  In this paper, we uncover a new connection between standard PI/PID
controllers and active disturbance rejection control (ADRC), from which we
establish formal conditions of equivalence between the two control schemes.
Using the equivalence, we devise a step-by-step procedure of transitioning from
PI/PID to error-based ADRC. We also show how to go from 1DOF to 2DOF ADRC while
retaining a standard 2DOF PI/PID structure. Both procedures facilitate
expressing error-based ADRC schemes as standard industrial 1DOF and 2DOF
controllers. This allows the designed controller to have the desired
characteristic of ADRC (i.e. strong robustness against internal and external
uncertainties) while still being expressed in a form that is familiar to
industrial practitioners, where PI/PID structures are still the workhorse of
modern control systems. The results of the paper ensure backward compatibility
of future ADRC-based solutions and foster the adoption of active disturbance
rejection-based methods in industrial practice as a viable alternative to
standard controllers. To further support the findings, a set of tests is
conducted in time and frequency domain, followed by a comparative analysis in
FPGA-in-the-loop simulation utilizing a realistic plant model.
