Steady-state error is the difference between the input and output of a control system as time approaches infinity. There are three main types of test inputs used to analyze steady-state error: step inputs for constant positions, ramp inputs for moving targets, and parabolic inputs for accelerating targets. The steady-state error can be zero, finite, or infinite depending on whether the output slope matches the input slope. Systems with higher static error constants have lower steady-state errors. Sensitivity refers to how changes in a system's parameters affect its transfer functions and performance.

1. Control Systems
Lec 13
Steady-state error

2. Introduction
• control systems analysis and design focus on
three specifications: (1) transient response, (2)
stability, and (3) steady-state errors.
• Steady-state error is the difference between
the input and the output for a prescribed test
input as t -> ∞
• In order to explain steady-state error, let us
assume a position control system, where the
output position follows the input commanded
position.

3. Test inputs

4. Test inputs
❑ Step inputs represent constant
position and thus are useful in
determining the ability of the
control system to position itself
with respect to a stationary
target, such as a satellite in
geostationary orbit
❑ position control system that tracks
a satellite that moves across the
sky at a constant angular velocity,
would be tested with a ramp input.
❑ parabolas, whose second
derivatives are constant, represent
constant acceleration inputs to
position control systems and can
be used to represent accelerating
targets, such as the missile

5. Test inputs
Output 1 has zero
steady-state error, and
Output 2 has a finite
steady-state error
For the ramp input
another possibility
exists. If the output’s
slope is different from
that of the input, then
the steady-state error is
infinite

6. Steady-state error for unity feedback
system
Closed-loop control system
error: a. general representation;
b. representation for unity
feedback systems
Final Value Theorem

7. Steady-state error for different inputs

8. Steady-state error for different inputs

9. Steady-state error for different inputs

10. Steady-state error for different inputs
❖ The value of the steady-state error decreases as the
static error constant increases.

11. Steady-state error for different inputs

12. Steady-state error for different inputs

13. Steady-state error for different inputs

14. Steady-state error for different inputs

15. Steady-state error for different inputs

16. System type

17. System type

18. Steady-State Error Specifications

19. Gain design to meet SS error spec

20. SS error for non-unity feedback system

21. SS error for disturbance

22. SS error for disturbance

23. Sensitivity
The degree to which changes in system parameters affect
system transfer functions, and hence performance, is called
sensitivity.

24. Sensitivity