Jonathan Scott said:
I associate "porpoising" with the undulating motion of a servo which is supposed to be in a specific position but the feedback mechanism has sufficient delay in it to cause overshoot.
Close enough!
Specifically, I was going for the sinusoidal oscillation that results in some process value for a system, when the proportional term is set too high in a PID [proportional-integral-derivative] loop or controller, for motion and other applications. It could refer to oscillations in pressure, temp, position, speed, solution strength, flow rate, or any variable in a dynamic system controlled with this type of algorithm, which in industry is pretty much any dynamic system where a set point value must be maintained. One common PID equation used is
where
K_p: Proportional gain, a tuning parameter
K_i: Integral gain, a tuning parameterK_
d: Derivative gain, a tuning parametere:
e: Error = SP - PV [set point - process value]
t: Time or instantaneous time (the present)
tau: Variable of integration; takes on values from time 0 to the present t.
http://en.wikipedia.org/wiki/PID_controller
A subject close to my own heart, the thing that sent me on the path to self-employment was a custom PID equation and algorithm that I wrote for a difficult problem. I also found an error in the Rockwell PID algorithm used in some of their industrial computers, so there is a firmware revision out their with my name on it [literally].
But you are correct that a number of problems can result in porpoising of the process value. And one that is often missed [that has made me a good bit of money in correcting] is not properly allowing for or calculating the feedback time. The PID loop update times are too short and are responding to data that you haven't actually received yet, so you continually get overshoots. So your example is a particularly good one.
Just fyi, another cause can be "windup" in the integral term, where either startup or some deviation in the normal process, or an abrupt change, can cause the value of the integral term to windup [continually add], causing a long delay in the recovery. This in turn can result in windup in other direction, which leads to long-term oscillations. Most controllers now come with anti-windup features but they still have to enabled, or some escape routine added to the code to prevent this if you're writing your own routine. Often you can just set a limit for the max/min value of the integral term.
