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3/2/2010
1
Lecture Note 10 :
System Type and PID Control
AE353, Spring 2010
Prof. Soon
‐
Jo Chung
([email protected])
Steady
‐
State Error: System Type
A system type: defined to be the degree of the polynomial
for which the steady
‐
state system error is a nonzero finite
constant.
The error will be zero for input polynomials below a certain
degree, and will be unbounded for inputs of higher degrees.
System Types are defined differently for Reference tracking
And Disturbance Rejection
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Summary: Errors as a Function of
System Type
Type\Input Step
Ramp
Parabola
Type
01
/
(
1
+
K
p
)
∞∞
10
1
/
K
v
∞
Type
20
0
1
/Ka
Example
No steady state errors
3/2/2010
3
System Type for General Case
•
Let’s assume that the feedback has a non
‐
unity gain
System Type w.r.t. Disturbance W
The system type w.r.t. disturbance inputs might be different from the system type w.r.t
reference inputs
Satellite Example
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This note was uploaded on 04/12/2010 for the course AE 353 taught by Professor Voulgaris,p during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Voulgaris,P

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