A frequency plot is useful because one gain change can affect slow disturbances and fast oscillations very differently. Lead and lag compensation give you a pole and zero to shape that tradeoff. The job is not finished when a margin number looks attractive: the motor still has a voltage limit.
Write the design goal before moving a zero
If the response is too slow or the phase margin near gain crossover is small, a lead network can add positive phase over a band. With C(s) = K(s+z)/(s+p), a lead has z < p. If persistent error under load matters more, a lag network puts p < z and raises relative low-frequency gain, typically paying a phase and speed cost. Neither statement predicts every closed-loop result without the plant and chosen gain.
A lag compensator with finite DC gain can reduce a constant-load error but cannot guarantee exactly zero steady error. An integrator has different behavior—and its own windup problem. This is why ‘lag versus I’ is a design comparison, not a naming exercise.
Use the frequency plot as a hypothesis
In EIGENROOM, move the lead zero toward its pole while keeping the motor model and load fixed. Observe where the loop phase changes, whether gain crossover moves, and whether a single phase margin remains meaningful. Then replay the output and requested voltage. The frequency workbench analyzes the sampled linear loop; it intentionally leaves out load, sensor noise, anti-windup and saturation.
If the requested voltage crosses ±12 V but applied voltage does not, that part of the time response is governed by a nonlinear limit. Do not use a comfortable Bode margin as proof that this saturated run is safe. Compare the same disturbance under both compensators and report the tradeoff in response, error and control effort.
Lead is usually a phase-shaping move; lag is usually a low-frequency-gain move. Verify the intended frequency change against the actual, limited actuator response.