Since we tend to learn by examples and we can all relate to the challenges of parenting, I came up with the following discussion of the relative advantages of PID and model predictive control (MPC) of a teenager for my Control Talk column in the September issue of Control Magazine.
Would Proportional-Integral-Derivative (PID) or Model Predict Control (MPC) be better as a parental advisory control algorithm? The PID excels at handling the unknown upsets, non-stationary behavior, and unpredictable nature of a teenager’s response and derivative action provides some preemptive action. However, the abrupt action by PID could amplify noise in a teenager’s behavior. But then there is the dead band from backlash and the resolution limit from friction. Maybe a lot of dither from the PID could keep the teenager off balance and minimize inaction if it doesn’t wear you out. There is inverse response to contend with where the teenager starts out doing the opposite of what was requested. Theoretically, MPC could build this behavior into its knowledge of the teenager’s future trajectory. Also, the patience of a MPC is inline with modern parenting ideas. But I not sure your can do enough pseudo random binary sequences (PRBS) or know the time to steady state of a teenager so my initial thought is proportional plus derivative (PD) with an adjustable bias to deal with the potentially unstable response. But then what do I really know anymore? I am an empty nester heading out for one of many vacations without children. All I need to know now is how to enjoy the antics of grandchildren and quickly return them to their rightful owner for process control.