Robust Control Toolbox™

Create options object for use with dksyn

Syntax

• dkitopt
  opt = dkitopt 
  opt = dkitopt('name1',value1,'name2',value2,...) 
  

Description

opt=dkitopt creates an object of class dkitopt, used to define user-specified options in the D-K iteration procedure performed with dksyn. All properties of opt are set to their default values.

options = dkitopt('name1',value1,'name2',value2,...) uses the trailing Property/Value pairs to set user-specified values of individual option properties. a dkitopt object called options with specific values assigned to certain properties. Property names specification is not case-insensitive, and only enough charaacers to uniquely specify the property name are required.

If the AutoIter property is set to 'off', the D-K iteration procedure is interactive. You are prompted to fit the D-Scale data and provide input on the control design process.

This table lists the dkitopt object properties.

Object Property	Description
FrequencyVector	Frequency vector used for analysis. Default is an empty matrix ([]) which results in the frequency range and number of points chosen automatically.
InitialController	Controller used to initiate first iteration. Default is an empty SS object.
AutoIter	Automated µ-synthesis mode. Default is 'on'.
DisplayWhileAutoIter	Displays iteration progress in AutoIter mode. Default is 'off'.
StartingIterationNumber	Starting iteration number. Default is 1.
NumberOfAutoIterations	Number of D-K iterations to perform. Default is 10.
AutoScalingOrder	Maximum state order for fitting D-scaling data. Default is 5.
AutoIterSmartTerminate	Automatic termination of iteration procedure based on progress of design iteration. Default is 'on'.
AutoIterSmartTerminateTol	Tolerance used by AutoIterSmartTerminate. Default is 0.005.
Default	Structure of property default values.
Meaning	Structure text description of each property.

          If the AutoIterSmartTerminate property is on, and a stopping criteria (described below) is satisfied, the iteration (performed by dksyn) will terminate before reaching the specified number of automated iterations (value of NumberOfAutoIterations). The stopping criteria involves the objective value (peak value, across frequency, of the upper bound for µ) in the current iteration, denoted v₀, as well as the previous two iterations, (denoted v_-1 and v_-2) and the value of AutoIterSmartTerminateTol. If

and

then the stopping criteria is satisfied (for lack of progress). The stopping criteria is also satisfied if

which captures a significant increase (undesirable) in the objective.

Example

This statement creates a dkitopt options object called opt with default property values.

• opt = dkitopt 
  Property Object Values: 
                FrequencyVector: [] 
              InitialController: [0x0 ss] 
                       AutoIter: 'on' 
           DisplayWhileAutoIter: 'off' 
        StartingIterationNumber: 1 
         NumberOfAutoIterations: 10 
               AutoScalingOrder: 5 
         AutoIterSmartTerminate: 'on' 
      AutoIterSmartTerminateTol: 0.0050 
                        Default: [1x1 struct] 
                        Meaning: [1x1 struct] 
  

The properties can be modified directly with assignment statements: here user-specified values for the frequency vector, the number of iterations, and the maximum state dimension of the D-scale fittings are set.

• opt.FrequencyVector = logspace(-2,3,80); 
  opt.NumberOfAutoIterations = 16; 
  opt.AutoScalingOrder = 16; 
  opt 
  Property Object Values: 
                FrequencyVector: [1x80 double] 
              InitialController: [0x0 ss] 
                       AutoIter: 'on' 
           DisplayWhileAutoIter: 'off' 
        StartingIterationNumber: 1 
         NumberOfAutoIterations: 16 
               AutoScalingOrder: 16 
         AutoIterSmartTerminate: 'on' 
      AutoIterSmartTerminateTol: 0.0050 
                        Default: [1x1 struct] 
                        Meaning: [1x1 struct] 
  

The same property/value pairs may be set with a single call to dkitopt.

• opt = dkitopt('FrequencyVector',logspace(-2,3,80),... 
                  'NumberOfAutoIterations',16,... 
                  'AutoScalingOrder',9); 
  

Algorithm

The dksyn command stops iterating before the total number of automated iterations ('NumberOfAutoIterations') if 'AutoIterSmartTerminate' is set to 'on' and a stopping criterion is satisfied. The stopping criterion involves the m(i) value of the current ith iteration, m(i-1) and m(i-2), the previous two iterations and the options property 'AutoIterSmartTerminateTol'. The D-K iteration procedure automatically terminates if the difference between each of the three µ values is less than the relative tolerance of AutoIterSmartTerminateTol xµ(i) or the current µ value µ(i) has increased relative to the µ value of the previous iteration µ(i-1) by 20xAutoIterSmartTerminateTol.

See Also
dksyn       Synthesize a robust controller via D-K iteration

h2syn       Synthesize a H2 optimal controller

hinfsyn     Synthesize a H optimal controller

mussv       Calculate bounds on the Structured Singular Value (µ)

robopt      Create a robustperf/robuststab option object

robuststab  Calculate stability margins of uncertain systems

robustperf  Calculate performance margins of uncertain systems

wcgopt      Create a wcgain option object

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