Before attempting to make the line follower itself proportional, we completed a variety of mini-projects in class to introduce us to the idea of proportional controls, and the under, over, and critical damping that comes with them.
We learned that damping reduces the size of the oscillations that occur in a system. Therefore, when a system is under-damped, it reaches its target with a velocity that is too high and experiences many large, overcompensating oscillations as the system keeps over-correcting itself as it tries to reach its target. The higher the system’s gain, the more out of control and under-damped its oscillations will be. When a system is over-damped, it decelerates too slowly, and therefore reaches its target too slowly, or not at all. A critically damped system reaches its goal as efficiently as possible, decelerating appropriately, so that the system’s velocity when it reaches its goal will require few and small oscillations, if any. We learned that fiddling with the gain affects how damped a system is, since it dictates how much the system will react to a certain change in error.
To learn about these principles, we made:
1. A 90 degree rotator
The goal of this mini-project was to have our motor rotate exactly 90 degrees, we found that a gain of 2 generally allowed this to happen. With a higher gain, the system overshot with large oscillations, and with a lower gain the system undershot 90 degrees.
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| Rotating arm program: gain (2), optimal rotation (90) |
In action:
2. Rotating control wheel
The goal of this mini-project was to create a system in which the motion of one motor was mirrored by the other. In this case, changing the gain affected the speed with which the mirroring motor (gray Lego part) mimicked the movement of the original motor (wheel), and the oscillations it went through after its initial movement.
In action:
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