4 Closed loop responses
Closed loop responses are available only in ``rootlocus'' mode.
There is a great deal of flexibility in rltool to see various closed
loop responses. First you will have to select one ``gain configuration'' out of
the possible two. Click on ``Settings-->Gain Configuration''. You will
see a selection dialogue box with two choices:
You can choose the gain to be in the forward path like the following
figure shows:
This corresponds to the option ``K in forward path''. You can choose
to put ``K in the feedback path''. However, ``K in forward path'' is
the default.
To see closed loop responses, click on ``Response-->Closed Loop''. You
will be prompted to click on a point of the rootlocus to select the
``operating point'' at which you want to see the closed loop
response. Once you select the operating point, you are done!
Rltool calculates the closed loop transfer function for the
configuration you have selected, i.e. the closed loop transfer
function for ``K in forward path'' is
and the closed loop transfer function for ``K in feedback path'' is
You will see a selection menu that shows the following:
-
The gain corresponding to operating point you selected.
- Whether the closed loop system is stable or unstable.
- Impulse response: Click here to see the impulse response!
- Step response selection: Unit step response is displayed. A
``details'' button in the step response also displays parameters such
as percent overshoot, rise time, settling time, z corresponding
to second order approximation etc.
- Ramp response: Unit ramp response.
- Arbitrary input: You can enter piece-wise linear, single valued
inputs through a graphics window. Use the mouse (press left button and
drag) to ``draw'' this input. There are a host of features like
``undo'', ``abort'' etc which can be used. You can also resize your
window to suit the range of your input. Click ``Edit-->Ok'' when you are
done. If your input is single-valued, you will see the response of the
closed loop system to this input.
- Sinusoidal input: The input is of the form
A sin (w t)
Output is simulated, by default for ONE CYCLE of the input and is
plotted. Other default settings are A=1 and w=1
rad/sec. These can be changed by clicking on ``Settings'' button in
the sinusoidal response window. You must close this window to return
to the response selection menu.
- Frequency response (bode plot) of closed loop system. There is a
choice in the units (Rad/sec) or (Hz). These are available in
``Options'' menu in the frequency response window.
- Sensitivity plot: Sensitivity is defined as the transfer function between the input u(t) and the error e(t). For the system shown in the above figure, the sensitivity can be found to be
This transfer function is evaluated on the imaginary axis (by substituting s=iw) and the resulting (magnitude) plot is shown for various values of w. Options are similar to above.
Click on ``cancel'' to close the response selection menu and return to
the main window of rltool.