Here is a semester project in the 2012 Mechatronic control systems engineering module at San Jose State University. This is a Proportional-Integral-Derivative controlled (PID), 6 degree of freedom (6-DOF) Stewart platform, which basically means it has six axes on the top plate. This prototype uses 6 radio controlled servo motors instead of the traditional use of hydraulic jacks or electronic actuators. (this video has sound)
A PID controller continuously calculates an error value as the difference between a measured process variable and a desired setpoint. The controller attempts to minimize the error over time by adjustment of a control variable, such as the position of a set of servo motors or actuators, to a new value, given by a weighted sum:
where Kp ,Ki , and Kd, all non-negative, denote the coefficients for the proportional, integral, and derivative terms, respectively (sometimes denoted P, I, and D).
- P accounts for present values of the error , and is determined by the direction and magnitude the correction needs to be applied (e.g. if the error is large and positive, the control variable will be large and negative),
- I accounts for past values of the error (e.g. if the output is not sufficient to reduce the size of the error, the control variable will accumulate over time, causing the controller to apply a stronger action through P), and
- D accounts for possible future values of the error, based on its current rate of change. This part determines when and at what rate it needs to reduce the magnitude of its action, e.g as the ball fast approaches the desired set point at the centre of the plate.