SCIENCE CHINA Information Sciences, Volume 61 , Issue 7 : 070223(2018) https://doi.org/10.1007/s11432-017-9403-x

On comparison of modified ADRCs for nonlinear uncertain systems with time delay

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  • ReceivedDec 17, 2017
  • AcceptedMar 7, 2018
  • PublishedJun 4, 2018


To tackle systems with both uncertainties and time delays, several modified active disturbance rejection control (ADRC) methods, including delayed designed ADRC (DD-ADRC), polynomial based predictive ADRC (PP-ADRC), Smith predictor based ADRC (SP-ADRC) and predictor observer based ADRC (PO-ADRC), have been proposed in the past years. This paper is aimed at rigorously investigating the performance of these modified ADRCs, such that the improvements of each method can be demonstrated. The capability to tackle time delay, the necessity of stable open loop and the performance of rejecting uncertainties for these methods are fully studied and compared. It is proven that large time delay cannot be tolerated for the stability of the closed-loop systems based on DD-ADRC and PP-ADRC. Moreover, stable open loop is shown to be necessary for stabilizing the closed-loop systems based on SP-ADRC. Furthermore, the performance of rejecting the “total disturbance” at low frequency for these modified ADRCs is evaluated and quantitatively discussed. Finally, the simulations of a boiler turbine system illustrate the theoretical results.


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  • Table 1   Comparison of the capabilities of modified ADRCs to reject uncertainty
    $\mathop{\lim}\limits_{\omega\to~0}\frac{G_{y\delta,a}(j\omega)}{G_{y\delta,b}(j\omega)},~~a,~b={\rm~DD,PP,SP,PO}$ The main part
    $\frac{G_{y\delta,{\rm~PP}}(j\omega)}{G_{y\delta,{\rm~DD}}(j\omega)}$ $\frac{~2\omega_o+KB}{\tau~\omega_o^2+2\omega_0+~KB}~$ $O(\frac{1}{\omega_o})$
    $\frac{G_{y\delta,{\rm~PP}}(j\omega)}{G_{y\delta,{\rm~SP}}(j\omega)}$ $~\frac{~A(2\omega_o~+KB)}{~\tau~A_K~\omega_o^2~+~2A\omega_o+~2AK}~$ $O(\frac{1}{\omega_o})$
    $\frac{G_{y\delta,{\rm~PP}}(j\omega)}{G_{y\delta,{\rm~PO}}(j\omega)}$ $~~\frac{~A^2(2\omega_o~+KB)~~}{~~(KB({\rm~e}^{A\tau}-1)+AA_K\tau)\omega_o^2~+~2A(BK~{\rm~e}^{A\tau}+A_K)~\omega_o~+~A^2BK{\rm~e}^{A\tau}~~~}~~~$ $O(\frac{1}{\omega_o})$
    $\frac{G_{y\delta,{\rm~DD}}(j\omega)}{G_{y\delta,{\rm~SP}}(j\omega)}$ $~~\frac{A(\tau~\omega_o^2+2\omega_o+BK)}{~\tau~A_K~\omega_o^2~+~2A\omega_o+~2AK}~$ $\frac{A}{A_K}+O(\frac{1}{\omega_o})$
    $\frac{G_{y\delta,{\rm~DD}}(j\omega)}{G_{y\delta,{\rm~PO}}(j\omega)}$ $~\frac{~A^2(\tau~\omega_o^2+2\omega_o+BK)~~}{~~(KB({\rm~e}^{A\tau}-1)+AA_K\tau)\omega_o^2~+~2A(BK~{\rm~e}^{A\tau}+A_K)~\omega_o~+~A^2BK{\rm~e}^{A\tau}~~~}~$ $~\frac{A^2~\tau~}~{~~KB({\rm~e}^{A\tau}-1)+AA_K\tau~~~}~+~O(\frac{1}{\omega_o})$
    $\frac{G_{y\delta,{\rm~SP}}(j\omega)}{G_{y\delta,{\rm~PO}}(j\omega)}$ $~~\frac{~A~(\tau~A_K~\omega_o^2~+~2A\omega_o+~2AK)~}~~{~~(KB({\rm~e}^{A\tau}-1)+AA_K\tau)\omega_o^2~+~2A(BK~{\rm~e}^{A\tau}+A_K)~\omega_o~+~A^2BK{\rm~e}^{A\tau}~~~}$ $~~\frac{A~A_K\tau}~{~~KB({\rm~e}^{A\tau}-1)+AA_K\tau~~~}~+~O(\frac{1}{\omega_o})~$

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