sdo.requirements.PhasePlaneEllipse class

Package: sdo.requirements
Superclasses:

Impose elliptic bound on phase plane trajectory of two signals

Description

Use the sdo.requirements.PhasePlaneEllipse object to impose an elliptic bound on the phase plane trajectory of two signals in a Simulink^® model. The phase plane trajectory is a plot of the two signals against each other. You specify the radii, center, and rotation of the bounding ellipse. You also specify whether you require the trajectory of the two signals to lie inside or outside the ellipse.

The following image shows the bounding ellipse and an example of the phase plane trajectory of two signals.

The X-Y plane is the phase plane defined by the two signals. r_x and r_y are the radii of the bounding ellipse along the x and y axes, and θ_R is the rotation of the ellipse about the center. The ellipse center is at (x₀,y₀). In the image, the phase plane trajectory of the signals lies within the bounding ellipse for all time-points t₁ to t_n.

You can use the object as an input to your cost function, and use the evalRequirement command in the cost function to evaluate whether your test signals satisfy the specified requirement. You can then use the cost function and sdo.optimize to perform parameter estimation or response optimization, subject to the satisfaction of the specified requirement. If you are performing sensitivity analysis, after you generate parameter samples, you can use the cost function and sdo.evaluate to evaluate the requirement for each generated sample.

Construction

requirement = sdo.requirements.PhasePlaneEllipse creates an sdo.requirements.PhasePlaneEllipse requirement object and assigns default values to its properties. Use dot notation to customize the properties.

Use the evalRequirement command to evaluate whether test signals satisfy the specified requirement.

requirement = sdo.requirements.PhasePlaneEllipse(Name,Value) creates the requirement object with additional options specified by one or more Name,Value pair arguments. Name is a property name and Value is the corresponding value. Name must appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Input Arguments

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Use Name,Value arguments to specify properties of the requirement object during object creation. For example, requirement = sdo.requirements.PhasePlaneEllipse('Type','>=') creates an sdo.requirements.PhasePlaneEllipse object and specifies the Type property as an outer bound.

Properties

Center — Location of center of ellipse

[0 0] (default) | 1-by-2 array

Location of center of bounding ellipse, specified as a 1-by-2 array with real finite values. The elements of the array specify x₀ and y₀, the x and y coordinates of the center location. To completely characterize the ellipse, also specify the Radius and Rotation properties of the ellipse. To see the equation of the ellipse, see Description.

Example: [1.5,-1]

Data Types: double

Description — Requirement description

'' (default) | character vector

Requirement description, specified as a character vector.

Example: 'Requirement 1 for myModel.'

Data Types: char

Method — Method for requirement evaluation

'Maximum' (default) | 'Residuals'

Method for requirement evaluation using the evalRequirement command, specified as one of the following:

• 'Maximum' — The evalRequirement command computes the signed minimum distance of each point in the phase plane trajectory to the bounding ellipse and returns a scalar that is the maximum of these distances.

• 'Residuals' — The evalRequirement command returns a column vector with the signed minimum distance of each point in the phase plane trajectory to the bounding ellipse. Use this method instead of 'Maximum' to see the distance of all of the trajectory points to the phase plane ellipse.

Data Types: char

Name — Name of requirement

'' (default) | character vector

Name of requirement, specified as a character vector.

Example: 'Requirement1'

Data Types: char

Radius — Radii of ellipse

[1 0.5] (default) | 1-by-2 array

Radii of ellipse, specified as a 1-by-2 array with real positive finite values. The elements of the array specify r_x and r_y, the x-axis and y-axis radii, before any rotation about the ellipse center. To completely characterize the ellipse, also specify the Center and Rotation properties of the ellipse. To see the equation of the ellipse, see Description.

Data Types: double

Rotation — Angle of rotation of ellipse about center

0 (default) | real finite scalar

Angle of rotation θ_R of ellipse about center in radians, specified as a real finite scalar. The angle of rotation is specified from the x-axis. To completely characterize the ellipse, also specify the Center and Radius properties of the ellipse. To see the equation of the ellipse, see Description.

Example: 'Requirement 1 for myModel.'

Data Types: double

Type — Type of bound

'<=' (default) | '>='

Type of bound, specified as one of the following:

• '<=' — Ellipse is an upper bound. The phase plane trajectory of the two signals should lie inside or on the ellipse.

• '>=' — Ellipse is a lower bound. The phase plane trajectory of the two signals should lie outside or on the ellipse.

Methods

evalRequirement

Evaluate satisfaction of elliptical bound on phase plane trajectory of two signals

Copy Semantics

Handle. To learn how handle classes affect copy operations, see Copying Objects.

Examples

Create Phase Plane Ellipse Requirement and Specify Ellipse Center

Create a requirement object with default properties.

Requirement = sdo.requirements.PhasePlaneEllipse;

The requirement object specifies the bounding ellipse as an upper bound with center located at [0,0], and no rotation. The x-axis radius of the ellipse is 1 and the y-axis radius is 0.5.

Specify the location of the center of the ellipse.

Requirement.Center = [1,0]

Requirement = 
  PhasePlaneEllipse with properties:

         Radius: [1 0.5000]
         Center: [1 0]
       Rotation: 0
           Type: '<='
         Method: 'Maximum'
           Name: ''
    Description: ''

You can now use the evalRequirement command to evaluate whether test signals satisfy the requirement.

Specify Bounding Ellipse as Lower Bound

Create a requirement object, and specify the bounding ellipse as a lower bound. Use default values for the location of the center, radii, and rotation of the bounding ellipse.

Requirement = sdo.requirements.PhasePlaneEllipse('Type','>=');

The requirement object specifies that the phase plane trajectory of test signals should lie outside the ellipse.

Version History

Introduced in R2016b