dkitopt :: Functions (Robust Control Toolbox™)

dkitopt

Purpose

Create options object for use with dksyn

Syntax

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

Description

opt=dkitopt creates an options object opt of class dkitopt, used to define user-specified options in the µ-synthesis command dksyn. All properties of opt are set to their default values.

opt = dkitopt('name1',value1,'name2',value2,...) accepts inputs as one or more Property/Value pairs to set user-specified values of individual properties of opt. Property names specification is not case-insensitive, and only enough characters to uniquely specify the property name are required.

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.

MixedMU
Accounts for real-valued uncertain parameters for µ-synthesis. For systems with atleast one real-valued uncertain parameter, closed-loop robust performance may improve when the option is set to 'on'. Default is 'off'.

AutoScalingOrder
State order for fitting D-scaling and G-scaling data for real or complex µ-synthesis. Default is [5 2], 5th order D-scalings and 2nd order G-scalings.

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.

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.
`MixedMU`	Accounts for real-valued uncertain parameters for µ-synthesis. For systems with atleast one real-valued uncertain parameter, closed-loop robust performance may improve when the option is set to `'on'.` Default is `'off'.`
`AutoScalingOrder`	State order for fitting D-scaling and G-scaling data for real or complex µ-synthesis. Default is [5 2], 5th order D-scalings and 2nd order G-scalings.
`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 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.

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.

Examples

This example 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
                      MixedMU: 'off'
             AutoScalingOrder: [5 2]
       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
                      MixedMU: 'off'
             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.

When the system contains some real-valued uncertain parameters and MixedMU is set to 'on', the dksyn command takes into account that the uncertain parameters are real and this may result in improved robust performance.