In my essay, I was using volition mostly as just a synonym for choice-making. So, it makes choices on which direction to push the pendulum. But maybe you are asking whether the PID controller “owns” the choices it makes? I would say it owns them more than a PID controller tuned by a human owns its choices, but less than a human owns his/her own choices. The human, after all, can modify how he/she goes about learning in the first place, while the PID controller you have described cannot modify its tuning algorithm.
In my essay, I was using volition mostly as just a synonym for choice-making. So, it makes choices on which direction to push the pendulum. But maybe you are asking whether the PID controller “owns” the choices it makes? I would say it owns them more than a PID controller tuned by a human owns its choices, but less than a human owns his/her own choices. The human, after all, can modify how he/she goes about learning in the first place, while the PID controller you have described cannot modify its tuning algorithm.