Phase current control

Controlability

The controller uses PWM modulation (fast switching of the transistors in various configurations) to generate the desired current in the inductor. The following picture depicts the typical current waveform of a PWM-fed inductor:

For current control to work properly, certain system conditions must be met. Most importantly, the motor inductance plays a crucial role. The rate of current change is directly determined by the inductance and DC voltage according to the following equation:

$\Delta I = \frac{1}{L} \int dU dt$

If we substitute $dU$ with the difference between link voltage and the actual back-EMF, and $dt$ with the duration of 50 microseconds (representing one PWM cycle), we can infer that the saw wave amplitude of the inductor current during a single cycle may be high enough to overshoot the measurement range and trigger short circuit protection. In such a case, we consider the motor to be uncontrollable. The solution is either:

• to minimize the voltage difference (reduce control error with fine-tuning of the PID loops and the REST algorithm).
• to increase the switching frequency. Switching frequency is fixed for the ESCx families. Please contact us for custom solution.
• to increase inductance (motor redesign with different winding or magnetic material).

It's also important to note that motor inductance is not constant; it tends to decrease as current increases, particularly as the magnetic circuit approaches saturation. This is a common issue with, for example, outrunner motors that lack sufficient magnetic material and reach saturation quickly. In these cases, the motor may become uncontrollable above a certain current threshold.

tip

• To check the dependency of inductance to the motor current, you can use the identsat procedure.

Another critical condition to consider is the impedance of the DC supply, typically a battery. For instance, if the DC resistance is significantly higher than the AC resistance, the control loop may encounter problems. This discrepancy can lead to higher current ripples, which may reduce the lifespan of the electrolytic capacitors and potentially induce hazardous states in the system. The mismatch between DC and AC impedance can compromise the stability and safety of the control system, making it essential to properly account for these characteristics in the design and implementation of the motor control system.

PID

The PID controllers are responsible for adjusting the voltages so that the target current is reached. In BLDC, only a single (scalar) current is treated, whereas in FOC, both torque (Q) and direct (D) axes are controlled separately.

info

• Hereby specified variables are located in the folder /driver/pid_iq resp. /driver/pid_id (VECTOR). From driver 6, the BLDC folders are named /driver/pid_current resp. /driver/pid_compl - see BLDC.
• The PID is abbreviation of 'Proportional-Integral-Derivative' closed loop regulation.
• In the current control loop, only the P- and I- terms are used.

VECTOR

• Q axis: Torque-generating axis
• D axis: Flux-generating axis

BLDC

From driver 6, the BLDC folders have their own names, because their values cannot be copied from VECTOR to BLDC (see the warning below). The different names prevent such a copy by mistake. Up to driver 5, they are named pid_iq and pid_id as in VECTOR.

BLDC folder (from driver 6)	Name up to driver 5	Purpose
pid_current	pid_iq	The (scalar) motor current loop.
pid_compl	pid_id	Complementary axis, for the identification procedures only.

• BLDC algorithm uses only parameters from pid_current.
• Parameters from pid_compl are not used during motor control. It is presented only for the embedded identification procedures (identlin, identrun, ...). Therefore, changing its parameter will not affect motor control performance.

warning

The gains are not interchangeable between VECTOR and BLDC. Do not copy the pid_iq / pid_id values of a VECTOR configuration (e.g. those identified by identlin) into pid_current / pid_compl, and vice versa.

info

In BLDC we recommend to keep the P-coefficient at zero (default), since the loop is not designated to correct fast current fluctuations commonly present in block commutation.

Parameters

In VECTOR, parameters and settings for both pid_iq and pid_id can be set independently, but typically there is little reason to keep the axes dynamics different. Usually, the lower the motor inductance, the lower the P and I value should be, and vice versa. Those parameters can be auto-identified with identlin procedure (from ESCx 5.0). In BLDC, identlin does not change the gains by default.

Parameter	Description
P	Proportional term in the PID loop.
I	Integral term in the PID loop.

dcr (from ESCx 5.0)

This parameter defines the coupling between DC link voltage and PID output scaling. The higher the number, the more the input voltage fluctuation is compensated, but also the more the DC ripple current and potential oscillation is pronounced.

Peak current limiting

PID controllers alone may not react quickly enough to meet demanding performance requirements or to handle emergency situations like short circuits. Therefore, the phase current is additionally hard-limited at ipeak by a fast protective mechanism. It resolves current overshoots immediately and prevents hazardous outcomes in emergency situations, while the PID loop maintains efficient operation under normal conditions.

The following picture illustrates the current waveform behavior respective to ipeak and iref under typical circumstances on a single motor phase: