Abstract
This paper investigates linear active disturbance rejection control (ADRC) for processes with time delay. In the past years several modified active disturbance rejection control methods, including Smith predictor based ADRC (SP-ADRC), predictor observer based ADRC (PO-ADRC) and delayed designed ADRC (DD-ADRC) have been proposed to tackle systems with time delay. In this paper it is shown that these modified ADRCs can be interpreted in the framework of a two-degree-of-freedom (TDOF) internal model control (IMC), so the analysis and design can all be done via the well-known IMC framework. With the aid of the TDOF-IMC framework, the three modified ADRCs are compared and some interesting conclusions are drawn. Analysis and simulation results show that PO-ADRC structure is the best delay compensation structure among the three methods. However, the overall performance of the three methods will also depend on the tuned parameters, and the robustness measure is helpful in tuning the parameters to achieve compromise in performance.
Highlights
Time delay exists widely in industrial processes
Analysis and simulation results show that predictor observer (PO)-active disturbance rejection control (ADRC) structure has the same structure as Smith predictor based ADRC (SP-ADRC) but with a more sophistic predictor, and has the same structure as designed ADRC (DD-ADRC) but with a predicted-state feedback control, it is the best delay compensation structure among the three methods
5) Originally predictor observer based ADRC (PO-ADRC) adopts the same extended state observer (ESO) as DD-ADRC but uses the predicted extended states in the state feedback, so it is expected to achieve better performance than DD-ADRC if the same model information is used in controller design and the controller gain Ko and observer gain Lo are the same
Summary
Time delay exists widely in industrial processes. Due to the existence of delay, the controlled variable cannot timely reflect the output of the system, leading to obvious overshoot, long settling time and even instability. Theorem 1: A pth-order DD-ADRC structure in Fig 3 can be changed into a TDOF-IMC structure, where the model of the controlled plant is. Proof : By taking Laplace transform of the state-space realization (57) of a pth-order PO-ADRC controller, we have sz(s) = Aez(s) + Beu(s) + eAeτ Lo(y(s) − Cee−Aeτ z(s)) u(s) = Ko(r(s) − z(s)) = Fr (s)r(s) − z(s). C 1(s) = 1 − Ko(sI − Ae + BeKo + eAeτ LoCee−Aeτ )−1Be (71) C 2(s) = Ko(sI − Ae + BeKo + eAeτ LoCee−Aeτ )−1Lo (72) The TDOF-IMC structure for PO-ADRC shown in Fig 8 can be changed to Fig 2, with the plant model. The delay does not ‘disappear’ in the controller design procedure, but compared with DD-ADRC, the design model is different
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