prescale
Optimal scaling of state-space models
Syntax
scaledsys = prescale(sys)
scaledsys = prescale(sys,focus)
[scaledsys,info] = prescale(...)
prescale(sys)
Description
scaledsys = prescale(sys) scales the entries
of the state vector of a state-space model sys to
maximize the accuracy of subsequent frequency-domain analysis. The
scaled model scaledsys is equivalent to sys.
scaledsys = prescale(sys,focus) specifies
a frequency interval focus = {fmin,fmax}
(in rad/TimeUnit, where TimeUnit is
the system's time units specified in the TimeUnit property of sys)
over which to maximize accuracy. This is useful when sys has
a combination of slow and fast dynamics and scaling cannot achieve
high accuracy over the entire dynamic range. By default, prescale attempts
to maximize accuracy in the frequency band with dominant dynamics.
[scaledsys,info] = prescale(...) also returns
a structure info with the fields shown in the following
table.
SL | Left scaling factors |
SR | Right scaling factors |
Freqs | Frequencies used to test accuracy |
RelAcc | Guaranteed relative accuracy at these frequencies |
The test frequencies lie in
the frequency interval focus when specified. The
scaled state-space matrices are
where TL = diag(SL) and TR = diag(SR). TL and TR are inverse of each other for explicit models (E = [ ]).
prescale(sys) opens an interactive GUI
for:
Visualizing accuracy trade-offs for
sys.Adjusting the frequency interval where the accuracy of
sysis maximized.
For more information on scaling and using the Scaling Tool GUI, see Scaling State-Space Models.
Tips
Most frequency-domain analysis commands perform automatic scaling
equivalent to scaledsys = prescale(sys).
You do not need to scale for time-domain simulations and doing
so may invalidate the initial condition x0 used
in initial and lsim simulations.