New results on the robust stability of control systems with a generalized disturbance observer

Nie, Zhuo‐Yun; Wang, Qing‐Guo; She, Jinhua; Liu, Ruijuan; Guo, Dongsheng

doi:10.1002/asjc.2188

Cited by 9 publications

(17 citation statements)

References 40 publications

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“…The common idea behind ADR schemes is to estimate the total disturbance by an observer and make feedback compensation in the input terminal. Recently, a modified DOB scheme is developed in Reference 27, which gives an intuitive understanding of total disturbance 32 and ADR concepts from the point of transfer function.…”

Section: Pid Tuning With Desired Model: Dr‐pidmentioning

confidence: 99%

“…(2) high‐frequency matching for the plants with no right‐half‐plane (RHP) zeros and low‐frequency matching for the plants with no RHP poles, that is

\{\begin{matrix} center \\ No RHP zeros : \lim_{s \to \infty} \frac{H_{R} false(s false)}{G false(s false) K false(s false)} = 1, \\ No RHP poles : \lim_{s \to 0} \frac{G false(s false) K false(s false)}{H_{R} false(s false)} = 1 . \end{matrix}

Note that, these two matching conditions (9) and (10) contribute the closed‐loop stability of the modified DOB Scheme 27 . As presented in (8), the order matching condition (9) is used to avoid the derivative dynamic of the internal disturbance

f_{1}

, such that it can be estimated by a proper disturbance observer.…”

Section: Pid Tuning With Desired Model: Dr‐pidmentioning

confidence: 99%

“…Obviously, the condition in (10) releases such all pass inverse compensation and supplies practical compensation in high frequency or low frequency for different plants. The detail explanation has been discussed in Reference 27.…”

Section: Pid Tuning With Desired Model: Dr‐pidmentioning

confidence: 99%

“…This information is used directly to formulate the PID controllers 14

C_{italicPID}^{italicZN} false(s false) = \frac{1.2 T}{italicKL} (1 + \frac{1}{2 Ls} + \frac{L}{2} s),

C_{italicPID}^{italicZN} false(s false) = \frac{0.6}{K_{180}} (1 + \frac{1}{0.5 T_{180} s} + 0.125 T_{180} s),

Recently, several active disturbance PID (DR‐PID) controllers are proposed in References 22–25 with equivalence to active disturbance rejection (ADR) schemes, such as active disturbance rejection control (ADRC) 26–28 and disturbance observer (DOB) 26,27 . The resultant control systems finally approach to the desired closed‐loop model.…”

Section: Introductionsmentioning

confidence: 99%

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A unifying Ziegler–Nichols tuning method based on active disturbance rejection

Nie

Wang

et al. 2021

Intl J Robust & Nonlinear

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The landmark Ziegler-Nichols (ZN) tuning method from 1942 for proportional-integral-derivative (PID) controller has had significant impacts on the industrial control industry to this day, even though it is thought to be an empirical method with little theoretical justifications. The situation has not changed much despite the fact that a large amount of research and applications has been reported over decades. This paper shows for the first time that the ZN tuning can be incorporated into the framework of active disturbance rejection (ADR), where the process dynamics is made to match the desired one. This leads to a unifying tuning method for the recently proposed disturbance rejection PID (DR-PID) controller, applicable to a wide range of industrial processes. Unlike the original ZN method, this new tuning method can be fully understood by the practitioner in their own language of bandwidth and phase characteristics. Moreover, it can also be fully validated via rigorous stability analysis. Finally, extensive simulation results are provided to illustrate the effectiveness of the unifying ZN tuning method.

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Section: Pid Tuning With Desired Model: Dr‐pidmentioning

confidence: 99%

“…(2) high‐frequency matching for the plants with no right‐half‐plane (RHP) zeros and low‐frequency matching for the plants with no RHP poles, that is

\{\begin{matrix} center \\ No RHP zeros : \lim_{s \to \infty} \frac{H_{R} false(s false)}{G false(s false) K false(s false)} = 1, \\ No RHP poles : \lim_{s \to 0} \frac{G false(s false) K false(s false)}{H_{R} false(s false)} = 1 . \end{matrix}

f_{1}

, such that it can be estimated by a proper disturbance observer.…”

Section: Pid Tuning With Desired Model: Dr‐pidmentioning

confidence: 99%

Section: Pid Tuning With Desired Model: Dr‐pidmentioning

confidence: 99%

“…This information is used directly to formulate the PID controllers 14

C_{italicPID}^{italicZN} false(s false) = \frac{1.2 T}{italicKL} (1 + \frac{1}{2 Ls} + \frac{L}{2} s),

C_{italicPID}^{italicZN} false(s false) = \frac{0.6}{K_{180}} (1 + \frac{1}{0.5 T_{180} s} + 0.125 T_{180} s),

Section: Introductionsmentioning

confidence: 99%

See 2 more Smart Citations

A unifying Ziegler–Nichols tuning method based on active disturbance rejection

Nie

Wang

et al. 2021

Intl J Robust & Nonlinear

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“…where c is the desired closed-loop bandwidth and K is the controller gain. Note that, DR-PID is derived from a modified DOB Scheme, 36 which includes a Q-filter for disturbance estimation…”

Section: Dr-pidmentioning

confidence: 99%

Periodic tracking for piezo‐actuated displacement stage based on disturbance rejection proportional integral derivative and repetitive control

Nie

Zhang

et al. 2021

Adv Control Appl

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Piezo-actuated displacement stage is often used to perform periodic scanning tasks, but the conventional control schemes may not satisfactorily track periodic reference signals. Our solution is a disturbance rejection proportional-integral-derivative (DR-PID)-based repetitive control (RC) scheme in which the hysteresis nonlinearity with the same period of reference input can be well suppressed by RC law. Stability criterions for the closed-loop system are developed based on small-gain theorem. A simple and effective design algorithm is obtained based on the stability conditions, such that DR-PID and RC can be designed separately. Finally, the validation and superiority of the proposed method are demonstrated by simulation studies.

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On disturbance rejection proportional–integral–differential control with model-free adaptation

Nie

Yan

et al. 2023

Control Theory Technol.

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New results on the robust stability of control systems with a generalized disturbance observer

Cited by 9 publications

References 40 publications

A unifying Ziegler–Nichols tuning method based on active disturbance rejection

A unifying Ziegler–Nichols tuning method based on active disturbance rejection

Periodic tracking for piezo‐actuated displacement stage based on disturbance rejection proportional integral derivative and repetitive control

On disturbance rejection proportional–integral–differential control with model-free adaptation

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