【精品】PPT课件 3.3 steady-state error Analysis of the linear system.ppt

steady-state error Analysis of the linear system
Why to analysis the steady-state error?
1) One of the objectives of the control systems is that the system output response follows a specific reference signal accurately in the steady state.
2) Because of friction and other imperfection, steady-state errors in the control systems are almost unavoidable
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steady-state error analysis of the linear system
Error and steady-state error
1. Error :
desired
output
G(s)
H(s)
-
Actual
output
For the system:
that is :
E(s)=R(s)-B(s)=R(s)-C(s)H(s)
Definition: the difference between the desired output (reference input R(s)) and the actual output (feedback signal B(s)).
For the unity feedback system:
E(s)=R(s)-C(s)
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E!(t)=r!(t)-c(t)
For the unity feedback system:
H(s)=1 → E!(s)=E(s)
Note: other definition
1/H(s)
G(s)H(s)
-
2. Steady-state error
Definition:
the difference between the reference input and the output in the steady state.
steady-state error analysis of the linear system
G(s)
H(s)
-
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G1(s)
G2(s)
H(s)
C(s)
-
-
Error expression
By input
By disturbance
Steady-state error expression
By input
By disturbance
steady-state error analysis of the linear system
3. For a system with
the disturbance
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Solving the steady-state error  — by the final value principle
Final Value Principle:
Note:
all roles of sE(s) must lie on
the left-half of the s-plane.
steady-state error only
caused by the input signals:
1) r(t)=A01(t)
----step function input
steady-state position error constant
kp=?
steady-state error analysis of the linear system
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In terms of to the number of the poles of G(s)H(s) at s=0
(corresponding with the number of the integral elements in the open loop systems), we name:
v=0 — type 0 system
v=1 — typeⅠsystem
v=2 — typeⅡsystem
Assume:
k for v=0 (type 0 system)
∞ for v=1 (typeⅠsystem)
∞ for v=2 (typeⅡsystem)
for t