Control Bandwidth

The highest signal frequency a closed-loop system can still keep up with, usually taken where the gain drops by 3 dB.

Feed a closed-loop control system sinusoidal commands at various frequencies: at low frequency the output tracks fully, and as frequency rises the output's amplitude shrinks and its lag grows; the frequency at which the amplitude has dropped to about 70.7% (i.e., −3 dB) of its low-frequency value is the closed-loop bandwidth. Higher bandwidth means a faster response and better rejection of fast disturbances. It's not the same as control frequency: control frequency is how many times per second commands are computed, while bandwidth is how fast the system can actually keep up — the former typically needs to be several times higher than the latter for the bandwidth to actually be achievable. In cascade control, the inner loop's bandwidth must be noticeably higher than the outer loop's — e.g., the current loop faster than the velocity loop, the velocity loop faster than the position loop. Legged robots have very short ground-contact times, requiring high-bandwidth force control; compliant elements, low-stiffness transmissions, and communication delay all limit the achievable bandwidth.

ExampleA first-order system G(s)=1/(τs+1) with τ=16 ms has a bandwidth of 1/τ = 62.5 rad/s, about 10 Hz: it tracks a 2 Hz sinusoidal command almost fully, but at 30 Hz the output amplitude has shrunk to roughly 30%. On real hardware, a single ground-contact phase on MIT Cheetah while running can be as short as about 85 milliseconds, which is why its proprioceptive actuators list ‘high-bandwidth force control’ as a design goal.

Also called

Closed-Loop Bandwidth, -3 dB Bandwidth, Force Control Bandwidth, Current Loop Bandwidth

Related

Control Frequency · Control Latency · Cascade Control · Proprioceptive Actuator · Force Control · Step Response Metrics (Overshoot / Settling Time / Steady-State Error)

Sources

MathWorks: bandwidth（增益首次低于直流值 70.79%，即 −3 dB 的频率） (Chinese)
Wikipedia: Bandwidth (signal processing)
Wensing et al., Proprioceptive Actuator Design in the MIT Cheetah: Impact Mitigation and High-Bandwidth Physical Interaction (IEEE T-RO 2017)