What does bandwidth refer to in the context of servo systems?

Most people are familiar with bandwidth as it relates to networking and WiFi service — for example, the 2.4 GHz and 5 GHz frequency bands on which WiFi signals are transmitted. But bandwidth also plays an important role in servo control and tuning.

The bandwidth of a servo control system indicates how quickly the system responds to changes in the input command — position, velocity, or torque. Each control loop in the system has its own bandwidth, and in cascaded control loops, the innermost loop (current control) should have the highest bandwidth. The next loop (velocity control) can have a lower bandwidth — in some applications, the velocity loop bandwidth can be an order of magnitude lower than the current loop bandwidth. And the outermost loop (position control) can have a bandwidth that is a magnitude lower than the velocity loop.

Cascaded Control Loops — In cascaded control loops, the innermost loop (current) should have the highest bandwidth.
*Image credit: nctu.edu*

Servo systems use control loops to determine how much current the servo drive should deliver to the motor in order to correct any errors between the commanded value (position, velocity, or torque) and the actual value. Most advanced servo systems use three control loops – one to control current, one to control velocity, and one to control position.

The technical definition for the bandwidth of a servo system is the frequency at which the closed-loop amplitude response reaches -3 dB.

Amplitude response is a measure of the amplitude of the output signal versus to the amplitude of the input signal. If the output perfectly matches the input, the output will have the same amplitude as the input signal — in other words, 0 dB amplitude gain.

The -3 dB amplitude response represents the point where the output gain (the ratio of the output to the input) equals 70.7 percent of its maximum, and correspondingly, where the power delivered to the load equals 50 percent of the input power.

servo bandwidth plot — The bandwidth of a servo system is the frequency range from 0 to the point at which the closed-loop amplitude response reaches -3 dB.
*Image credit: Rockwell*

Amplitude response and its companion, phase response, together make up the frequency response of the servo system. Frequency response is a key measure of the system’s stability and is represented with a Bode plot.

Bode Plot — A Bode plot shows both the amplitude response (top) and the phase response (bottom) for a range of frequencies.
*Image credit: University of Michigan*

Generally speaking, the higher the bandwidth of the servo control, the higher the gains can be set in the control loops. Theoretically, the most dynamic performance is achieved when the system has the highest bandwidth and the highest control loop gains possible.

However, high bandwidth means the control system will force the motor to respond aggressively to changes in the input command. The means the motor will need to accelerate faster and produce more force/torque — both of which require more power, which in turn, generates heat. So the motor’s thermal characteristics — its ability to dissipate or withstand heat — can be a limiting factor in the control system’s bandwidth. The bandwidth of a servo control system can also limited by factors such as the load-to-motor inertia ratio and system compliance, as well as the resolution of the feedback device and the update rate of the control loops.