Equivalence Among Flat Filters, Dirty Derivative-Based PID Controllers, ADRC, and Integral Reconstructor-Based Sliding Mode Control

We explore the equivalence among flat filters, dirty derivative-based proportional integral derivative (PID) controllers, active disturbance rejection control, and integral reconstructor-based sliding mode control, in the context of SISO second-order, perturbed, pure integration systems. This is the prevailing paradigmatic class of differentially flat systems or feedback linearizable systems. The equivalence is valid beyond the second-order pure...