Active disturbance rejection control

Active disturbance rejection control[1][2] (or ADRC) inherits from proportional integral derivative (PID) control. It embraces the power of nonlinear feedback. It is a robust control method that is based on extension of the system model with an additional and fictitious state variable representing everything that the user does not include in the mathematical description of the base system to be controlled. This virtual state (sum of internal and external disturbances, usually denoted as a "total disturbance") is estimated online with a state eyewitness and used in the control signal in order to decouple the system from the actual perturbation acting on the plant. This disturbance rejection feature allows users to treat the considered system with a simpler model insofar as the negative effects of modeling uncertainty are compensated in real time. As a result, the operator does not need a precise analytical description of the base system; one can model the unknown parts of the dynamics as internal disturbances in the base system. This method's robustness and adaptivity suit scenarios in which full knowledge of the system is not available.

Component

Tracking differentiator

A tracking differentiator solves the trade off between Rapidity and Overstrike and improves a controller's anti-noise ability. The convergence of ADRC is proved by Guo and his students.[3][4]

Extended state observer

The classical observer is only concerned with the status of the system. An extended state observer (ESO) keeps track of the system's status as well as external disturbances. It can also estimate an unknown model's perturbation. As a result, ADRC does not rely on any particular mathematical model of disturbance. Nonlinear ESO (NESO) is a subtype of general ESO that uses a nonlinear discontinuous function of the output estimate error. NESO are comparable to sliding mode observers in that both use a nonlinear function of output estimation error (rather than a linear function as in linear, high gain, and extended observers). A sliding mode observer's discontinuity is at the origin, but the NESO's discontinuity is at a preset error threshold.

Nonlinear PID

PID control is successful because of error feedback. Because ADRC employs nonlinear state error feedback, Han[5] refers to it as Nonlinear PID. Weighted state errors can also be used as feedback in a linearization system.

References
  1. CACT Archived 2015-04-12 at the Wayback Machine, Center for Advanced Control Technologies, Cleveland State University, USA.
  2. , Han J. From PID to active disturbance rejection control[J]. IEEE transactions on Industrial Electronics, 2009, 56(3): 900-906.
  3. , Guo, Bao-Zhu, and Zhi-Liang Zhao. "On convergence of tracking differentiator." International Journal of Control 84.4 (2011): 693-701.
  4. , Guo B Z, Zhao Z L. On convergence of the nonlinear active disturbance rejection control for MIMO systems[J]. SIAM Journal on Control and Optimization, 2013, 51(2): 1727-1757.
  5. Han, Jingqing (March 2009). "From PID to Active Disturbance Rejection Control". IEEE Transactions on Industrial Electronics. 56 (3): 900–906. doi:10.1109/TIE.2008.2011621. ISSN 1557-9948. S2CID 206698917.
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