varyingGoal

Create a tuning goal that specifies variable gain and phase margins across a grid of design points.

Suppose you use the following 5-by-5 grid of design points to tune your controller.

[alpha,V] = ndgrid(linspace(0,20,5),linspace(700,1300,5));

Suppose further that you have 5-by-5 arrays of target gain margins and target phase margins corresponding to each of the design points, such as the following.

[GM,PM] = ndgrid(linspace(7,20,5),linspace(45,70,5));

To enforce the specified margins at each design point, first create a template for the margins goal. The template is a function that takes gain and phase margin values and returns a TuningGoal.Margins object with those margins.

FH = @(gm,pm) TuningGoal.Margins('u',gm,pm);

Use the template and the margin arrays to create the varying goal.

VG = varyingGoal(FH,GM,PM);

To make it easier to trace which goal applies to which design point, use the SamplingGrid property to attach the design-point information to VG.

VG.SamplingGrid = struct('alpha',alpha,'V',V);

Use VG with systune as you would use any other tuning goal. Use viewGoal to visualize the tuning goal and identify design points that fail to meet the target margins.

Create a tuning goal that specifies a loop shape that varies with one scheduling variable, a.

Suppose you want to specify a loop shape with a crossover frequency that varies as 2*a over three design points. To enforce this requirement, first create a template for the loop-shape goal. The template is a function that takes a numeric scalar input parameter and returns a TuningGoal.LoopShape object. The function input must be scalar, so the function constructs the LTI models representing the loop shapes.

a = [5;10;15];
s = tf('s');
FH = @(A) TuningGoal.LoopShape('u',2*A/s);

Here, 'u' is an Analysis Point in the system, the location at which you want to impose the loop-shape requirements.

Use the template and the array to create the varying goal.

VG = varyingGoal(FH,a);

Attach the design-point information to VG.

VG.SamplingGrid = struct('a',a);

Now each value of a is associated with a tuning goal that enforces the corresponding loop shape. For example, confirm that the third entry in a, a = 15, is associated with the third loop shape, 30/s.

LS3 = getGoal(VG,'index',3);
tf(LS3.LoopGain)

ans =
 
  30
  --
  s
 
Continuous-time transfer function.

Create a tuning goal that specifies variable gain and phase margins across a grid of design points. Configure the tuning goal to be evaluated with a loop opening at a location 'LO' and to apply only in the frequency range between 1 and 100 rad/s.

Specify the grid of design points and the corresponding grid of target gain margins and phase margins. Also, create the template function for the varying margins goal.

[alpha,V] = ndgrid(linspace(0,20,5),linspace(700,1300,5));
[GM,PM] = ndgrid(linspace(7,20,5),linspace(45,70,5));
FH = @(gm,pm) TuningGoal.Margins('u',gm,pm);

Use the template function and the margin arrays to create the varying goal. Also, use Name,Value pairs to specify:

The property names and values that you specify for the underlying tuning goal are stored in the Settings property of the varying goal.

VG = varyingGoal(FH,GM,PM,'Openings','LO','Focus',[1,100])

VG = 
  varyingGoal with properties:

        Template: @(gm,pm)TuningGoal.Margins('u',gm,pm)
      Parameters: {[5x5 double]  [5x5 double]}
        Settings: {'Openings'  'LO'  'Focus'  [1 100]}
    SamplingGrid: [1x1 struct]
            Name: ''

  Variable tuning goal acting over a 5x5 grid of (gm,pm) values.

To make it easier to trace which goal applies to which design point, use the SamplingGrid property to attach the design-point information to VG.

VG.SamplingGrid = struct('alpha',alpha,'V',V);