Mathematical Modelling of DC Motor

We require a set of parameters and presumptions to model a DC motor mathematically. I can help you through the process of developing a mathematical model for a DC motor even if I am unable to directly access external websites like "https://technicalmujtaba95.blogspot.com". Let's move on with the presumptions and essential variables.

Assumptions:

Stable-state conditions are present for the motor's operation.

The field and armature windings are ideal conductors.

The core is not magnetically saturated.

There are no losses from friction or windage.

Parameters:

Armature resistance: R

Armature inductance: L

Armature voltage: Va

Back EMF: E

Armature current: Ia

Motor torque: T

Motor speed: ω

To begin the modeling, we'll consider the electrical equations of the motor:

Kirchhoff's voltage law (KVL) for the armature circuit:

Va - Ia * R - E = 0

The back EMF is proportional to the motor speed:

E = Kω

Torque is proportional to the armature current:

T = Kt * Ia

The mechanical equation relating torque and speed:

T = J * (dω/dt)

In these equations, K is a constant, J represents the moment of inertia of the rotor, and Kt is the torque constant.

Now, let's combine the equations and introduce the differential equations:

Va - Ia * R - Kω = 0 (from KVL)

E = Kω (back EMF)

T = Kt * Ia (torque)

T = J * (dω/dt) (mechanical equation)

Differentiating the back EMF equation with respect to time:

dE/dt = K * dω/dt

Substituting the back EMF equation into the KVL equation:

Va - Ia * R - K * ω = 0

Now, we can write the complete set of differential equations for the DC motor:

Va - Ia * R - K * ω = 0 (1)

E = Kω (2)

T = Kt * Ia (3)

T = J * (dω/dt) (4)

By solving these equations simultaneously, you can obtain the dynamic behavior of the DC motor.

It should be noted that the aforementioned modelling strategy relies on a straightforward DC motor and ignores intricate phenomena like magnetic saturation, armature response, and other losses. For more precise predictions, other parameters may need to be included to the model depending on the particular motor and its properties.