ledkompensatorn

The ledkompensatorn, or lead compensator, is a component used in control systems to introduce phase lead into the open-loop transfer function. It is designed to improve transient response and increase phase margin, enabling faster response without compromising stability.

Mathematically, a lead compensator has the form C(s) = K (s + z) / (s + p), with p > 0 and z > p. In Bode terms, the magnitude is modest, but the phase angle is positive in a certain frequency range, with the maximum lead around the geometric mean sqrt(p z). By selecting z > p, the compensator shifts the open-loop phase upward, increasing phase margin and potentially the closed-loop bandwidth.

Design and tuning involve choosing the zero z and pole p to meet target performance. The ratio z/p and the location relative to the system poles determine the amount and frequency of phase lead. In practice, one often selects p and z to place the pole and zero to shape the Bode plot, sometimes using root locus or frequency-domain methods. Lead compensation is frequently implemented with a simple RC network in analog electronics or as a digital filter in discrete-time controllers.

Relation to lag compensators: a lag compensator uses p > z and aims to improve low-frequency gain and steady-state error without adding phase lead at crossover. Lead and lag can be combined to form lead-lag compensators for more flexible tuning.

Applications include stabilization and performance improvement in aerospace, robotics, and process control, where faster response and adequate phase margin are required. The term ledkompensatorn is commonly used in Swedish-language control theory literature.