# Can't figure out this PMDC motor model

I was going through a series of experiments on PMDC motor where I found out the following block diagram representing the system:

I'm new to this field and I'm trying to get a little ahead of my college studies but I got stuck on this diagram as I don't know what represents what in this diagram. I have a bit idea on PWM waves, duty cycle, H-bridge, DC motors, etc. Can you please give some ideas how to deal with this?

• Please provide a link to the source from which you have taken this diagram. Please edit into the question the descriptions of all symbols used so that no guessing is required from our part. Please also mention what it is that you did not understand and what you did understand from reading the source material.
– AJN
Jul 6 at 13:00
• You haven't provided what you do understand. PWM, H-bridge, and duty-cycle have nothing to do with what you've provided.
– john
Jul 6 at 13:23

This model that you are showing is using voltage to control motor speed. The model is broken up into two transfer functions.

The left most transfer function is your electrical dynamics consisting of $$\L\$$ coil inductance {H}, $$\R\$$ coil resistance {Ohms}. The electrical dynamics convert Voltage (input) -> Current (output). Current is converted to motor torque using $$\K_t\$$ torque constant {Nm/A}.

The summation of the motor torque $$\T\$$ with a disturbance torque (or load torque) $$\T_L\$$ is typically modeled like this. This allows for you to easy apply step disturbances to your controller and see how the controller responds. Note that any time you have a torque disturbance, you will need an integrator to reject error.

The right side transfer function is your mechanical dynamics consisting of $$\J\$$ rotational inertia {kgm^2} and $$\B\$$ rotational friction {Nms/rad}. Note that the rotational inertia consists of all the inertias connected to the motor. Similarly the rotational friction consists of all frictional elements combined. This transfer function converts torque (input) -> speed (output)

What you're seeing is a very common model for a PM DC motor, except for TL(s). I don't know what it is but it should be explained elsewhere in your course material. You seem to be taking a course in control systems, and looking ahead. Looking too far, I think. You certainly know what "R","L","I","V" mean. "w", in this case, is the angular velocity of the motor, not the frequency of an output electrical signal, which might be why you're confused. "T" is torque. "J" is the moment of inertia of the motor and its load. "B" is the viscous friction of the motor and load. Kt is a constant for the motor in newton-meters per ampere. Kb is the back EMF constant for the motor in volt-seconds per radian. Knowing that, it's all algebra to come up with the result. Note that La doesn't appear in the solution. It must be considered negligible.

• TL(s) is a torque disturbance acting on the motor's shaft. Jul 7 at 4:07

The diagram is called the block transfer function for the system where the system includes the PMDC motor and the equivalent mechanical load. The equivalent mechanical load is the load as "seen by" the motor shaft either directly or reflected through a gearbox or driveline. This 10 minute video shows the derivation of the block diagram transfer function for a motor with equivalent mechanical load:

https://youtu.be/cDCvJtaG9m4

The transfer function can be expressed in block diagram form where the top path is the feedforward path and the bottom path is the feedback path for the system. The feedforward path is wherein electrical input current in the armature converts to mechanical output torque across the air gap. The feedback path is wherein the angular speed of the motor shaft induces back-emf voltage in the generating coils of the motor windings. Integration in the time domain is expressed as 1/s via the Laplace transform.

If the load has a non-inertial torque, for example a car driving uphill experiences a load torque due to the force of gravity translated through the driveline, then this would be given by the input marked TL(s) in the diagram. The variable "s" is the Laplace operator. The other variables are typical notations for the system parameters as described in derivations of the transfer function.