Lead / Lag Compensator Designer
Pole/zero ratio, time constant and corner frequencies from a target phase boost.
Bending phase where you need it
A lead compensator adds phase to lift the phase margin near crossover; a lag compensator trades a little phase for extra low-frequency gain (less steady-state error). Both are a zero/pole pair, set by one ratio and one frequency:
The maximum phase φₘ happens exactly at ωₘ = 1/(T√α), half-way (in
log frequency) between the zero at 1/T and the pole at 1/(αT). A single
lead section tops out around ~60° (the spread gets impractical beyond that —
cascade two if you need more), and it comes with a gain of 1/√α at ωₘ that you must
account for in the loop gain. Lag is the mirror image: a pole-then-zero that drops high-frequency
gain to buy low-frequency accuracy. Check the result against a target phase margin with the
damping converter.