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System Type (# free integrators)
As you will recall, whether the steady-state error [discussed on the last page] is
zero
some particular non-zero but finite value
or
infinite
is a function both of
System Type
and of
The type of input, typically either a
step
input or
ramp
input.
Also recall:
The 'system type' is defined as the number of
free integrators
in that system's transfer function.
Each 'free integrator' is simply a pole at zero.
For each free integrator ('pole at zero'), there exists a corresponding eigenvalue 'lambda=0' in the denominator.
Thus, the system type is essentially the 'power in s' which you can
factor out of the denominator
of the transfer function.
Here is the summarized table provided in the lecture notes, relating System Type to steady-state error:
-
System Type
(= # free integrators in TF)
Input to System
0
1
2
Step
1/(1+OLTF(s)) {lim as s->0}
0
0
Ramp
infinite
1/(OLTF(s)) {lim as s->0}
0
gonzo@mit.edu
page 5 (of 10)
2.010 Tutorial #6, 30-Oct-00