### Proportional Integral Derivative (PID)

IMC Tuning Correlations. The most common tuning correlation for PID control is the IMC (Internal Model Control) rules. IMC is an extension of lambda tuning by accounting for time delay. The parameters `K_c`, `tau_p`, and `theta_p` are obtained by fitting dynamic input and output data to a first-order plus dead-time (FOPDT) model. $$mat{Aggressive,Tuning:} quad tau_c = max left( 0.1 ...