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.
Moving on, the simulation was done in simulink using a model by Roger Asenstrup.
|Model in Simulink|
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
Mechanical Damping: 12e-5 Nms/rad
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.
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)|
Case 2: Zero Friction
|Case 2 plot|
|Case 2 plot (zoomed)|
Case 3: Heavy Load / Stalled
|Case 3 plot|
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 II, III - Interlude