Bi-directional PID control

Question

I am currently a Mechanical engineering student and I am trying to create a device that will balance two weights by moving the fulcrum between them. The whole thing looks like a see-saw with a motor and gyroscope attached, mostly because that's exactly what it is.

The problem I am having is getting the motor to move the board to place its center of mass above the motor in order to balance the load. The motor has a large gear on it that meshes with a linear gear across the bottom of the board. I am using an arduino mega to control a Spark motor controller using PWM. My first idea was to simply measure the angle from the gyro(between -4 and 4 degrees) and activate the motor whenever it did not read 0 degrees(level). This threw the board off of the motor. Later I decided that a PID loop would be a better solution. I wanted to have something like this video shows. https://www.youtube.com/watch?v=fusr9eTceEo The problem is that as far as I know, PID only works in one direction. A gas pedal in a car is a good example because the PID loop can only give more or less gas and cannot hit the brake pedal. In my case I need two PID loops in order to control the position both left and right. Currently I am running the two loops side by side using the Arduino library with the angle as the input and the motor power as the output. I take the difference between the outputs and the resulting positive or negative value goes to the motor. I really don't think this is the right way to do this as I still cannot even balance the board itself. What do I need to do in order get the right motion?

Answer 1

There's nothing about a PID loop that restricts it to positive values. The inability to use negative numbers is a limitation of the throttle, not the PID controller. Try the math.

$$ u(t) = K_p e(t) + K_i \int_0^t e(\tau)d\tau + K_d {de(t) \over dt}$$

• \$e(t)\$ is the error at time \$t\$.
• \$u(t)\$ is the control value, the input to the motor controller.
• \$K_p\$, \$K_i\$, and \$K_d\$ are the coefficients, which you adjust to get the response you want from the PID controller.

Say we define "0" to be level, positive values tipping to the right, and negative values tipping to the left. The goal is to come up with some input to the motor controller \$u(t)\$ that makes the tip \$e(t)\$ zero.

A zero \$u(t)\$ means the motor isn't driven at all. A positive \$u(t)\$ drives the motor to shift the fulcrum right, whereas a negative \$u(t)\$ does the opposite.

To keep things simple let's say \$K_p = K_i = 1\$, and \$K_d = 0\$.

Lay it's tipping left. That means \$e(t)\$ is negative. \$K_p e(t)\$ is then negative, and \$ K_i \int e(t)dt \$ is decreasing, and will become negative if it isn't already. We'll ignore the derivative term because you might not need it.

Thus, \$u(t)\$ is negative or is tending towards negative, which will shift the fulcrum to the left.

Answer 2

Chris is correct and PID commonly operate to give positive and negative outputs - even your car cruise control example is out of data, modern radar controlled cruise controls can indeed operate the brakes as well as the throttle. A more general example is called a servo. Small scale ones are used for models.

Here is another example of an Arduino using a PID loop to balance a beam in a different way:

Beam balancing example