Steady-State Error
The persistent difference between a system's desired output and its actual output after transient responses have settled.
Steady-State Error
Steady-state error (SSE) represents the long-term deviation between a system's desired setpoint and its final output value after all transient response behaviors have dissipated. This fundamental concept in control systems helps engineers evaluate and improve system performance.
Understanding Steady-State Error
The steady-state error can be understood through three key components:
- Reference Input (R): The desired value or setpoint
- Actual Output (C): The system's final stabilized output
- Error (E): The difference between reference and output (R - C)
Classification of Input Types
SSE behavior varies depending on the input signal type:
- Step Input: Sudden change to constant value
- Ramp Input: Linearly increasing signal
- Parabolic Input: Quadratically increasing signal
Each input type creates different system response characteristics and steady-state error properties.
System Type and Error Constants
The steady-state error relates directly to the system type number and corresponding error constants:
- Position Error Constant (Kp)
- velocity error constant (Kv)
- Acceleration Error Constant (Ka)
Reduction Techniques
Engineers can minimize steady-state error through several methods:
- PID Control
- integral control
- feedforward compensation techniques
- System type modification
Mathematical Expression
For a unity feedback system, the steady-state error can be expressed as:
SSE = lim(t→∞) [r(t) - c(t)]
Where:
- r(t) is the reference input
- c(t) is the system output
Industrial Applications
Steady-state error analysis is crucial in:
- industrial automation processes
- robotics position control
- temperature control systems
- servo mechanisms
Performance Specifications
Common specifications related to steady-state error include:
- Maximum allowable error
- Time to reach steady state
- Error bandwidth
- stability margins requirements
Understanding and managing steady-state error is essential for designing robust closed-loop systems that meet performance requirements in real-world applications.