On transfer function representation and frequency response of linear Active Disturbance Rejection Control

The algebraic relationship between the transfer function and the state space representations of Linear Active Disturbance Rejection Control (LADRC) is derived, upon which the unique frequency response characteristics of LADRC can be seen and understood. The transfer function form of LADRC for arbitrary order plant is derived from its state space representation and this allows that the open loop frequency characteristics of the LADRC based control system to be conveniently obtained and analyzed. The frequency response of LADRC not only shows excellent loop gain shape but also validates the original ADRC design concept: that the internal and external disturbances can be estimated in real time and cancelled. This time, the evidence comes not from simulation, or test, or time-domain analysis, but in the language of practicing engineers: frequency response.