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The Control ObjectsThe Control Format

1.4 Traditional Notations

When using the notebook front end, you will often find it useful to represent the control objects in their traditional typeset form. That can be done either by applying the Mathematica function TraditionalForm or by selecting an expression that contains one or more control objects and executing the menu command Cell RightTriangle Convert To RightTriangle TraditionalForm (or the corresponding keyboard shortcut, as described in the documentation for your copy of Mathematica). The Control Format palette provided in Control System Professional allows you to switch between automatic display of results in the traditional form and standard Mathematica output.

This is a single-input, two-output TransferFunction object in TraditionalForm. Since the object is believed to be in the continuous-time domain, the variable ScriptS is used. The superscripted letter ScriptCapitalT distinguishes the result from a regular matrix.

In[6]:=

Out[6]//TraditionalForm=

This is the TraditionalForm of the discretized object. It displays using the variable ScriptZ. The subscript gives the value of the sampling period.

In[7]:=

Out[7]//TraditionalForm=

This is a possible state-space realization of the above system in TraditionalForm. The superscripted letter ScriptCapitalS identifies the StateSpace object, while the small subscripted bullet character denotes the continuous-time domain.

In[8]:=

Out[8]//TraditionalForm=

Additionally, Control System Professional provides the function EquationForm that allows you to display the StateSpace objects as the familiar state-space equations. These have the conventional form for both continuous-time and discrete-time systems. Note that EquationForm disregards the value of the sampling period.

This represents the above StateSpace object as a pair of matrix state-space equations.

In[9]:=

Out[9]//EquationForm=

For the discretized system, the state-space equations are displayed as difference rather than differential equations.

In[10]:=

Out[10]//EquationForm=

Here is the same system in TraditionalForm.

In[11]:=

Out[11]//TraditionalForm=

Both TraditionalForm and EquationForm provide convenient formatting. Neither changes the internal representation of the objects. In this respect, the functions behave much like OutputForm or MatrixForm (and all other members of the $OutputForms list).

Despite different formatting, the previous result is still the StateSpace object.

In[12]:=%

Out[12]=

Typically, you can freely copy, paste, and edit the typeset representations of control objects. When editing, however, exercise caution to prevent destruction of the invisible tags that allow an unambiguous interpretation of the object in typeset form. As a rule of thumb, you will typically find it safe to select exactly the part of expression that you want to edit or to drag across the entire object and choose Edit RightTriangle Copy when you want to copy the object as a whole (or, better yet, copy the entire cell that contains the control object).

The Control ObjectsThe Control Format



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