What system of ODE's does Simscape Electrical's DC Motor Block use?

I've been having trouble getting the DC Motor block's results for current and rotational velocity to match what I obtain when using coupled differential equations in an ODE45 script. The results are very far apart and I'm not sure what is causing this.

The systems of equations I've implemented in ODE45 is standard in the DC motor literature, and is as follows:

Where I is the current (A), L is the armature inductance (H), R is the armature resistance (Ω), is the motor electrical constant (), is the voltage of the constant voltage source (V), J is the armature's mass moment of inertia (), is the motor's torque constant (), and b is the motor damping ().

However, I've noticed that in the DC Motor block documentation, the equation for torque across the motor is given as (where λ is the damping constant). When I add the first term into my differential equation model, the results of ODE45 and Simscape Electrical become very close. I assume that this is the set of equations that Simscape is using, but I don't like to use equations without understanding them. Where does this added term come from? I don't believe I've seen it in the literature.

I've attached plots showing current and rotational velocity of the motor for the three models, so that you can see the discrepancies. (Note that there is zero damping in any of the models, yet only the classical differential equation model shows a rising angular velocity -- the other models eventually reach some steady-state non-zero angular velocity.)

Any insight into what is happening here would be appreciated.

Answer 1

[Sam Chak]

Because and , therefore .

Note that you already have the term in your differential equation .

[Michael P]

Okay, I see. In that case, I should not be using this in my differential equation model, correct? Also, this equality only holds at steady-state (since i(t) is an exponential in general)?

Any ideas on where the discrepancy between the standard differential equation model and the Simscape model might come from?

[Sam Chak]

Hi Michael,

Could you show the MATLAB code for the Classic Differential Equations model?

[Michael P]

Hi Sam,

Sorry for the late response. It turns out that my problem was caused by an incorrect unit conversion. After correctly performing the unit converison, the Simscape model exactly matched the differential equation model using ODE45.

Thanks.