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

From PID to ADRC and back: expressing error-based active disturbance rejection control schemes as standard industrial 1DOF and 2DOF controllers