  actual2normalized(a,[1 3 5]) 
  ans = 
     -1.0000   -0.0000    1.0000 
  actual2normalized(a,[2 4]) 
  ans = 
     -0.5000    0.5000 
  actual2normalized(a,[0 6]) 
  ans = 
     -1.5000    1.5000 
  

Graph the normalized distance for several values. The nominal point is shown as a red circle. Note that the relationship between a normalized distance and a numerical difference is linear.

• values = linspace(-3,9,250); 
  ndist = actual2normalized(a,values); 
  plot(values,ndist) 
  
  
  
  

Uncertain Real Parameter with Nonsymmetric Range

Next, create an unasymmetric parameter. It still is true that the end points are 1 normalized unit from nominal, and the nominal is 0 normalized units from nominal, moreover points inside the range are less than 1 unit from nominal, and points outside the range are greater than 1 unit from nominal. However, the relationship between the normalized distance and numerical difference is nonlinear.

• au = ureal('a',4,'range',[1 5]); 
  actual2normalized(a,[1 4 5]) 
  ans = 
     -1.0000    0.5000    1.0000 
  actual2normalized(a,[2 4.5]) 
  ans = 
     -0.5000    0.7500 
  actual2normalized(a,[0 6]) 
  ans = 
     -1.5000    1.5000 
  

Graph the normalized distance for several values. Note that the relationship between normalized distance and numerical difference is very nonlinear.

• ndistu = actual2normalized(au,values); 
  plot(values,ndistu,au.NominalValue,0,'ro') 
  
  
  
  

Algorithm

For details on the normalize distance, see Normalizing Functions for Uncertain Atoms.

See Also
normalized2actual  Converts normalized to actual value

robuststab  Calculate robust stability margin

robustperf  Calculate robust performance margin

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