LeadLagRegler

LeadLagRegler, commonly referred to in English as a lead-lag controller, is a compensator used in negative feedback control to shape the closed-loop response of a system. It combines a lead network and a lag network to address both transient performance and steady-state accuracy.

The typical transfer function of a lead-lag controller is a product of two first-order elements: C(s) = K · (τ1 s + 1)/(α τ1 s + 1) · (τ2 s + 1)/(β τ2 s + 1). Here τ1, τ2 > 0, α ∈ (0, 1) and β > 1. The lead portion (α < 1) places a zero and a pole so that the phase margin is increased over a certain frequency range, improving speed of response and damping. The lag portion (β > 1) places a pole and a zero to boost low-frequency gain, thereby reducing steady-state error, while having only a modest negative impact on high-frequency dynamics.

Design and tuning typically aim to achieve a desired balance between transient response and steady-state performance. This involves selecting parameters to place the lead’s phase boost where it is most beneficial and configuring the lag to meet accuracy targets without excessively slowing the response. Methods such as Bode plots, root locus, or optimization are commonly used.

Applications include precision positioning, robotics, and process control, where faster response without sacrificing long-term accuracy is required. Advantages include simultaneous improvement of speed and steady-state error; drawbacks include potential noise sensitivity and complexity in tuning.