PID Controllers & Underactuation:
There are many applications for which exact equilibriums need to be kept. An altitude controller on an airplane set to 10-thousand feet, for example, should not oscillate between 9-thousand and 11-thousand feet for an average altitude of 10-thousand feet. The controller should instead modulate the pitch of the airplane such that the plane is always near 10-thousand feet with little oscillation. This is where PID controllers are needed. They keep an output stable by considering where a system is, where it has been, and where it's going. These data points are calculated by taking the proportionate, integral, and derivative of a system's error function, the error function e(t) being the difference between the system's actual state and desired state at time t. I and my teammates tried to implement a PID controller onto a cart to keep an inverted pendulum balanced. The pendulum cart is one of the canonical underactuated robots, making this project a sort of update to my acrobot.
Picture of Assembled Cart
The Result:
Below are some diagrams of the cart construction. The cart was designed with serious time constraints (about 1 week start to finish) and resultantly lacks aesthetic appeal.
Cart Diagram & Assembled Cart Images
Below are the test videos of the cart. The video on the left shows the maiden drive of the cart with only the proportionate controller working. The video on the right shows the cart with a full PID controller working. The cart had some inherent limitations as the wheels had fairly low friction, causing them to slightly slip at any moderate torque. This is part of the reason for the heavy drill battery -- increasing friction with the ground. The full PID controller is nonetheless much better than the P-controller, as is evident in the videos.