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Chapter 8 H-Infinity Synthesis
Xmath Interactive Control Design Module 8-6 ni.com
Manipulating the Design Parameters
The parameters γ, ρ, and ν can be changed using the associated slider or
variable edit box. If the user types in a value that is outside the current slider
range, the slider range will automatically adjust. The user can change the
ranges for the sliders using the Ranges
window. Refer to the Infeasible
Parameter Values section for what happens when the requested value of γ
is infeasible.
The parameter γ also can be changed graphically, by grabbing and
dragging the dashed horizontal line in the singular value plot.
Manipulating the Weight Transfer Function
When Weight Zero Editing is enabled, the user can graphically
manipulate the zeros of the weight transfer function W on the plot labeled
Weight Poles & Zeros. Refer to the Graphically Manipulating Poles and
Zeros section of Chapter 2, Introduction to SISO Design, for a general
discussion of how to move, add, delete, or edit these zeros graphically.
Infeasible Parameter Values
If the user requests an infeasible value for γ, then it will be reset to an
approximation of the optimal (that is, smallest possible feasible) value, γ
opt
.
In this case, four (logarithmic) bisection iterations are used to determine γ,
a feasible value of γ such that:
where γ
new
is the value that γ is reset to
γ
opt
is the optimal (smallest possible feasible) value of γ
γ
prev
is the previous value of γ
γ
req
is the value of γ requested by the user
After the H∞ Synthesis
window has determined a lower bound on γ
opt
, it is
displayed in the singular value plot. It will disappear if the user changes the
control cost, sensor noise, or output weight parameters.
γ
new
()log γ
opt
()log–
γ
prev
()log γ
req
()log–
16
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