Using The Alternate Plant Window; Robustness To Plant Variations; Adding Unmodeled Dynamics - National Instruments Xmath Interactive Control Design Module ICDM User Manual

Using the Alternate Plant Window

Robustness to Plant Variations

Adding Unmodeled Dynamics

© National Instruments Corporation
You can switch between high frequency and DC normalization by clicking
the appropriate buttons. If the alternate plant has a pole or zero at s = 0, then
you cannot switch to DC normalization.
The Alternate Plant window is used to analyze the robustness of a given
controller to changes or unmodeled dynamics in the plant.
The simplest test is to start with the plant (which is the default value of the
alternate plant), and then vary the gain and the poles and zeros of the
alternate plant. A robust system will not show excessive differences
between the responses with the plant and the alternate plant. With this
method, you can easily see the effects of plant gain, pole, and zero
variations.
With DC normalization, varying the poles and zeros affects at high
frequencies but does not change the DC gain. This is appropriate when
the plant variations and modeling errors are more pronounced at high
frequencies.
Starting with P = P and then adding a pole-zero pair is a good way to see
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the effects of a little "unmodeled plant dynamics" on the system. Notice
that when you add a pole-zero pair, you have not yet changed the alternate
plant transfer function. The change occurs smoothly as you drag the zero
away from the pole.
• To add a little excess phase and rolloff in the loop, create a real
pole-zero pair and separate them a bit, with the pole to the right of the
zero. This simulates the effect of unmodeled "diffusion dynamics" in
the system.
• To add a little lightly damped dynamics, create a lightly damped
pole-zero pair (that is, with small negative real part) and then drag the
pole and zero away from each other. This will create a resonance
typical of a neglected mode in a mechanical system.
• To simulate the effect of an unmodeled time delay in the loop, create a
real pole-zero pair at s = –2/T and then drag the zero to s = –2/T
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10-5 Xmath Interactive Control Design Module
Chapter 10 Alternate Plant Window
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