Can I map a torque input to a braking pressure?

I am studying the eATV model proposed by MathWorks (https://it.mathworks.com/matlabcentral/fileexchange/81623-electric-vehicle-powered-by-bldc-motor), but I am stuck trying to understand the relationship they have imposed:

Does power not require angular velocity in rad/s?

Where do the gains -0.01 and 1 in the transformation come from?

I am trying to mathematically characterize the relationship but I am unable to do so.

Furthermore, in PS-Simulink towards the brake pedal, they use N/m^2 and not bar as expected by the input block (https://it.mathworks.com/help/sdl/ref/discbrake.html#:~:text=Physical%20signal%20port%20associated%20with%20cylinder%20pressure%2C%20in%20bars.).

Thank you all so much.

Answer 1

[Sam Chak]

Hi @Leonardo

I cannot provide the physical explanation of how the student author derived the model. Mathematically, the 1st-order transfer function’s output requires approximately time units to rise from 0 and converge to A, where A is the response amplitude (steady state).

v   = 30;               % wheel speed in RPM
Tr  = -10;              % brake torque requirement
A   = v*Tr*(-0.01)*1;   % Amplitude (steady state value of brake pressure)
s   = tf('s');
tau = 0.1;
G   = A/(tau*s + 1)

G =
 
      3
  ---------
  0.1 s + 1
 
Continuous-time transfer function.

step(G, 1), grid on
xline(0.5, '--')

●

Despite the physical signal port of the Disk Brake measuring brake pressure in bars, the Simscape unit manager can automatically verify units within a physical network and perform the necessary conversions, provided the user correctly specifies the incoming signal unit (N/m^2, i.e., pascal, Pa).

[Leonardo]

Thank you so much for your reply. I had assumed the first-order FDT referred to a hypothetical delay to simulate braking, however, the lack of a direct relationship between power and pressure led me to map the input torque as a normalized value and calculate the maximum theoretical pressure applicable to my wheels using the tire's dynamic friction coefficient. This is how I solved the problem.