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Chapter 2
Robustness Analysis
2-4
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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 th
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 inputs of 
SysH
 are 
signal in Figure 2-2, and the last k outputs are signal q. To create a Nominal 
System, refer to thCreating 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 
a SISO tracking system with three uncertainties. 
δ
1
 is a multiplicative 
actuator uncertainty, while 
δ
2
 and 
δ
3
 are multiplicative sensor uncertainties. 
Known Closed-Loop System
w
r
z
q
H(s)
size 
k
size 
k