National Instruments 370757C-01 用户手册

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[WCMAG, NOMMAG] = wcbode (SysH, delb, {input, output, 

graph})

The 

wcbode( )

 function computes and plots the worst-case gain of a 

closed-loop transfer function. 

This function is useful for checking a system that already has been verified 
to be robustly stable using 

smargin( )

. For example, a system can have a 

minimum stability margin of 4 dB, so it is robustly stable. If the worst-case 
gain from a function input to the output it commands has a 20 dB peak, then 
even though the system is robustly stable, the design is unacceptable. On 
the other hand, if you verify that the perturbed closed-loop transfer function 
increases only 2 dB over the nominal, then the design is probably 
acceptable. 

The 

wcbode( )

 function computes and plots an approximation to 

ω), the largest possible magnitude of a perturbed closed-loop 

transfer function that can be caused by uncertain transfer functions that 
satisfy the magnitude bound. The 

wcbode( )

 function is conservative: 

it does not under-report the maximum of the perturbed transfer function. 

A large value of 

wcbode( )

 indicates instability: wcgain(

ω) = ∞. In this 

case, 

wcbode( )

 returns a maximum value of ten times the maximum of 

the nominal transfer function over all frequencies. Consequently, the 
window is clipped at 20 dB above the maximum of the nominal transfer 
function over all frequencies.

The 

wcbode( )

 function also plots the 

nominal transfer function for reference.

The 

wcbode( )

 function can be used to analyze performance degradation 

for the system you have been using (Figure 2-3). The transfer function, 
which should be small, is from reference to error (input 1 to output 1). 
Figure 2-6 shows the results of the following function call:

[NOMMAG,WCMAG]=wcbode(H,delb,{input=1,output=1});

The performance degradation due to the uncertainties is small but not 
negligible.