Table 1.

Active inference as a general framework for PID controllers.

Criterion	Mapped to	Advantages in Active Inference
Load disturbance response	${\mu }_{{\pi }_{\tilde{z}}}$	Intuitively expressed via the expected inverse variance of the observations (i.e., precision), with low variance implying a fast response and vice versa (see Section 4.2 and Section 4.3)
Set-point change response	${\mu }_{{\pi }_{\tilde{w}}}$	Natural formulation of PID controllers with two degrees of freedom derived from sensory and process precisions and expressed as a Bayesian inference process (see Section 4.2)
Measurement noise response	${\mu }_{{\pi }_{\tilde{z}}}$	Straightforward interpretation of PID gains as (expected) inverse variances of different embedding orders of measurement noise (see Appendix B)
Robustness to model uncertainty	${\mu }_{{\pi }_{\tilde{w}}}$	Direct mapping of model uncertainty to expected variances of the fluctuations, representing unknown dynamics, of the system to control (see Appendix B)