A Generalized PID Interpretation for High-Order LADRC and Cascade LADRC for Servo Systems

It is well known that proportional-integral-derivative (PID) controllers are dominant in industrial scenarios. PID with high-order derivative or integral terms named generalized PID is superior to the PID. However, there is little literature investigating how to tune the parameters of the generalized PID to enhance the disturbance rejection ability. Toward that end, this article illustrates that the cascade controllers based on the first-order linear active disturbance rejection controllers (LADRCs) (cascade LADRCs) and high-order LADRCs can be interpreted as the generalized PID with low-pass filters for speed servo systems and position servo systems, which in turn is an alternative method to realize the generalized PID. Moreover, the differences between the high-order LADRC and cascade LADRCs are the generalized integral terms, which can be quantified by integral time multiplied absolute error. The proposed LADRC controllers are verified and compared with the current controllers by simulations in MATLAB/Simulink. Finally, one experimental example of the LADRC controllers is implemented on the position servo dc motor system platform.