## Tuesday, November 22, 2011

### Understanding the DC Motor Part III

In this part, simulations for the permanent magnet DC motor will be shown. Several cases will be given to show the nature of the DC motor and how they act. Although simulation can give a good representation of the motor, the simulation will not be exactly like the real motor because of modelling error and unmodeled dynamics.

Modelling error and Unmodeled Dynamics

Quick fact about modelling error and unmodeled dynamics. Modelling error is when the parameters in the simulation is not exactly like the real motor for example motor resistance. Maybe one could measure the resistance but the value is prone to error due to measurements error. Secondly, the unmodeled dynamics. Although the model can be derived from first principle, surely there are some "things" that cannot be expected from the motor. Maybe there are some imperfection in the motor that causes the motor cannot turn correctly. This is when the order of the motor increases.

Simulation Model

Moving on, the simulation was done in simulink using a model by Roger Asenstrup.
The motor parameters used in this simulation is the original value in the motor model (except for the damping friction).

Resistance: 2.06 Ohm
Inductance: 0.238 mH
Back EMF Constant: 1/((406*2*pi)/60)
Torque Constant: 0.0235 Nm/A
Rotoe Inertia: 1.07e-6

Of course this value is not exactly the same for all motors. Each motors has their own parameters. Also to explain, the motor current, motor speed and motor position were plotted.

Simulation Cases

Three cases will be shown:
1) The normal situation for a motor
2) If there is not friction
3) If the load is very big (heavy)

Case 1: Normal situation
 Case 1 plot

 Case 1 plot (zoomed)
In a normal situation, a motor will work like so: The applied voltage will cause a surge in motor current. It will increase with a decay due to the motor inductance. As soon as the motor current causes the motor to rotate, the back EMF will reduce the current to the motor. In the end, the motor will move in a constant speed (as long as the applied voltage is constant). Note that there is a constant value in the motor current (This will be explain in the second case).

Case 2: Zero Friction
 Case 2 plot

 Case 2 plot (zoomed)
In the second case, the damping value in the simulation was reduced to zero. The applied voltage will cause the surge in motor current. After the motor current causes the motor to rotate, the back EMF will reduce the motor current to zero. Due to zero friction, the motor need not have any torque to keep it moving (Newton's First Law of Motion). In other words, in a motor with friction, the current is actually used to counter the friction.

Case 3: Heavy Load / Stalled
 Case 3 plot
The value of damping is 12e-5 but the value of inertia is 1.07. In the case of stalled motor, the applied voltage will cause the motor current to surge, then the value will not reduce due to no back EMF present (The motor cannot move because it is stalled). This is when care should be taken to the motor driver design. If the driver cannot withstand high continuous current, the drive will burn.

Concluding Remarks

Now, we have known the motor nature, more or less but note that all this simulation was done in open loop configuration. Let's say 1 V will cause the motor to move in certain velocity, changing the motor load will change the velocity. In the next part, let's move into motor control using proportional, integral and derivative controller.

p/s: Please click on the pictures to enlarge.

Check out the full series

Part I
Part II
Part III
Part II, III - Interlude
Part IV