Continuous

LeadLag Block

Lead-lag compensator: G(s) = (τ₁s + 1) / (τ₂s + 1). Used for phase compensation in control systems.

# LeadLag Block

Description

Lead-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

G(s) = (τ₁·s + 1) / (τ₂·s + 1)

| 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 |

Parameters

leadTime (τ₁)

Lead time constant (seconds). Set to 0 for a pure lag filter.

lagTime (τ₂)

Lag time constant (seconds). Must be > 0.

Remarks

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