Chapter 2 RobustnessAnalysis
MATRIXx Xmath Robust Control Module 2-4 ni.com
smargin( )marg = smargin(SysH, delb {scaling, graph})
The smargin( ) function plots an approximation to the stability margin
of the system as a function of frequency. For a full discussion of
smargin( ) syntax, refer to the MATRIXx Help. The approximation is
exact if the number of uncertain transfer functions is less than four and
scaling="OPT" (optimum scaling).
In other cases, the approximation is generally considered to be extremely
good. Refer to the Approximation with Scaled Singular Values section. The
approximation is always conservative. smargin( ) always will report a
margin that is less than or equal to the actual margin.
The smargin( ) function counts the columns in delb to calculate the
number of uncertainties k. It then assumes that the last k inputs of SysH are
signal r in Figure2-2, and the last k outputs are signal q. To create a Nominal
System, refer to the Creating a Nominal System section.
Figure 2-2. Nominal Closed-Loop System
Creating a Nominal System
To better understand how to create H(s) in Figure 2-3, you will examine
aSISO tracking system with three uncertainties. δ1 is a multiplicative
actuator uncertainty, while δ2 and δ3 are multiplicative sensor uncertainties.
Known Closed-Loop System
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H(s)
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