The practical industrial approach is somehow different. The last controller is the current controller in the cascade.

^{simulate this circuit – Schematic created using CircuitLab}

Have a look here:

Brushless motor dynamics (BLDC transfer function)?

DC motor differential equation

The practical industrial approach is somehow different. The last controller is the current controller in the cascade.

^{simulate this circuit – Schematic created using CircuitLab}

Have a look here:

Brushless motor dynamics (BLDC transfer function)?

DC motor differential equation

What you want is a kind of sticky constant, but this would turn the system to be non-linear, then there is not such way of doing Laplace, since Laplace is a mathematical description of the linear system.

The practical industrial approach is somehow different. The last controller is the current controller in the cascade.

^{simulate this circuit – Schematic created using CircuitLab}

The practical industrial approach is somehow different. The last controller is the current controller in the cascade.

^{simulate this circuit – Schematic created using CircuitLab}

Have a look here:

Brushless motor dynamics (BLDC transfer function)?

DC motor differential equation