Domains of PID controller coefficients which guarantee stability and performance for LTI time-delay systems

Bozorg, Mohammad; Termeh, Faezeh

doi:10.1016/j.automatica.2011.06.002

Cited by 18 publications

(14 citation statements)

References 14 publications

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“…Analysis of the critical gains corresponding to a single pole, or pole-pair on the imaginary axis, based on the parameter space method [17], [18], shows that in the nominal case the optimal tuning satisfying (17) always guarantees a closed loop stability. Thus, with respect to control of unstable plants, the ideal PID control ideally doubles the range of admissible products A = aT d .…”

Section: Stability Requirementsmentioning

confidence: 99%

Filter choice for an effective measurement noise attenuation in PI and PID controllers

Huba

2015

2015 IEEE International Conference on Mechatronics (ICM)

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This paper shows by simulation and by a relative total variance performance measures that in control of lag dominated first order time delayed plants appropriately filtered PID control may significantly increase the loop performance with respect to filtered PI control. By analyzing the impact of higher order low pass filters designed by a modified multiple real dominant pole approach it shows that in the case of filtered PI control it may be beneficial to use a filter order n > 1. For the PID control the most interesting performance may be achieved for n > 2.

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Section: Stability Requirementsmentioning

confidence: 99%

Filter choice for an effective measurement noise attenuation in PI and PID controllers

Huba

2015

2015 IEEE International Conference on Mechatronics (ICM)

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“…[12,34] consider to optimum performance by using genetic algorithm in the stabilizing region. Some other researchers try to guarantee a performance specification for the closed-loop system by robust H ∞ design approach combining with the stabilizing domain [35]. It has to be noted that by extending the work [13,16,22], the problems of PI/PID stabilization of second-order delay processes has been discussed in [12,20,21], where, however, the result is limited to some special second-order delay processes (see Remark 3).…”

Section: Introductionmentioning

confidence: 99%

Proportional-integral controller for stabilization of second-order delay processes

Wang

Liu

Yang

2014

Int. J. Control Autom. Syst.

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This paper considers the problem of determining the complete stabilizing set of proportional-integral (PI) controllers for a second-order process with time delay by employing a version of the Hermite-Biehler theorem applicable to quasipolynomials. With the poles of open-loop system being complex, we first provide the result to find the admissible range of the proportional gain. Then by choosing a fixed proportional gain in this range, we can ascertain the complete region of integral gain which can stabilize the second-order delay process. Similarly, the result for the case of open-loop real poles is also obtained. It is mentioned that the condition to obtain the parameter set for stabilizing the given plant is sufficient and necessary.

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“…T. Consultant et al (2006), Wang (2007a), Wang (2007b), Ou et al (2009), Oliveira et al (2009), Hohenbichler (2009, Bozorg et al (2011), andPadula et al (2012). However, excepting being able to judge if a characteristic equation with time delay is Hurwitz, the extension of the Hermite-Biehler Theorem does not provide any information about its root distribution.…”

Section: Introductionmentioning

confidence: 99%

Controller design for delay systems via eigenvalue assignment – on a new result in the distribution of quasi-polynomial roots

Wang

Liu

Yang

2015

International Journal of Control

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This paper considers the eigenvalue distribution of a linear time-invariant (LTI) system with time delays and its application to some controllers design for a delay plant via eigenvalue assignment. First, a new result on the root distribution for a class of quasi-polynomials is developed based on the extension of the Hermite-Biehler Theorem. Then such result is applied to proportional-integral (PI) controller parameter design for a first-order plant with time delay through pole placement. The complete region of PI gains can be obtained so that the rightmost eigenvalues in the infinite eigenspectrum of the closed-loop system with delay plant are assigned to desired positions in the complex plane. Further, on the basis of the previous result, this paper also extended the PI control to the proportional-integral-derivative (PID) control. It is worth pointing out that this work aims to improve the performance of the closed-loop system on the premise of guaranteeing the stability.

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Domains of PID controller coefficients which guarantee stability and performance for LTI time-delay systems

Cited by 18 publications

References 14 publications

Filter choice for an effective measurement noise attenuation in PI and PID controllers

Filter choice for an effective measurement noise attenuation in PI and PID controllers

Proportional-integral controller for stabilization of second-order delay processes

Controller design for delay systems via eigenvalue assignment – on a new result in the distribution of quasi-polynomial roots

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