Frequency parameterization of H∞ PID controllers via relay feedback: A graphical approach

Li, Yinya; Qi, Guoqing; Sheng, Andong

doi:10.1016/j.jprocont.2011.02.006

Cited by 11 publications

(16 citation statements)

References 37 publications

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“…5 that the G D × G P plane is divided into regions whose boundaries were defined by applying (11) and (15). According to the D-decomposition technique, these regions in Fig.…”

Section: Results For a Single Disc Rotating Systemmentioning

confidence: 99%

“…The three previous conditions allow one to decompose the controller parameter space in regions with a fixed number of stable and unstable roots (root invariant regions) [15,17]. However, it is noteworthy that there is no guarantee of the existence of a region and this set may be empty, or all regions can result in instability [28].…”

Section: D-decomposition Techniquementioning

confidence: 99%

“…Hence, given the frequency response of the system to be controlled P(jω), the controller parameter space (G D × G P plane) can be partitioned into root invariant regions whose boundaries are defined by (11), (13) and (15). The only information required for the analysis is the frequency response of the open-loop system.…”

Section: Complex Root Boundarymentioning

confidence: 99%

“…where the performance criterion (16) represents the closedloop transfer function of the system, the criterion (17) represents the sensitivity function of the system, and the criterion (18) represents the complementary sensitivity function of the system [15].…”

Section: Performance Criteriamentioning

confidence: 99%

“…Later, the theory for designing PID controllers was presented [12], whose equations for finding the stabilising gains were formally deduced in [13]. By knowing the gains that stabilise the closed-loop system, one can find sets of gains that optimise any performance criteria, thus achieving closed-loop stability and robustness [14,15].…”

Section: Introductionmentioning

confidence: 99%

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PD controller synthesis from open-loop response measurements of rotating system

Buttini

Nicoletti

2012

IET Control Theory &Amp; Applications

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Abstract:In this work, a method of computing PD stabilising gains for rotating systems is presented based on the D-decomposition technique, which requires the sole knowledge of frequency response functions. By applying this method to a rotating system with electromagnetic actuators, it is demonstrated that the stability boundary locus in the plane of feedback gains can be easily plotted, and the most suitable gains can be found to minimise the resonant peak of the system. Experimental results for a Laval rotor show the feasibility of not only controlling lateral shaft vibration and assuring stability, but also helps in predicting the final vibration level achieved by the closed-loop system. These results are obtained based solely on the input-output response information of the system as a whole.

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“…5 that the G D × G P plane is divided into regions whose boundaries were defined by applying (11) and (15). According to the D-decomposition technique, these regions in Fig.…”

Section: Results For a Single Disc Rotating Systemmentioning

confidence: 99%

Section: D-decomposition Techniquementioning

confidence: 99%

Section: Complex Root Boundarymentioning

confidence: 99%

Section: Performance Criteriamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

PD controller synthesis from open-loop response measurements of rotating system

Buttini

Nicoletti

2012

IET Control Theory &Amp; Applications

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Robust and nonlinear control literature survey (No. 25)

2011

Intl J Robust & Nonlinear

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Active disturbance rejection control for nonlinear fractional‐order systems

Gao

2015

Intl J Robust & Nonlinear

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Summary This paper investigates active disturbance rejection control involving the fractional‐order tracking differentiator, the fractional‐order PID controller with compensation and the fractional‐order extended state observer for nonlinear fractional‐order systems. Firstly, the fractional‐order optimal‐time control scheme is studied to propose the fractional‐order tracking differentiator by the Hamilton function and fractional‐order optimal conditions. Secondly, the linear fractional‐order extend state observer is offered to acquire the estimated value of the sum of nonlinear functions and disturbances existing in the investigated nonlinear fractional‐order plant. For the disturbance existing in the feedback output, the effect of the disturbance is discussed to choose a reasonable parameter in fractional‐order extended state observer. Thirdly, by this observed value, the nonlinear fractional‐order plant is converted into a linear fractional‐order plant by adding the compensation in the controller. With the aid of real root boundary, complex root boundary, and imaginary boot boundary, the approximate stabilizing boundary with respect to the integral and differential coefficients is determined for the given proportional coefficient, integral order and differential order. By choosing the suitable parameters, the fractional‐order active disturbance rejection control scheme can deal with the unknown nonlinear functions and disturbances. Finally, the illustrative examples are given to verify the effectiveness of fractional‐order active disturbance rejection control scheme. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

Frequency parameterization of H∞ PID controllers via relay feedback: A graphical approach

Cited by 11 publications

References 37 publications

PD controller synthesis from open-loop response measurements of rotating system

PD controller synthesis from open-loop response measurements of rotating system

Robust and nonlinear control literature survey (No. 25)

Active disturbance rejection control for nonlinear fractional‐order systems

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