Steady-State Errors in Control Systems: Definition and Analysis, Slides of Design

Steady-state errors, a performance criterion in control systems analysis and design. the definition of steady-state errors, test inputs, and methods to obtain steady-state errors using the final value theorem. The document also explores steady-state errors for unity feedback systems and different input types, such as step, ramp, and parabolic inputs.

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2021/2022

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SEE 2113 KAWALAN: PEMODELAN DAN SIMULASI
ZHI
4-43
Steady-State Errors
Three performance criteria in analysis and design
of control systems:
o Transient response
o Stability
o Steady-state errors
Transient response of 1st and 2nd order systems
have been discussed in previous lectures.
This section focuses on steady-state errors of the
time response of a particular system.
Definition
Steady-state error is the difference between the
input and the output for a prescribed test input as
t.
Test inputs used for steady-state error analysis and
design are summarized in Table 7.1.
Use for stable systems only.
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Steady-State Errors

  • Three performance criteria in analysis and design of control systems:

o Transient response

o Stability

o Steady-state errors

  • Transient response of 1 st^ and 2nd^ order systems have been discussed in previous lectures.
  • This section focuses on steady-state errors of the time response of a particular system.

Definition

  • Steady-state error is the difference between the input and the output for a prescribed test input as t → ∞.
  • Test inputs used for steady-state error analysis and design are summarized in Table 7.1.
  • Use for stable systems only.
  • Table 7.
  • Steady-state error, ess can be obtained using the final value theorem:
  • Example : Find the steady-state error for an open

loop system with 7 10

s s

G s and the input

is unit step input.

Steady-state errors for Unity Feedback

Systems

  • Consider a unity feedback system
  • Assume system is stable, we can apply the final value theorem:
  • The steady-state error depends on the input signal.

Ramp Input

  • Consider the case when (^2)

s

r t = t R s =.

  • Hence, to have zero steady state error for a ramp input,
  • This can only happen if

Parabolic input

  • Consider the case when (^2 )

s

r t = t R s =.

  • Hence, to have zero steady state error for a ramp input,
  • This can only happen if
  • If n=2 ,
  • Example : Find the steady-state error for input

5 u ( t ), 5 tu ( t ), 5 t^2 u ( t ) to the system shown below. The function u ( t ) is the unit step.