# Overall system bandwidth of a servo system

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#### Carsten Horn

I have an servo system and i want to know some datas:
1. Overall System Bandwith
We conect an sinus function generator to the servo controller.
The amplitude is adjusted so that we have nominal tourqe of the motor.
We see actual speed and set speed on a Oscilloscope.
We increase the frequency at the input to the phase shift between input
signal and output signal 45° amount to. (or the amplitude is 0.707 of the
input)

2. Bandwith of the speed and current controller.
Speed and current controllers are digitally executed with us. I think that the bandwidth of a
digital controller is only defined by the update time of the controller.
So the update time of the current controller is 64us and for the speed controller is 128us.
Do you know the exakt Bandwith of the both controller ?

Thank you for information.
Carsten Horn

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#### Tom Bullock

For a critically damped type one servo with no fancy compensation, the bandwidth is the point where the output is 0.707 of the input and the phase shift from input to output is 45 degrees.
This is true no matter whether it's the position, velocity, or torque loop.

With today's technology, the update time seldom is the limiting factor in determining the loop bandwidth. As long as the loop is updated at least 4 times per cycle at the bandwidth (10 would be ideal), it will be other factors that limit the bandwidth. Inertia is a major factor, but there are others. For instance, if we
consider the 64 microsecond update time, 4 times this would be about 0.25 milliseconds meaning it could support a bandwidth as high as 4,000 Hertz. Since some torque loops are approaching
2,000 Hertz today, the 64 microsecond update is needed. Forward your mailing address to me and I'll send you an article describing the equations for the electrical and mechanical time constants and the resulting resonant frequency. Another rule of thumb is that the resonance be at least 4 times the bandwidth. Tom
Thomas B. Bullock
President Bull's Eye Marketing, Inc. Industrial Controls Consulting
Division [email protected] (920) 929-6544

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#### Kaufman, George

Please visit www.MotionOnline.com and download the Handbook of AC Servo Systems. There is a section on the construction of current, velocity, and position loops. There is also a discussion of
bandwidth.

Best regards,
George Kaufman