This following model in Simulink is used to simulate the hyperloop pod.
The model takes in an input force from a PID controller and outputs the following:
- The force exerted on the pod
- The acceleration of the pod
- The velocity of the pod
- The position of the pod
The plant was put in the following model, to tune a continous parallel PID controller:
These were the plant parameters:
| Parameter | Value |
|---|---|
| Maximum Possible Magnetic Force | 55 N |
| Minimum Possible Magnetic Force | 0 N |
| Pod Mass | 5 kg |
| Initial Height | 0 m |
| Simulation Time | 0.5 s |
These were the tuned PID values:
| Parameter | Value |
|---|---|
| Proportional Gain ( Kp ) | 58024.7697722311 |
| Integral Gain ( Ki ) | 679104.182905479 |
| Derivative Gain ( Kd ) | 1217.40122699774 |
| Filter Coefficient ( N ) | 1363.49256355405 |
The sytem was simulated for the time outlined above. The PID controller outputed the following in Newtons:
The plant limited the PID output based on the magnetic force capabilities outlined above to the following graph (N):
This lead to the total acceleration on the pod (ms-2):
The velocity of the pod over this period was (ms-1):
This graph shows the position of the pod over the simulation period, with the blue line at the set point of 5 mm.
Note the y axis is on the scale of 10-3 meters
The previously found tuned gains worked well in a discrete PID controller with a sample time of 3.27 * 10-4 s (sample time found experimentally on a SB-Freeduino).