Lead-Lag
ContinuousLead-lag compensator with transfer function G(s) = (τ₁s + 1) / (τ₂s + 1). When τ₁ > τ₂ it acts as a lead compensator (phase advance), when τ₁ < τ₂ it acts as a lag compensator (phase delay).
Mathematical Model
| Condition | Behaviour | Application |
|---|---|---|
| τ₁ > τ₂ | Lead: phase advance, +90° max | Improve stability margin |
| τ₁ < τ₂ | Lag: phase delay, -90° max | Reduce high-frequency gain |
| τ₁ = τ₂ | Unity: G(s) = 1 | No effect |
Inputs & Outputs
| Direction | ID | Label | Type | Status |
|---|---|---|---|---|
| → In | in |
In | number | Required |
| ← Out | out |
Out | number | Output |
Parameters
| Parameters | Label | Type | Default | Description |
|---|---|---|---|---|
leadTime |
Lead Time Constant (τ₁) | number | 1 |
|
lagTime |
Lag Time Constant (τ₂) | number | 0.1 |
Usage Examples
- Zie de ingebouwde voorbeelden in de handleiding voor een demonstratie van dit blok.
Remarks & Best Practices
- Lead compensator (τ₁ > τ₂): Adds phase advance (+90° max), improves stability margin and bandwidth
- Lag compensator (τ₁ < τ₂): Adds phase delay (−90° max), reduces steady-state error at the cost of bandwidth
- Lag time constraint: τ₂ must be > 0; for a pure lead compensator set τ₂ to a small value (e.g., 0.001)
- Cascading: Multiple lead-lag sections in series create higher-order compensators (e.g., lead-lag-lead)
- Numerical integration: Uses the same forward Euler method as TransferFunction; stability follows the same constraints
Related Components
- TransferFunction: General continuous transfer function G(s)
- PIDController: PID control with derivative filtering