Current, speed and position loops: fastest on the inside

Motor control is a cascade with the current loop innermost and the speed and position loops outside. Bandwidth allocation and tuning order.

Cascade structure

Three nested loops. The output of an outer loop is the target of the inner one. The further in, the faster.

position target → [position P] → speed target → [speed PI] → iq target → [current PI ×2] → voltage → motor
                    ↑ encoder position            ↑ calculated speed       ↑ phase currents

Bandwidth allocation

Loop	Period	Bandwidth (example)
Current	10 to 20 kHz (PWM-synchronised, ISR)	~1 kHz
Speed	1 to 2 kHz	~100 Hz
Position	0.5 to 1 kHz	~10 to 20 Hz

An outer loop has to be 5 to 10 times slower than the loop inside it, so that it can be designed as if the inner loop has already reached its target.

Tuning order

Current loop: calculate the PI gains from the motor's R and L (pole-zero cancellation: Kp = L·ωc, Ki = R·ωc) and check the iq step response
Speed loop: initial values from the inertia J and Kt, then adjust under load
Position loop: a single P (+ speed feedforward) is usually enough

3D labRun what you have read so far→

Feedforward

If you know the target speed or acceleration, add the corresponding output in advance. Feedback then handles only the remaining error, which greatly reduces the tracking error.

Practical points

Put a limit on each loop's output (maximum current, maximum speed). Handle them together so the inner limit does not wind up the outer loop's integrator
Noise in the speed calculation limits the speed-loop gain. Encoder resolution and the speed filter decide the performance
This is where control engineering, firmware and power electronics meet inside one piece of code