hallchart
=========

Draws the Hall chart



Calling Sequence
~~~~~~~~~~~~~~~~


::

    hallchart([ modules [,args [,colors]]])



::






Arguments
~~~~~~~~~

:modules real vector ( modules (in dB))
: :args real vector (phases (in degree))
: :colors a scalar or a vector, the color indices for isogain and iso
  phase curves
:



Description
~~~~~~~~~~~

plot the Hall'chart: iso-module and iso-argument contours of `y/(1+y)`
in the `real(y)`, `imag(y)` plane

`hallchart` may be used in cunjunction with `nyquist`_.

The default values for `modules` and `args` are respectively :

`[-20 -10 -6 -4 -2 2 4 6 10 20]`

`[-90 -60 -45 -30 -15 15 30 45 60 90]`

This function superseeds the `m_circle`_ function



Graphics entities organization
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The `hallchart` function create a single compound object which is
generaly the last child of the current axes. This compound object
contains a set of compound objects, one for each grid curve. The first
ones are the iso module curves and the last one the iso-argument
contours. Each of these compound objects contains a Polyline object
(the curve) and a Text object (the label). The following piece of code
can be used to change the color of the ith iso module curve:


::

    `clf`_();hallchart()
    ax=`gca`_();//handle on current axes
    c=ax.children($).children;// the handles on the chart grid curves
    i=4; //the index of the -4dB curve
    ci=c(i); //the handle on the -4dB curve
    ci.children(1).foreground=`color`_('red'); //draw it in red
    
    j=3; // the index of the -45° curve
    cj=c(10+j); //the handle on the -45° curve
    cj.children(1).thickness=3;//draw it thicker




Examples
~~~~~~~~


::

    //Hall chart
    `clf`_();hallchart()





::

    //Hall chart as a grid for nyquist
    s=`poly`_(0,'s');
    Plant=`syslin`_('c',16000/((s+1)*(s+10)*(s+100)));
    //two degree of freedom PID
    tau=0.2;xsi=1.2;
    PID=`syslin`_('c',(1/(2*xsi*tau*s))*(1+2*xsi*tau*s+tau^2*s^2));
    `clf`_();
    `nyquist`_([Plant;Plant*PID],0.5,100,["Plant";"Plant and PID corrector"]);
    hallchart(colors=`color`_('light gray')*[1 1])
    //move the caption in the lower rigth corner
    ax=`gca`_();Leg=ax.children(1);
    Leg.legend_location="in_lower_right";






See Also
~~~~~~~~


+ `nyquist`_ nyquist plot
+ `nicholschart`_ Nichols chart


.. _m_circle: m_circle.html
.. _nicholschart: nicholschart.html
.. _nyquist: nyquist.html